# IEEE 802.11ad Based Joint Radar Communication Transceiver: Design, Prototype
and Performance Analysis

Akanksha Sneh, Soumya Jain, V Sri Sindhu, Shobha Sundar Ram, , and Sumit Darak
All authors are with the Indraprastha Institute of Information Technology
Delhi, New Delhi 110020 India. E-mail: {soumya20325,sri20326,akankshas,sumit,
<EMAIL_ADDRESS>
###### Abstract

Rapid beam alignment is required to support high gain millimeter wave (mmW)
communication links between a base station (BS) and mobile users (MU). The
standard IEEE 802.11ad protocol enables beam alignment at the BS and MU
through a lengthy beam training procedure accomplished through additional
packet overhead. However, this results in reduced latency and throughput.
Auxiliary radar functionality embedded within the communication protocol has
been proposed in prior literature to enable rapid beam alignment of
communication beams without the requirement of channel overheads. In this
work, we propose a complete architectural framework of a joint radar-
communication wireless transceiver wherein radar based detection of MU is
realized to enable subsequent narrow beam communication. We provide a software
prototype implementation with transceiver design details, signal models and
signal processing algorithms. The prototype is experimentally evaluated with
realistic simulations in free space and Rician propagation conditions and
demonstrated to accelerate the beam alignment by a factor of four while
reducing the overall bit error rate (BER) resulting in significant improvement
in throughput with respect to standard 802.11ad. Likewise, the radar
performance is found to be comparable to commonly used mmW radars.

###### Index Terms:

joint radar-communication, IEEE 802.11ad, transceiver design, millimeter wave
communication, beam alignment

##  I Introduction

An overarching objective of next generation intelligent transportation systems
is to enable vehicle-to-everything (V2X) capabilities along key transport
routes. This is to encourage sharing of road and vehicle information
pertaining to environmental sensing for reducing road fatalities, and
improving driving conditions eventually leading to autonomous driving [1].
Currently, three modes of vehicular communications have been identiﬁed:
_dedicated short-range communication services (DSRC)_ on IEEE 802.11p based
wireless technology [2]; _device-to-device_ (D2D) based V2X communications in
long-term evolution (LTE) [3], and _cellular LTE-V2X communications_ [4]. All
three modes operate in sub-6 GHz spectrum; are restricted to tens of Megabits
per second (Mbps) data rates and oﬀer latency of the order of several hundred
milliseconds (ms). However, sharing of time-critical high deﬁnition three-
dimensional environmental maps of congested road conditions between vehicles
requires Gigabits per second (Gbps) data rates and ultra-low latency.

Millimeter wave (mmW) unlicensed spectrum (above 24 GHz) oﬀers a viable
solution for high bandwidth connected vehicles [5]. However, there are major
challenges associated with the practical deployment of mmW transceivers. Due
to the high propagation loss at these carrier frequencies, they are meant to
operate in short-range line-of-sight (LOS) conditions with highly directional
beams realized through beamforming. In high mobility environments, rapid beam
training and management result in considerable overhead and signiﬁcant
deterioration of latency [6]. Alternatively, auxiliary sensors such as GPS or
standalone radars can aid in beam alignment of the communication systems [7].
However, the deployment of auxiliary sensors increases the cost and complexity
in terms of synchronization and data processing as well as poses challenges in
terms of interference. In this work, we propose to augment radar functionality
within the communications transceiver to enable rapid beam alignment of the
communication beams.

Joint radar communication (JRC) systems have been extensively explored over
the last several decades over three broad paradigms. The first set of works
considered the _coexistence_ of radar and communications systems on a common
spectrum prompted by RF congestion issues [8, 9, 10, 11]. Here, the main
objective is to mitigate the mutual interference between the two systems with
[9] or without cooperation [10]. Examples include communication systems that
operate as cognitive radio on federally allocated radar bands [11]; or
cognitive radar that operates on communication bands [12]. In the second
paradigm, _passive radar_ receivers are developed and deployed with
communication transmitters serving as opportunistic illuminators for
surveillance and remote sensing applications [13]. In the third paradigm, RF
front ends - sharing spectrum and hardware - are _co-designed_ for both radar
sensing and communication functionalities [14, 15]. Here the communication
signals are embedded within a traditional radar framework [16, 17] or the
radar signals are embedded within the communication uplink or downlink signals
[18]. In the other frameworks, either communication or the radar signal is
treated as an interference signal or an uncooperative channel [19] and hence
the functionality of the two systems is not fully exploited as in the co-
design approach. Our work focuses on co-design of an IEEE 802.11ad based dual-
functional transceiver that is capable of joint radar remote sensing and
communications.

The IEEE 802.11ad standard specifies the media access control (MAC) and
physical layer (PHY) protocols for implementing wireless local area networks
through high data rate short range directional communication in the mmW
spectrum [20]. Preliminary studies have demonstrated the eﬀectiveness of JRC
implemented upon IEEE 802.11ad for dynamic target tracking [21, 22, 23]. In
[21], the authors proposed a method of using the IEEE 802.11ad beamforming
training protocol for detecting radar targets. In [24], the authors leveraged
the high data rate (1.76GSa/s) and the Golay sequences within the channel
estimation fields of the single carrier preamble in the IEEE 802.11ad packet
to demonstrate radar ranging with fine range resolution and low sidelobes of a
single point target. The authors in [25, 23] proposed a modification to the
preamble structure to enable Doppler resilient radar ranging of extended
dynamic automotive targets. All of these works focused on developing radar
signal processing algorithms without complete architectural details of the JRC
transceivers and system-level performance analysis. Further, these works make
assumptions on the radar waveform that would introduce significant limitations
on the performance of the joint transceiver in realistic conditions. From a
prototype perspective, there has been limited work in the design, prototype
and experimental demonstrations of co-designed multi-functional transceivers
[26, 27, 28]. In [26], a hardware prototype of a JRC system was demonstrated
where radar and communications transmit waveforms were realized with index
modulation via generalized spatial modulation. The transmitting antennas were
divided into two sub-arrays, one for radar and the other for communication. In
[27], a fully digital JRC architecture on hardware was demonstrated with a
common transmitter for radar and communication, a monostatic radar receiver,
and a separate communication receiver. A hardware prototype was also developed
in [28], where IEEE 802.11ay access points were retrofitted for human
detection and sensing in an indoor scenario. To the best of our knowledge,
there is no software or hardware prototype for end-to-end JRC co-designed
transceiver in the prior art.

In this work, we propose a complete end-to-end architecture followed by a
software implementation of a joint radar-communication framework based on IEEE
802.11ad for rapid beam alignment that is capable of half duplex communication
and three-dimensional radar processing along range, azimuth and Doppler. The
contributions of the paper can be summarized as follows:

  1. 1.

Standard IEEE 802.11ad packet consists of optional beam refinement fields
allocated for beamforming training to locate the mobile user [20]. The length
of these fields is directly proportional to the number of beams supported by
the transmitter. Compared to standard beam alignment for IEEE 802.11ad, we
demonstrate that our proposed architecture accelerates the beam alignment by a
factor of four by omitting the beam training fields.

  2. 2.

Standard IEEE 802.11ad framework utilizes a lengthy beam training procedure
between the access point/base station (BS) 111In this work, we use the terms
base station and access point interchangeably and the mobile user (MU) 222In
this work we use the terms mobile user and radar target interchangeably. Also,
static clutter is differentiated from radar target.. In our work, we implement
three-dimensional (range-Doppler-Angle of Arrival) radar signal processing
instead of the cumbersome beam training procedure. Through range processing,
we detect point and extended targets in the radar field-of-view; through
Doppler processing, we identify MU from static clutter; and through digital
beamforming, we directly estimate the angle of arrival (AoA) of the MU.

  3. 3.

We provide a complete end-to-end prototype of the IEEE 802.11ad based JRC
system realized using Matlab. This includes the design of BS with
communication transmitter and receiver architecture along with the radar
signal processor. We provide an in-depth discussion on the relevant radar and
communication signal models, design details and signal processing algorithms.
We have made our source codes open for interested readers.

  4. 4.

The proposed software prototype is experimentally evaluated for simulated
point and extended targets under free space and Rician channel conditions and
its communication metrics (throughput and latency) are benchmarked against the
standard IEEE 802.11ad protocol. The radar performance metrics are likewise
benchmarked against frequency modulated continuous waveforms commonly used in
mmW radars.

The paper is organized as follows. In Section II, we present a comprehensive
overview of the system architecture of the proposed JRC transceiver followed
by its signal modeling in Section.III. In Section.IV, we present the
simulation setup for evaluating the performance of the proposed prototype. In
Section.V, we present the resultant beam alignment timing realized by the
proposed radar-enhanced IEEE 802.11ad and contrast it with the standard IEEE
802.1ad beam alignment procedure. Further, we present the communication link
metrics and the radar performance metrics for different types of targets
(point and extended) along different trajectories. We conclude the paper with
a summary of the findings and a discussion on future works in Section.VI.
_Notation:_ Vectors and matrices are indicated with boldface lower and upper
case characters respectively, while variables are indicated with regular
characters. Radar and communication transmitted signals are indicated by
$\mathbf{x}$ and $\mathbf{y}$ respectively while the received signals that
have undergone one-way and two-way propagation are shown with
$\hat{\mathbf{y}}$ and
$\hat{\vphantom{\rule{1.0pt}{5.71527pt}}\smash{\hat{\mathbf{y}}}}$
respectively. Vector superscript $T$ and $\ast$ denotes transpose and complex
conjugate respectively. We use the square braces, $[\cdot]$, to indicate
discrete-time sequences, and the curly braces, $(\cdot)$, to indicate
continuous time signals. The terms BS-TX and BS-RX denote the transmitter and
receiver, respectively, at the BS while MU-TX and MU-RX denote the transmitter
and receiver at the non-access point station or MU. The uni-directional
communication between BS-TX and MU-RX is referred to as downlink (DL) while
the communication between MU-TX and BS-RX is referred to as uplink (UL).

##  II System Architecture of the JRC Transceiver

Directional communication links are required to overcome the atmospheric
attenuation associated with mmW propagation. Hence, BS and MU must each
determine the best beams prior to $\operatorname{\mathbf{y}_{DL}}$ and
$\operatorname{\mathbf{y}_{UL}}$ communication. The standard protocol utilizes
in-packet training for selecting the optimum pair of pre-determined beams at
the BS and MU [29]. In our proposed work, the radar functionality within the
BS is used for beam alignment instead to reduce the overall beam alignment
time. In this section, we present an overview of both the standard and the
proposed JRC architectures and emphasize the modifications introduced in the
former to realize the latter.

###  II-A Standard 802.11ad Transceiver Architecture

We begin by providing a brief description of the PHY layer of the IEEE
802.11ad packet structure [20]. The IEEE standard enables data and header
transmission in three different modes: control, single carrier (SC), both at
1.76GHz sampling frequency, and orthogonal frequency division multiplexing
(OFDM) mode at 2.64GHz sampling frequency [20]. We model the data in our
entire analysis in OFDM mode to enable high communication throughput and low
latency. As shown in Fig.1(a), a packet consists of preamble, header, data,
and beam refinement protocol (BRF).

Figure 1: (a) IEEE 802.11ad JRC transmit packet structure; Expanded (b)
preamble structure and (c) BRF structure.

The preamble has Golay sequences that exhibit perfect auto-correlation
properties (with zero sidelobes) which make them suitable for radar remote
sensing and channel estimation for communication [24]. The preamble is
followed by a header which provides necessary control information to decode
and demodulate the received data. The header is followed by data after which
BRF fields with Golay sequences are provided for enabling beam training
between BS and MU. The number of BRF fields has to be in multiples of 4 up to
a maximum of 64 fields.

The wireless transceiver architecture for supporting standard 802.11ad
communication is presented in Fig.2(a).

Figure 2: (a) Standard 802.11ad system architecture and (b) corresponding
timing diagram for _Stage-1_ beam alignment based on beam training procedure.

The 802.11ad packets ($\mathbf{y}_{DL}$) are generated in the BS-TX and
subsequently passed through the digital front end (DFE) consisting of a
digital-to-analog converter (DAC). Subsequently, the analog signal is
modulated with an RF carrier in the analog front end (AFE), amplified and
transmitted through a transmit phased antenna array. During the beam alignment
phase, which we will henceforth refer to as _Stage 1_ , the preamble, header
and data of the $\operatorname{\mathbf{y}_{DL}}$ packet are transmitted
through a quasi-omnidirectional beam. $M$ additional BRF fields are appended
to the $\operatorname{\mathbf{y}_{DL}}$ packet and transmitted along $M$
distinct pre-determined beams supported by the BS-TX phased array. Suitable
antenna weight vectors (AWV) are applied at the BS-TX phased array to steer
each BRF along the corresponding beam direction. The received signal at the
phased array on the MU-RX, $\hat{\mathbf{y}}_{DL}$, is down-converted,
digitized and processed to obtain the data. Based on the number of antennas in
the MU-RX, $N$ total beams may be supported through analog beamforming at the
MU. Based on [29], the BS will repeat the transmission of the
$\operatorname{\mathbf{y}_{DL}}$ packet $N$ times and each packet will be
received sequentially by different beams at MU as shown in the timing diagram
in Fig.2(b). To summarize, $M$ training fields in the
$\operatorname{\hat{\mathbf{y}}_{DL}}$ packet are received through $N$ beams
of the MU-RX leading to an overall complexity of $M\times N$. The best beam
pair for the BS-TX and MU-RX will be estimated after the $N$ packets are
processed at the MU-RX. If we assume reciprocity in the propagation
environment, then the beam alignment procedure between BS-TX and MU-RX for
$\operatorname{\mathbf{y}_{DL}}$ will provide the necessary information to
support the $\operatorname{\mathbf{y}_{UL}}$ communication between MU-TX and
BS-RX (as the same antennas support both the TX and RX functionalities at both
BS and MU in half-duplex mode). The total duration for the beam alignment is
the duration of the $N$ DL packets each appended with M training fields, the
propagation time between the BS and MU and the receiver communication
processing (RCP) time at the MU. Once the beam alignment is completed and
communicated to the BS, we enter _Stage 2_ , where the data packets are
transmitted between the BS and MU along the best beam pair without the need
for BRF. The beam alignment process is repeated again depending on the
mobility of the MU and the corresponding signal-to-noise ratio (SNR) estimated
at the BS and MU becomes poor.

Algorithm 1 Beam alignment procedure for standard 802.11ad

  1. Step 1:

BS-TX sends $n=1,2\cdots,N$ downlink packets, each with $M$ BRF fields. Each
$m^{th}$ BRF field is directed along $m^{th}$ pre-determined BS beam.

  2. Step 2:

MU-RX receives $N$ packets along $n=1,2,\cdots,N$ pre-determined MU beams.

  3. Step 3:

The $N$ received packets are processed at MU-RX (RCP) sequentially to
determine best beam pair $(\tilde{m},\tilde{n})$.

  4. Step 4:

MU-TX communicates about the $\tilde{m}$ beam to BS through $\mathbf{y}_{UL}$
without BRF field over the $\tilde{n}^{th}$ beam.

  5. Step 5:

The BS-RX receives and processes $\hat{\mathbf{y}}_{UL}$ and BS learns about
its best beam ,i.e. $\tilde{m}$ for subsequent _Stage-2_. This completes
_Stage -1_ for the standard architecture.

The steps for beam alignment in _Stage-1_ are summarized in Algorithm1.

###  II-B Proposed JRC Based 802.11ad Transceiver

Now discuss the proposed JRC framework at the BS, as shown in Fig.3(a), to
reduce the latency caused by the beam alignment procedure.

Figure 3: (a) Proposed JRC system architecture with beam alignment of BS
through radar signal processing and corresponding (b) timing diagram of JRC
_Version-1_ where beam alignment of MU is through longer uplink packet with
multiple ($N$) BRF fields; (c) Timing for JRC _Version-2_ where beam alignment
of MU is through reception of multiple ($N$) downlink packets through separate
MU beams.

During the beam alignment _Stage 1_ , the transmitter at the BS-TX generates
both radar ($\operatorname{\mathbf{x}_{p}}$) and communication waveforms
($\operatorname{\mathbf{y}_{DL}}$). The optional BRF training fields used in
$\operatorname{\mathbf{y}_{DL}}$ for the standard are omitted here resulting
in a shorter communication waveform.

In prior art in [30, 23], the radar waveform was embedded within the
communication packet. However, there are several limitations to this signal
model. First, short ranges typical of automotive environments ($\sim$40 to
200m), result in very short two-way propagation times (of the order of several
nanoseconds), which fall within the duration of the
$\operatorname{\mathbf{y}_{DL}}$ packet (which is of several microseconds).
Hence, the signal model suggested in the prior art would require separate sets
of mmW antennas and hardware to support simultaneous transmission of
$\operatorname{\mathbf{y}_{DL}}$ through BS-TX while receiving the
$\hat{\vphantom{\rule{1.0pt}{5.71527pt}}\smash{\hat{\mathbf{x}}}}_{p}$
scattered from MU at BS-RX. Second, the system must manage the interference
introduced by the strong transmission signal received directly at the receiver
in order to be able to detect the weak radar scattered signal. Third, the
reciprocity in the propagation channels for $\operatorname{\mathbf{y}_{DL}}$
and $\operatorname{\mathbf{y}_{UL}}$ communications would no longer hold,
requiring separate beam alignment procedures for
$\operatorname{\mathbf{y}_{DL}}$ and $\operatorname{\mathbf{y}_{UL}}$.

For all these reasons, we propose that a separate radar waveform composed of
just a section of the 802.11ad preamble is transmitted by BS-TX antennas
through a quasi-omnidirectional beam. $P$ pulses of the radar waveform,
denoted by $\operatorname{\mathbf{x}_{p}},p=1:P$, are transmitted at a pulse
repetition interval of $T_{PRI}$ as shown in the timing diagram presented in
Fig.3(b) and (c). Due to the short duty cycle of the radar pulse with respect
to the $T_{PRI}$, the same mmW front-end can be used for both radar
transmission at BS-TX and reception at BS-RX. The radar signals are
upconverted from baseband to analog in the DFE and subsequently to mmW in the
AFE. Since the radar waveform is composed of the 802.11ad packet preamble
features, the same DFE and AFE and phased antenna array can be used for
generating and transmitting both $\operatorname{\mathbf{x}_{p}}$ and
$\operatorname{\mathbf{y}_{DL}}$ without increasing the cost and complexity of
the system hardware. The transmitted signal $\operatorname{\mathbf{x}_{p}}$
scatters at the MU and is received at the BS-RX where it is down-converted and
digitized at the AFE and DFE. We introduce a radar-communication decision unit
at the BS-RX for identifying scattered returns of
$\hat{\vphantom{\rule{1.0pt}{5.71527pt}}\smash{\hat{\mathbf{x}}}}_{p}$ from
the scattered
$\operatorname{\hat{\vphantom{\rule{1.0pt}{5.71527pt}}\smash{\hat{\mathbf{y}}}}_{DL}}$
and uplink packet $\operatorname{\hat{\mathbf{y}}_{UL}}$. The scattered
$\hat{\vphantom{\rule{1.0pt}{5.71527pt}}\smash{\hat{\mathbf{x}}}}_{p}$ are
processed at the radar signal processing unit (RSP) where the MU are detected
based on their range returns, identified from static clutter based on their
Doppler and subsequently located in the angular space. This information from
the RSP is used as feedback to the beamformer to enable the alignment at the
BS-TX and BS-RX during _Stage 2_. The total time required for beam alignment
at BS is therefore the duration of the $P$ pulse repetition intervals
($P\times T_{PRI}$), and the radar signal processing time. Since these packets
are considerably shorter than $\operatorname{\mathbf{y}_{DL}}$, the total
duration for beam alignment is expected to be considerably lower than the
standard. Note that in our proposed architecture, the RSP is introduced only
in the BS and not in the MU. In other words, we have proposed digital
beamforming at the BS-RX but retained analog beamforming at BS-TX, MU-TX, and
MU-RX due to cost and complexity considerations. Hence, the beam alignment at
the MU will be carried out as per the standard protocol. This architectural
design choice is made since the number of beams at the BS are typically much
greater than at the MU due to the higher number of antennas at the BS compared
to the MU. We propose two versions for the beam alignment at the MU as shown
in Fig.3(b) and (c). _Version-1_ of the JRC architecture as shown in Fig.3(b),
is where the MU sends a $\operatorname{\mathbf{y}_{UL}}$ packet with $N$ BRF
fields along $N$ pre-determined beams. Then the best beam is determined at the
BS-RX and subsequently communicated to the MU through the next
$\operatorname{\mathbf{y}_{DL}}$. Therefore, the total duration for beam
alignment at the MU is based on the length of one long packet
$\operatorname{\mathbf{y}_{UL}}$ with $N$ BRF, propagation delay, and
processing times at BS and MU.

Algorithm 2 Beam alignment procedure for JRC

  1. Step 1:

BS-TX transmits $P$ packets of $\mathbf{x}_{p}$ with $50\%$ duty cycle through
quasi omnidirectional beams which are reflected from the MU and other targets
in the environment.

  2. Step 2:

The received $P$ packets of
$\hat{\vphantom{\rule{1.0pt}{5.86597pt}}\smash{\hat{x}}}_{p}$ are identified
at the radar/comm detection unit and processed at BS-RSP to determine the
azimuth of MU $(\theta_{b})$. Meanwhile, BS-TX transmits quasi-omnidirectional
$\mathbf{y}_{DL}$ packets without BRF fields.

  3. Step 3:

Version-1: The first $\hat{\mathbf{y}}_{DL}$ is received and processed at MU-
RX (RCP). Then the MU-TX transmits $\mathbf{y}_{UL}$ with $N$ BRF fields.
Version-2: The first $N$ received $\hat{\mathbf{y}}_{DL}$ packets are
processed at MU-RCP and the correlation gains from preamble determines best
beam, $\tilde{n}$. The duration of _Stage-1_ is based on the greater of the
lengths of the two durations - RSP at BS and RCP at MU.

  4. Step 4:

Version-1: The received $\hat{\mathbf{y}}_{UL}$ is identified at the
radar/comm detection unit and processed at BS-RCP when the best beam,
$\tilde{n}^{th}$ is determined.

  5. Step 5:

Version-1: The next $\mathbf{y}_{DL}$ is transmitted without BRF fields along
$\theta_{b}$ to MU along with information regarding $\tilde{n}^{th}$ BRF
field.

  6. Step 6:

Version-1: The directional $\hat{\mathbf{y}}_{DL}$ is received and processed
at MU-RCP to learn about $\tilde{n}^{th}$ BRF field. This completes _Stage-1_.

_Version-2_ of the JRC architecture as shown in Fig.3(c) on the other hand, is
similar to Fig.2(b) where $N$ $\operatorname{\hat{\mathbf{y}}_{DL}}$ packets
are received along $N$ beams at the MU to determine the best beam at MU. The
duration of _Stage 1_ is based on the duration to determine the correlation
gains of preambles of $N$ DL packets in _Version-2_ along with the propagation
time and the communication processing time. Again, since the time complexity
is of the order of $N$ rather than $M\times N$, we expect that the beam
alignment will be quicker for the MU thereby supporting lower latency. The
steps for beam alignment in _Stage-1_ for both versions are summarized in
Algorithm2.

Thus the duration of the beam alignment stage for all three architectures is a
function of the signal/packet lengths and the signal processing times. More
details on the comparison of the timing values are provided in Section.VA with
suitable examples.

##  III JRC Signal Model

In this section, we provide a detailed discussion of the JRC signal model and
the corresponding software prototype required to generate the signal at the
transmitter and process the signal at the receiver.

###  III-A JRC Transmitter Signal Model

The different blocks of the waveform generator within the transmitter are
shown in Fig.4(a).

Figure 4: (a) IEEE 802.11ad JRC waveform generation; (b) preamble and BRF
processing; and (c) header and data processing.

We will describe the generation of each part of the packet.

Preamble and BRF field processing: Both the preamble and BRF fields are always
SC modulated even when header and data fields are modulated with OFDM. The
preamble is divided into the short training field (STF) and the channel
estimation field (CEF) as shown in Fig.1(b). The STF consists of sixteen
repetitions of 128-bit Golay sequences denoted by $\mathbf{g}_{a_{128}}$
followed by one repetition of $-\mathbf{g}_{a_{128}}$. The STF bits are phase-
shifted by integer multiples of $\pi/2$ as shown in -

$\displaystyle\mathbf{y}_{STF}[mT_{c}]=\begin{cases}\mathbf{g}_{a_{128}}[m\%128]exp(+j\frac{\pi}{2}m);\\\
\;\;\;\;\;\;\;\;\;m=0,1,\cdots,16\times 128-1\\\
-\mathbf{g}_{a_{128}}[m\%128]exp(+j\frac{\pi}{2}m);\\\
\;\;\;\;\;\;\;\;\;m=16\times 128\cdots(17\times 128)-1.\end{cases}$ (1)

Here, $T_{c}$ is bit period and it is reciprocal of the sampling frequency of
1.76GHz and $\%$ indicates a modulus operation. The CEF consists of a 512-bit
Golay complementary pair, denoted by $\mathbf{g}_{u_{512}}$ and
$\mathbf{g}_{v_{512}}$ followed by a 128 bit Golay sequence denoted by
$\mathbf{g}_{v_{128}}$ which are similarly modulated to

$\displaystyle\begin{split}\mathbf{y}_{CEF}[mT_{c}]=&\left(\mathbf{g}_{u_{512}}[m]+\mathbf{g}_{v_{512}}[m-512]+\mathbf{g}_{v_{128}}[m-1024]\right)\\\
&exp(+j\frac{\pi}{2}m);m=0,1,\cdots 1151.\end{split}$ (2)

Together, they are concatenated to form the total preamble $\mathbf{y}_{mod}$.
The sampling frequency for OFDM data bits is 2.64GHz which is 1.5 times that
of SC used for preamble data bits and hence up-conversion and down-conversion
of the Golay sequences are required. First, the preamble bits are upsampled by
a factor of three as shown below -

$\displaystyle\mathbf{y}_{upsample}\left[m\frac{T_{s}}{2}\right]=\begin{cases}\mathbf{y}_{mod}[m\frac{T_{c}}{3}];&m=0,3,6\cdots\\\
0;&\text{otherwise}.\end{cases}$ (3)

Here, $T_{s}$ is the sampling time corresponding to 2.64GHz. The up-sampled
signal is subsequently smoothened by a linear digital filter where
$\mathbf{h}_{filt}[k],k=1\cdots K$ are the filter coefficients [20] to obtain

$\displaystyle\begin{split}\mathbf{y}_{filt}\left[m\frac{T_{s}}{2}\right]=\sum_{k=1}^{K}\mathbf{y}_{upsample}\left[(m-k)\frac{T_{s}}{2}\right]\mathbf{h}_{filt}[k],\\\
m=0,1,\cdots 4992;k=1,2\cdots K.\end{split}$ (4)

Then the signal is downsampled by a factor of 2 to obtain

$\displaystyle\begin{split}\mathbf{y}_{preamble}[mT_{s}]=\mathbf{y}_{filt}\left[2m\frac{T_{s}}{2}-\frac{K-1}{2}\frac{T_{s}}{2}\right]\\\
m=0,1,\cdots 4992.\end{split}$ (5)

The total length of $\mathbf{y}_{preamble}$ is 4992 and it is of 1.89$\mu s$
duration. The steps for generating the preamble bits are summarized in
Fig.4(b). The radar waveform is generated using the CEF bits as indicated in
Fig.1(b). Hence each $p^{th}$ frame of the radar waveform corresponds to a
uniquely generated
$\operatorname{\mathbf{x}_{p}}=\mathbf{y}_{preamble}[4033:4800]$ consisting of
$M^{\prime}=768$ samples. Since radar bits are already sampled at 2.64GHz,
there is no need for sample rate conversion. Note that the radar waveform
across consecutive $T_{PRI}$ are not identical as they generated from
different seeds used for generating Golay complementary sequences.

The BRF fields are optional fields to be used when beam alignment is required.
Each BRF consists of two sub fields - automatic gain control (AGC) and
training (TRN) fields - as shown in Fig.1(c). The AGC subfields consist of 64
bit Golay sequences, $\mathbf{g}_{a_{64}}$, repeated $M$ times where $M$ is
the total number of beams supported by analog beamforming for the phased array
in BS-TX. The BRF fields consist of the CEF followed by complementary 128 bit
Golay sequences, $\mathbf{g}_{a_{128}}$ and $-\mathbf{g}_{b_{128}}$, arranged
as shown in Fig.1(c) and replicated $M/4$ times. The CEF in the BRF is
identical to the the CEF in the preamble. The bits in the BRF are generated at
a chip duration of $T_{c}$ and subsequently processed in a manner identical to
the preamble as shown in Fig.4(b) to obtain $\mathbf{y}_{BRF}$. Their total
duration can be calculated as ${2.845\times[(M/4)]\mu}s$. In the proposed JRC
architecture, these fields are not needed and skipped during _Stage 1_. In the
standard architecture, these are used in _Stage 1_ but skipped in _Stage 2_.

Header and data processing: The 802.11ad standard specifies that data and
header are modulated over 336 data subcarriers per OFDM symbol and transmitted
over a minimum of 20 OFDM symbols if the optional BRF fields are used. In our
proposed JRC, the number of OFDM symbols, $N_{sym}$, will be based on the
amount of data to be transmitted as BRF are omitted. An additional OFDM symbol
is used (for both standard and JRC) to specify the control information in the
header such as amount of data transmitted, and information regarding the
modulation and coding schemes (MCS) which must be subsequently used at the BS-
RX and MU-RX to recover the data in $\operatorname{\hat{\mathbf{y}}_{DL}}$ and
$\operatorname{\hat{\mathbf{y}}_{UL}}$ respectively. Based on the
specifications, the header must be modulated with quadrature phase shift
keying with $3/4$ coding rate ($1$ parity bit for every $3$ data bits). The
standard supports the BPSK, QPSK, 16 bit QAM and 64 bit QAM modulations, and
$1/2$, $3/4$, $5/8$, and $13/16$ coding rates for the data. In this work, we
use the same MCS for both data and header for simplicity. The header and data
are processed as shown in Fig.4(c). Two data bits are mapped to each of the
336 data subcarriers corresponding to a single OFDM symbol. At a $3/4$ coding
rate, this corresponds to $3/4\times 672=504$ bits per OFDM symbol per packet.
If the number of data bits are less than an integral multiple of $504$,
appropriate zero padding is done. Each block of $504$ data bits is
sequentially passed through a scrambler which is a linear feedback shift
register. The first seven bits of the header provide a unique scrambler
initialization key to enable bit recovery at the receiver. The scrambled bits
are then passed through a low density parity check (LDPC) encoder with the
$3/4$ code rate. The standard specifies a parity check matrix,
$\mathbf{\mathcal{H}}$, that operates upon the code word $\mathbf{c}$ formed
of data bits followed by parity bits of a single OFDM symbol such that
$\mathbf{\mathcal{H}}\mathbf{c^{T}}=0$. After LDPC encoding, each frame has
672 bits which are then modulated into the QPSK WLAN constellation followed by
multiplication with a unit matrix, termed as $Q$ matrix [20], to randomise the
amplitude of the modulated bits. The outcome of the operations are the 336
modulated complex samples per OFDM symbol, to which additional DC, NULL and
pilot symbols are added, resulting in 512 complex symbols. Next, OFDM
modulation is performed comprising of 512-IFFT and 128-length cyclic prefix
(CP) addition. At the end, weighted overlap-and-add (WOLA) windowing is
performed on the OFDM modulated header and data to control the out-of-band
emission [31] to obtain $\mathbf{y}_{data}$. In the end, a scheduler combines
the header and data with preamble, and BRF samples to form the packet which is
then further processed by DFE and AFE.

Both the radar signal and the communication signals are converted from digital
to analog as shown in

$\displaystyle\operatorname{\mathbf{x}_{p}}(t)=\sum_{m=0}^{M^{\prime}}\operatorname{\mathbf{x}_{p}}[mT_{s}]\delta\left(t-mT_{s}\right),$
(6)
$\displaystyle\operatorname{\mathbf{y}_{DL}}(t)=\sum_{m=0}^{M}\operatorname{\mathbf{y}_{DL}}[mT_{s}]\delta\left(t-mT_{s}\right).$
(7)

Here $M^{\prime}=768$ (512 Golay samples upsampled by a factor of 1.5)
indicates the number of samples within the radar signal which remains fixed
since it is independent of data. The number of samples within
$\mathbf{y}_{DL}$ varies based on the amount of data to be transmitted and the
corresponding $N_{sym}$ OFDM symbols. These signals are then amplified such
that energy $E_{s}$ is imparted to each symbol. The amplifier output is
convolved with a root raised cosine transmit shaping filter, $\mathbf{h}_{T}$,
and then upconverted to the mmW carrier frequency $f_{c}$ as shown in

$\displaystyle\operatorname{\mathbf{x}_{p}}_{up}(t)=\sqrt{E_{s}}\left(\operatorname{\mathbf{x}_{p}}(t)\ast\mathbf{h}_{T}(t)\right)e^{+j2\pi
f_{c}t}$ (8)
$\displaystyle\operatorname{\mathbf{y}_{DL}}_{up}(t)=\sqrt{Es}\left(\operatorname{\mathbf{y}_{DL}}(t)\ast\mathbf{h}_{T}(t)\right)e^{+j2\pi
f_{c}t}.$ (9)

Then the signals are transmitted through analog beamforming through an
$N_{BS}$ element uniform linear array (ULA) after application of the antenna
weight vector, $\mathbf{w}_{BSTX}\in\mathcal{C}^{N_{BS}\times 1}$, as shown in

$\displaystyle\mathbf{X}_{p_{up}}(t)=\mathbf{w}_{BSTX}\operatorname{\mathbf{x}_{p}}_{up}^{T}(t),$
(10)
$\displaystyle\mathbf{Y}_{{DL}_{up}}(t)=\mathbf{w}_{BSTX}\operatorname{\mathbf{y}_{DL}}_{up}^{T}(t).$
(11)

The above process is repeated till all the $P$ radar packets are transmitted
followed by the communication packets after a guard time interval. In
_Stage-1_ , the antenna weight vector (AWV) is chosen to support a quasi-
omnidirectional beam. At the end of _Stage-1_ , when $\theta$ of the MU is
determined, then the AWV is selected to support a directional beam along
$\theta$.

###  III-B Radar Signal Detection and Processing

In this section, we first discuss the received radar signal model and then the
radar signal processing in detail. The radar transmits signal
$\mathbf{X}_{p_{up}}(t)$ is scattered by the dynamic MU and received at the
$N_{BS}$ element ULA at the BS-RX. If we assume that the MU is a dynamic
target with $B$ point scatterers, each at range $r_{b}(t)$, then the received
signal at the BS-RX antenna array is

$\displaystyle\hat{\vphantom{\rule{1.0pt}{5.86597pt}}\smash{\hat{\mathbf{X}}}}_{p_{up}}(t)=\sum_{b=1}^{B}a_{b}\mathbf{u}_{\theta_{b}(t)}\mathbf{u}^{T}_{\theta_{b}(t)}\left[\mathbf{X}_{p_{up}}(t)\ast\mathbf{H}^{2}\left(\frac{2r_{b}(t)}{c}\right)\right]+\mathbf{Z}(t).$
(12)

Here $a_{b}$ captures the amplitude of the reflection at each point scatterer
and
$\mathbf{H}^{2}=[\mathbf{h}^{2}(\frac{2r_{1}(t)}{c})\cdots\mathbf{h}^{2}(\frac{2r_{B}(t)}{c})]$
is the two-way propagation factor which is a function of the time-varying
range of each $b^{th}$ point scatterer. The steering vector from the antenna
array to and from $\theta_{b}$ is given by
$\mathbf{u}_{\theta_{b}}^{T}=[1\;\;e^{jkd_{BS}\sin\theta_{b}}\;\;\cdots]$
where $k$ is the propagation constant at $f_{c}$ and $d_{BS}$ is the uniform
element spacing. We assume that the MU is within the maximum unambiguous range
of the target i.e. $\frac{2r_{b}(t)}{c}<T_{PRI}$. $\mathbf{Z}$ is the additive
circular symmetric white Gaussian noise at the $N_{BS}$ receiver chains. We
assume that each point scatterer is moving with a constant radial velocity
$v_{b}$, then $r_{b}(t)=r_{ob}-v_{b}(t)t$ where $r_{ob}$ is the initial
distance from the BS. After down-conversion and digitization and in the
absence of multipath, (12) is

$\displaystyle\hat{\vphantom{\rule{1.0pt}{5.86597pt}}\smash{\hat{\mathbf{X}}}}_{p}[m]=\sum_{b=1}^{B}a_{b}\mathbf{u}_{\theta_{b}[m]}\mathbf{u}^{T}_{\theta_{b}[m]}\mathbf{X}_{p}\left[m-m_{b}\right]e^{-j2\pi
f_{D_{b}}pT_{PRI}}+\mathbf{Z}[m],$ (13)

where $m_{b}$ is the sample index corresponding to the time delay
($\frac{2r_{b}(t)}{c}$) and $f_{D_{b}}=\frac{2v_{b}f_{c}}{c}$ is the Doppler
frequency of the $b^{th}$ point scatterer. Note that the received signal in
(13) forms a data cube across fast time ($m=1:M^{\prime}$), slow time
($p=1:P$) and the $n=1:N_{BS}$ receiver elements. The radar received signal,
$\hat{\vphantom{\rule{1.0pt}{5.71527pt}}\smash{\hat{\mathbf{X}}}}_{p}[m]$ in
(13), is distinguished from uplink signal $\mathbf{Y}_{UP}[m]$ by the radar-
communication detection unit based on positive correlation with
$\mathbf{X}_{p}[m]$ sequence. Note that Golay sequences in the
$\hat{\vphantom{\rule{1.0pt}{5.71527pt}}\smash{\hat{\mathbf{X}}}}_{p}$ will be
distinct from the sequence in $\mathbf{Y}_{UP}$. Then, the data cube is
processed within the RSP as shown in Fig.5 to estimate the range ($r_{b}$),
azimuth ($\theta_{b}$) and Doppler velocity ($v_{b}$) of the MU.

Figure 5: Radar signal processing block: Input radar data cube is first
processed to obtain range-azimuth ambiguity plots. Multiple targets are
detected using CLEAN. Corresponding Dopplers of each target are estimated
through pulse-pair processing.

In BS-TX, the radar signal consisting of the Golay sequence was up-sampled
from the original 1.76GHz to 2.64GHz to match the sampling rate of the OFDM
modulated data. Hence, the first step in the RSP of the BS-RX is to down-
sample the fast time data from each $p^{th}$ packet and $n^{th}$ antenna, by a
factor of 1.5, to 1.76GHz (from 768 samples to 512 samples) to obtain
$\hat{\vphantom{\rule{1.0pt}{5.71527pt}}\smash{\hat{\mathbf{X}}}}_{p_{ds}}[m]$.
The fast time samples from each RF chain of the first packet (shown with the
red dotted rectangle in Fig.5) are cross-correlated with the corresponding
Golay sequence as shown in

$\displaystyle\mathbf{\chi}_{1}[r]=\hat{\vphantom{\rule{1.0pt}{5.86597pt}}\smash{\hat{\mathbf{X}}}}_{1_{ds}}[m]\ast\mathbf{G}_{u_{512}}[m],m=1:512,$
(14)

where $\mathbf{G}_{u_{512}}\in\mathcal{R}^{512\times N_{BS}}$ consists of the
$N_{BS}$ copies of the column vector $\mathbf{g}_{u_{512}}$. The cross-
correlation operation provides a peak at $m_{b}$ corresponding to the range of
the $b^{th}$ point scatterer provided the SNR is sufficient. The range axis
spans 512 bins with a range resolution of $cT_{c}/2$. Then one-dimensional
Fourier transform is carried out after zero-padding across the $N_{BS}$
elements to obtain the range-azimuth ambiguity plot
$\tilde{\chi}_{1}[m,\theta]=\text{DFT}\\{\chi_{1}\\}$. The azimuth axis spans
from $-90^{\circ}$ to $90^{\circ}$ (if the antenna spacing is half-wavelength)
with a bin size governed by the zero-padding factor. The MU (one or multiple)
are identified based on peaks in the range-azimuth ambiguity plot. In order to
detect multiple targets across a large dynamic range, the CLEAN algorithm is
implemented [32, 33]. This is an iterative algorithm, wherein in each $i^{th}$
step the strongest target is identified based on the peak, $a_{i}$, in the 2D
ambiguity plot
$\underset{r_{i},\theta_{i}}{\arg\max}||\tilde{\chi}^{i}[r,\theta]||$. Then
the 2D point spread response, $\Upsilon[r_{i},\theta_{i}]$, of the peak target
at this position is removed from the ambiguity plot to generate a residual
plot $\tilde{\chi}^{i+1}_{1}=\tilde{\chi}^{i}_{1}-\Upsilon[r_{i},\theta_{i}]$,
that is utilized for the subsequent step. The above two steps are iterated
till the strength of the residue plot falls below a predefined threshold. The
output of the CLEAN algorithm is the list of possible targets, $i=1:I$,
determined in each $i^{th}$ step of the CLEAN algorithm and their
corresponding amplitudes and 2D positions ($a_{i},r_{i},\theta_{i}$). Target
returns that fall very close to each other in the range-azimuth ambiguity plot
possibly arise from a single extended target and are clustered together. Note
that some of the targets may not be MU and may be static clutter in the BS
environment. Hence, we next implement Doppler processing on the returns. While
many algorithms may be used for estimating Doppler velocity [34, 24], we
implement the computationally efficient pulse pair processing which requires
only two consecutive radar packets and is performed only for those cells in
the range-azimuth ambiguity plots corresponding to the localized targets as
shown in

$\displaystyle f_{D_{i}}=\frac{-1}{2\pi
T_{PRI}}\arg\left[\tilde{\chi}_{2}[r_{i},\theta_{i}]\ast\tilde{\chi}_{1}[r_{i},\theta_{i}]\right].$
(15)

Based on estimated Doppler $f_{D_{b}}$, we determine if the $i^{th}$ target is
static or dynamic. If it is dynamic, then it is regarded as an MU and its
$\theta_{i}$ is used to determine the antenna weight vector
$\mathbf{w}_{BSTX}$ in the subsequent _Stage-2_ as discussed in Section II.

###  III-C Communication Received Signal Processing

The aim of the communication receiver is to demodulate and decode the
transmitted data correctly. It performs the same tasks as the communication
transmitter but in reverse order. The transmitter output propagates from BS-TX
to the MU-RX at range $r$ and azimuth $\theta$ through the steering vector
$\mathbf{u}_{\theta}^{T}$. If the MU-RX consists of $N_{MU}$ element ULA, then
the received signal at the MU-RX after analog beamforming with antenna weight
vector, $\mathbf{w}_{MURX}\in\mathcal{C}^{N_{MU}\times 1}$, is

$\displaystyle\hat{\mathbf{y}}_{{DL}_{up}}(t)=\mathbf{w}_{MURX}^{T}\mathbf{u}_{\phi}\mathbf{u}_{\theta}^{T}\left[\mathbf{Y}_{{DL}_{up}}(t)\ast\mathbf{h}^{1}\left(\frac{r(t)}{c}\right)\right]+\mathbf{\zeta},$
(16)

where $\mathbf{u}_{\phi}^{T}=[1\;e^{jkd_{MU}\sin\phi}\;\cdots]$ is the
steering vector for the BS at $\phi$ with respect to MU-RX for $d_{MU}$
antenna element spacing, $\mathbf{h}^{1}(\frac{r(t)}{c})$ is the one-way
propagation factor for each MU and $\zeta$ is the additive circular-symmetric
white Gaussian noise.

Figure 6: Data recovery at communication receiver

The received RF signal is amplified, then down-converted and digitized before
it is further processed through the blocks shown in Fig.6 to extract data from
$\hat{\mathbf{y}}_{DL}$.

The first step is to perform OFDM demodulation which consists of cyclic-prefix
removal followed by 512-FFT. Then, least-squares-based channel estimation is
performed using the extracted pilots. Then, minimum mean square error [35]
based channel equalization is carried out on the 336 data symbols in each OFDM
symbol. This is followed by soft data demodulation [36, 37] and LDPC channel
decoding [38].The output of the LDPC decoder is passed through the
descrambling block, where a dummy header of 57 bits is added and padded bits
are removed and passed through the same scrambling block as the one used in
the transmitter. The output after descrambling is the decoded data bits
extracted from $\hat{\mathbf{y}}_{DL}$. Similar processing is also done at BS-
RX to recover the data transmitted over the uplink $\hat{\mathbf{y}}_{UL}$ .

##  IV Simulation Setup

In this section, we describe the simulation setup for evaluating the
communication link metrics and the radar performance metrics.

###  IV-A Target Model

We consider a three-dimensional Cartesian space where $xy$ forms the ground
and $z$ is the height axis. The target motion along two trajectories over a
duration of 1s is shown in Fig.7(a) and (b). For the first trajectory, we
assume that the JRC is located at $[0m,0m,0m]$ and the target starts from
$[-5m,10m,0m]$ and moves along the $x$-axis in a direction tangential to the
JRC. For the second trajectory, the JRC is assumed to be at $[-13m,15m,0m]$
while the target starts at $[-3m,15m,0m]$ and moves along the $x$ axis in a
radial direction away from the JRC. We consider two types of dynamic target
models/MU - the first is a simple isotropic point target and the second is an
extended target with multiple point scatterers and aspect angle dependence. We
consider two extended targets - a pedestrian and a mid-size car. For both
trajectories, the pedestrian moves with a constant velocity of 1.5m/s while
the car moves with a velocity of 10m/s. The animation data for the walking
pedestrian are obtained from motion capture technology [39, 40]. The data
describes the dynamics of a collection of 27 body parts of a skeleton at a
frame rate of 60Hz. Each body part is modeled as an ellipsoid, as shown in
Fig.7(c), whose radar cross-section is obtained through analytical
expressions.

Figure 7: Trajectories followed by a target/MU with respect to JRC: (a)
tangential motion (b) Radial motion. (c) Point scatterer model of pedestrian
(MU), and (d) 2D range-azimuth ambiguity plot for pedestrian. (e) Point
scatterer model of a mid-size car (MU) and (f) 2D range-azimuth plot for the
car.

Based on the methods described in the previous section, we generate the range-
azimuth ambiguity plot of the human and display the result for one time frame
in Fig.7(d). The figure shows that the human is essentially a spatially small
target and the point scatterers are clustered together within a small region
of the ambiguity plot. Our second extended target is a mid-size car modelled
using a 3D computer-aided design. The car is animated along the above
mentioned trajectories based on the methodology described in [41, 42]. The
metallic parts of the mid-size car are rendered into $6905$ triangular facets
and their 3D centroids are identified as the collection of point scatterers as
shown in Fig.7(e). The corresponding range-azimuth ambiguity plot for one
timeframe is displayed in Fig.7(f). The result shows that the car is a larger
spatial target than the pedestrian and thus results in a slightly wider spread
along range and azimuth. The centroid of the car returns is determined by
clustering. In both cases, the Dopplers were non-zero, indicating that these
are dynamic targets and not static clutter.

###  IV-B Channel Model

We consider two types of channel models to model the two-way radar propagation
($\mathbf{h}^{2}$) and one-way communication propagation ($\mathbf{h}^{1}$)
channels. First, we consider an idealistic free space channel model with a
direct line-of-sight (LOS) between the BS and MU and no multipath/non-line-of-
sight (NLOS). The one-way propagation path between the BS and MU which are $r$
distance apart is given by

$\displaystyle\mathbf{h}^{1}\left(\frac{r(t)}{c}\right)=\sqrt{\frac{G_{BS}(\theta)G_{MU}(\phi)L_{f}(r)\lambda^{2}}{(4\pi
r(t))^{2}}}\delta\left(t-\frac{r(t)}{c}\right),$ (17)

where $G_{BS}$ and $G_{MU}$ are the element patterns of the BS and MU antenna
arrays, $L_{f}(r)$ is the atmospheric attenuation and $\delta(\cdot)$ is the
Dirac-delta function. Similarly, the two-way propagation from the BS to the MU
and back, for the radar signal is shown as

$\displaystyle\mathbf{h}^{2}\left(\frac{2r(t)}{c}\right)=\sqrt{\frac{G_{BS}^{2}(\theta(t))L_{f}(2r)\lambda^{2}}{(4\pi)^{3}r^{4}(t)}}\delta\left(t-\frac{2r(t)}{c}\right).$
(18)

Second, we consider the _Rician_ fading model which has been popularly used to
model outdoor mmW communication [43]. Here, the propagation is characterised
by a dominant LOS component and additional NLOS components. The communication
signal received at MU-RX shown in (16) is modified for the fading channel
model as

$\displaystyle\begin{split}\hat{\mathbf{y}}_{{DL}_{up}}(t)=\mathbf{w}_{MURX}^{T}\mathbf{u}_{\phi}\mathbf{u}_{\theta}^{T}\left[\mathbf{Y}_{{DL}_{up}}(t)\ast\sqrt{\frac{\operatorname{\mathcal{J}}}{\operatorname{\mathcal{J}}+1}}\mathbf{h}^{1}\left(\frac{r(t)}{c}\right)\right]\\\
+\left[\mathbf{\rho}_{nlos}(t)\ast\sqrt{\frac{1}{\operatorname{\mathcal{J}}+1}}\mathbf{h}^{1}\left(\frac{r(t)}{c}\right)\right]+\mathbf{\zeta},\end{split}$
(19)

where $\operatorname{\mathcal{J}}$ is a Rician factor that is empirically
determined for different propagation environments such as rural, urban and
suburban [44]. The first term in (19) models the direct path in the one-way
propagation factor while $\mathbf{\rho}_{nlos}(t)$ denotes the signal arising
from the multipath that is modeled by an independent and identically
distributed complex Gaussian random variable with zero mean and unit variance.
The fading channel for two-way propagation of the radar signal
$\hat{\vphantom{\rule{1.0pt}{5.71527pt}}\smash{\hat{\mathbf{X}}}}_{p_{up}(t)}$
is modeled by squaring the one-way propagation model in (19) for each antenna
element at the BS-RX.

##  V Numerical Results

###  V-A Timing Analysis

In this section, we compare the time taken for beam alignment - the duration
of _Stage-1_ \- for the standard IEEE 802.11ad and the two versions of the
proposed JRC. The timing analysis is carried out based on the architecture
presented in Section.II and the results are reported in Table.I.

TABLE I: Timing analysis for beam alignment for Standard, JRC _Version-1_ , and JRC _Version-2_ Signals |  Signal Processing | Standard | JRC _Version- 1_ | JRC _Version-2_
---|---|---|---|---
|  |  Duration |  Packets |  Total |  Duration |  Packets |  Total |  Duration |  Packets |  Total
DL Packet $\mathbf{y}_{DL}$ (in $\mathbf{\mu}s$) |  |  29.73 |  4 |  118.9 |  4.5 |  1 |  4.5 |  4.5 |  4 |  18
UL Packet $\mathbf{y}_{UL}$ (in $\mathbf{\mu}s$) |  |  4.5 |  1 |  4.5 |  9.82 |  1 |  9.82 |  - |  - |  -
Comm Idle Time (in $\mathbf{\mu}s$) |  |  1 |  3 |  3 |  - |  - |  - |  1 |  3 |  3
Radar Waveform $\mathbf{x}_{Dp}$ (in $\mathbf{\mu}s$) |  |  - |  - |  - |  0.29 |  2 |  0.58 |  0.29 |  2 |  0.58
Pulse Repetition Interval $T_{PRI}$ (in $\mathbf{\mu}s$) |  |  - |  - |  - |  0.29 |  2 |  0.58 |  0.29 |  2 |  0.58
|  RCP on $\hat{\mathbf{y}}_{DL}$ (in ms) |  16 |  4 |  64 |  16 |  2 |  32 |  |  - |  -
|  RCP on $\hat{\mathbf{y}}_{UL}$ (in ms) |  16 |  1 |  16 |  16 |  1 |  16 |  - |  - |  -
|  Receive Preamble Correlation $\hat{\mathbf{y}}_{DL}$ (in ms) |  - |  - |  - |  - |  - |  - |  - |  - |  4.5
|  Radar/Comm Detection Unit (in ms) |  - |  - |  - |  2.5 |  2 |  5 |  2.5 |  1 |  2.5
|  Preamble Bits Extraction (in ms) |  - |  - |  - |  1.6 |  - |  1.6 |  1.6 |  - |  1.6
|  RSP on $\hat{\vphantom{\rule{1.0pt}{5.71527pt}}\smash{\hat{\mathbf{x}}}}_{p},p=1,2$ (in ms) |  - |  - |  - |  16 |  - |  16 |  16 |  - |  16
Total time for beam alignment at BS | 64+16+0.10=80.1 | 16+2.5+1.6 =20.1 | 16+2.5+1.6 =20.1
Total time for beam alignment at MU | 64 ms | 16+16+2.5=34.5 | 4.5 ms
Total time for completion of _Stage 1_ | 80.1 ms | 34.5 ms | 20.1 ms

For both versions of the JRC and the standard architectures, we assume that
the BS and MU have a ULA of 32 antennas and 4 antennas respectively. The total
beam alignment time is based on the number of packets, their duration as well
as the processing time of packets which are of the order of milliseconds. In
this work, all the processing is carried out in floating-point in MATLAB 2021a
on an Intel Core i7 processor with 128 GB RAM. The one-way and two-way
propagation times for communication and radar are neglected since they are
comparably much shorter (of the order of nanoseconds) over the short ranges of
the MU with respect to the BS than the signal lengths and signal processing
times.

In the standard protocol, $\mathbf{y}_{DL}$ consists of 32 BRF fields in
addition to the preamble, header and data to support beam alignment at the BS.
This results in a packet length of 29.73$\mu s$ duration for $N_{sym}=20$ data
symbols which is the minimum specified by the protocol. This packet is
transmitted $4$ times with an inter-packet guard spacing of 1$\mu s$ to
support beam alignment at the MU. This information is then communicated
through the subsequent $\mathbf{y}_{UL}$ transmitted over the MU’s best beam
to the BS where it is processed. Then, the next $\mathbf{y}_{DL}$ is
transmitted over the BS’s best beam and received by the MU’s best beam in
_Stage-2_. The overall beam alignment duration for BS and MU are 80.1ms and
64ms respectively. The _Stage-1_ alignment time is computed by the total time
required for both BS and MU beam alignment (the greatest value of the two
times). Note that in the standard beam alignment, the overall duration is a
function of the communication packet length and hence the number of OFDM data
symbols. Also, the packets are long since they must include the BRF fields for
all possible beams from the BS and repeated for all possible beams of the MU.
The recovery of data bits from the received data packet is computationally
intensive and hence requires a long time. After the data bit recovery from
each packet, the BRF fields are processed for the correlation gains,
generating an $M\times N$ matrix. Finally, the $(\tilde{m},\tilde{n})^{th}$
element of the matrix with the highest correlation gain where $\tilde{m}$ and
$\tilde{n}$ provide the best beam among the $M$ BS beams and $N$ MU beams
respectively. All the above factors result in a long beam alignment phase.

Figure 8: RMSE results for range, azimuth and Doppler velocity estimates from
Monte-Carlo based numerical experiments of single and multiple point
targets/MU in free space and Rician propagation conditions with JRC and FMCW
radar.

Next, we consider the _Stage-1_ beam alignment duration of the JRC. The two
symbols of radar waveform ($\mathbf{x}_{1}$ and $\mathbf{x}_{2}$) are each of
very short duration (0.29$\mu s$) since they consist of only 512 samples and
are transmitted ahead of a $\mathbf{y}_{DL}$ packet with $N_{sym}=10$ symbols
of data (without BRF fields). The $T_{PRI}$ for each radar signal is 0.58$\mu
s$ which results in a maximum detectable range of approximately 87m. The
reflected received signals,
$\hat{\vphantom{\rule{1.0pt}{5.71527pt}}\smash{\hat{\mathbf{x}}}}_{p},p=1,2$,
are detected in the radar-communication detection unit and subsequently
processed to estimate the MU’s range, Doppler, and azimuth angle. The azimuth
angle of arrival forms the beam direction for the subsequent transmission of
packets in _Stage-2_. Note that the beam is directed exactly at the most
recent position of the target, unlike the standard where the transmission in
_Stage-2_ is along the optimum pre-determined beams. Hence the total time
required at the BS for beam alignment is 20ms. This time requirement is
entirely independent of the number of OFDM data symbols that are transmitted
in $\mathbf{y}_{DL}$. Further, since the BRF fields are omitted in
$\mathbf{y}_{DL}$, the minimum number of OFDM data symbols that must be
transmitted in the packet is no longer 20 and instead directly based on the
amount of data that is to be transmitted. The JRC is only included in the BS
and not in the MU. Hence, we present two different versions of beam alignment
at the MU.

In JRC _Version-1_ , $\mathbf{y}_{DL}$ is first received at MU with a quasi-
omnidirectional beam. Once the data are processed, the MU transmits the
$\mathbf{y}_{UL}$ with four BRF fields, such that each field is transmitted
through each of the 4 different pre-determined beams of the MU. The received
$\hat{\mathbf{y}}_{UL}$ is processed at the BS to determine the best
$\tilde{n}^{th}$ beam of the MU. This information is communicated to the MU
through the next $\mathbf{y}_{DL}$. Hence, the total duration for beam
alignment at MU is 34.5ms which is shorter than the standard. In JRC
_Version-2_ , the BS sends four consecutive $\mathbf{y}_{DL}$ packets. Each of
these packets consists of 10 OFDM symbols and zero BRF fields. The MU receives
each packet through the corresponding 4 pre-determined beams, one at a time.
All four data packets are processed to estimate the best $\tilde{n}^{th}$ beam
at the MU and the time taken for beam alignment at MU is 4.5ms. The short
processing time is because the best beam is determined using the parallel
correlation operation on the Golay sequences of the preamble of the multiple
packets. From this timing analysis, it is evident that the JRC-based
architecture provides faster beam alignment than the standard for the same
number of beams at BS and MU. This can be attributed to two factors - first,
the reduction of the packet duration due to the omission of the BRF fields due
to radar-based beam alignment at the BS. This also reduces the total number of
packets that have to be transmitted to support the beam alignment at the MU
(especially in _Version-1_). Second, digital beamforming and subsequent radar
signal processing at the BS-RX support the detection and localization of the
MU. This becomes even more advantageous when there are multiple MU in the
channel since the above beam refinement protocol for multiple MU can be
carried out in parallel since the radar can detect multiple targets. This is
not possible with the standard protocol.

###  V-B Radar Metrics

In this section, we evaluate the performance of the 802.11ad-based radar and
then benchmark it with the frequency modulated continuous wave (FMCW) which is
commonly used in mmW radars. The FMCW radar signal parameters such as carrier
frequency ($f_{c}$), sampling time ($T_{s}$), PRI ($T_{PRI}$), and the number
of radar pulses are selected to be identical to that of the JRC waveform. The
chirp factor for the FMCW waveform is 600MHz/$\mu s$.

First, we perform Monte-Carlo simulations with 10000 iterations for different
radar target scenarios at various SNRs. We consider single and multiple target
cases under free space and Rician propagation conditions. The value of
($\operatorname{\mathcal{J}}$) is chosen as 7dB in our work to model the
channel according to the rural environment [44]. For the single target
scenario, in each iteration of the Monte-Carlo simulation, we consider the
point target’s location to be uniformly distributed in the 2D Cartesian space
within 60m $\times$ 60m while the velocity of the target is varied uniformly
from -30m/s to 30m/s. The RCS is varied based on the Swerling-1 model with the
mean RCS selected randomly from 10m2, 1m2, 0.1m2 and 0.01m2. In the multi-
target scenario, the number of targets for each iteration is varied based on
the Poisson distribution with the average number of targets taken as 2. A
target is localized through radar signal processing to provide range, azimuth,
and Doppler estimates. We calculate the accuracy of these estimates by
calculating the root mean square error (RMSE) of the estimates of the target
with the ground truth as shown in Fig. 8 for different SNR.

In both free space and Rician conditions, we observe that the RMSE of the
estimates decreases with an increase in the SNR for both JRC and FMCW
waveforms. For the single target conditions, the lowest RMSE at the highest
SNR corresponds to the resolution sizes of the estimates. In other words, the
RMSE for range estimation is the range resolution which is a function of the
signal bandwidth, while the RMSE for azimuth estimation is governed by the
aperture size at the BS. Even though the Doppler velocity is estimated through
a very short coherent processing interval of just two radar packets, the
Doppler velocity estimate shows a low error because the targets were first
resolved in range and azimuth before the Doppler processing was carried out.
For all three parameters - range, azimuth, and Doppler - the error estimates
for the JRC waveform are comparable with that of the FMCW waveform. Next, we
consider the multiple targets scenario for the free space conditions. Here, we
observe that the errors have increased especially when the SNR is poor. The
errors for both single and multiple targets under Rician conditions are
substantially worse than the free space conditions. This is especially true
for the multiple target scenario under poor SNR. However, it is important to
note that the performance of the JRC waveform is not any worse than that of
the conventional FMCW under these circumstances.

Next, we repeat the experiment for the two extended dynamic targets - the
pedestrian and the midsize car - discussed in Section.IV. The two targets
follow the trajectories shown in Fig.7a and b. The ground truth value
considered for the calculation of RMSE is the root node point of the multiple-
point scatterers on the target. The range, Doppler, and azimuth estimates are
reported for free space and Rician propagation conditions using both the JRC
waveform and the FMCW in Fig.9 and Fig.10.

Figure 9:  RMSE results for range, azimuth and Doppler velocity estimates of
single pedestrian (extended target) in free space and Rician propagation
conditions with JRC and FMCW radar.

The RMSE for a pedestrian deteriorates with lower SNR values under both free
space and Rician fading conditions. The pedestrian has a narrower spatial
extent along the range dimension when compared to the azimuth width.
Additionally, the antenna aperture at the BS is fairly narrow. Due to these
reasons, the RMSE error for azimuth is high when compared to that of the
range. The RMSE for Doppler velocity is sufficient to distinguish a moving
pedestrian from static clutter. All three estimates deteriorate with the
Rician propagation conditions. However, in all of the cases, the results for
the JRC waveform are comparable to that of the FMCW radar. In the case of the
mid-size car, the RMSE error for range, azimuth, and Doppler are slightly
greater than that of the pedestrian since the target is spatially larger and
hence the ground truth (at the center of the car) may deviate from the
positions of the point scatterers on the chassis of the car that are
identified by the radar.

Figure 10:  RMSE results for range, azimuth and Doppler velocity estimates of
a single mid-size car (extended target) in free space and Rician propagation
conditions with JRC and FMCW radar.

In this case, the error from the JRC is slightly higher than that of the FMCW
waveform (approximately 1 degree in azimuth). Also, the results from the
Rician deteriorate slightly with respect to the free space conditions.

###  V-C Communication Metrics

In this section, we report the communication metric - the bit error rate (BER)
and throughput - that are calculated on $\hat{\mathbf{y}}_{DL}$ at MU in Fig.
11 and Fig. 12. The BER is the number of error bits out of the total
transmitted data bits and is computed for the two different trajectories of
the MU and for both free space and Rician channel conditions. The
communication receiver is modeled with a system noise temperature of 290K
which gives rise to a mean noise floor of -71.7dBm for a receiver bandwidth of
2.64GHz. As the MU moves along the trajectory, the SNR changes based on the
distance between the MU and the BS. We plot the BER over the entire duration
of each trajectory.

We first discuss the results for the tangential line trajectory-1 under free
space conditions, which are displayed in Fig.11(a) and (b).

Figure 11: Time-varying BER for Tangential trajectory-1 in free space
conditions for (a) short duration of 0.2s, (b) long duration of 1s; and Rician
space conditions for (c) short duration of 0.2s, (d) long duration of 1s.

During _Stage-1_ , we observe that the BER of standard and both versions of
JRC are high and then fall in Fig.11(a). This corresponds to the poor BER
during _Stage-1_ because of the poor link metrics arising from the low gain
quasi-omnidirectional beams at the BS and MU. This stage is followed by low
BER during _Stage-2_ with directional links. The _Stage-1_ duration for
standard, JRC-_Version-1_ and JRC-_Version-2_ are approximately 0.08s, 0.03s
and 0.02s respectively. Hence, the BER is poor for the standard for a longer
duration than the JRC versions. Interestingly, the BER for _Version-1_ falls
within the same time as _Version-2_ even though theoretically the former takes
longer to complete the beam alignment. This is because the BS beam is aligned
within this interval for both versions and the high gain from the BS’s ULA
contributes towards lowering the BER even when the beam alignment is not
completed at the MU for the first version. Thus, for free space conditions, we
realize an improvement in the beam alignment by a factor of four for both the
JRC versions when compared to the standard. Due to the nature of the
trajectory, the mobile target crosses a narrow beam within a short duration of
time and frequent beam alignment is required as shown in Fig.7a. When the
target is outside of the beam, we observe a deterioration of the BER due to a
fall in the SNR in _Stage-2_. This can be observed, for example, between 0.12s
and 0.2s in Fig.11(b) for standard, and between 0.15s to 0.17s for the JRC
versions.

Figure 12: Time-varying BER for radial trajectory-2 in free space conditions
for (a) short duration of 0.2s, (b) long duration of 1s; and Rician space
conditions for (c) short duration of 0.2s, (d) Long duration of 1s.

Since the standard protocol enables the selection of one of the pre-determined
beams while the JRC versions enable directional beams at the recent most
angular position of the target, the latter results in better SNR and less
frequent beam alignment. The performances of both the standard and the JRC
versions deteriorate in Rician conditions resulting in higher BER (as observed
in Fig.11(c) and (d)) due to strong interference from multipath. Again, we
observe that the beam alignment is more rapid for the JRC versions than
standard in Fig.11c which lowers the overall BER by a factor varying from 8 to
32%.

Next, we discuss the results for the radial trajectory-2 in free space
conditions which are displayed in Fig.12(a) and (b). Again, the beam alignment
duration for the two versions of JRC is much lower than that of the standard
in Fig.12a. The faster beam alignment (again by a factor of four) at the MU
for _Version-2_ enables slightly superior performance as evidenced by the
results. From Fig.12(b), we observe that this trajectory requires less
frequent beam alignment between the MU and BS (Fig.7b). Once the best beams
are identified, the MU remains within the beam for the remaining duration of
the motion. The results for the Rician conditions, shown in Fig.12 (c) and
(d), are much poorer than the free space conditions due to the strong
interference from the multipath.

Figure 13: Comparison of number of packets communicated over 1 second
duration.

Next, we compare the number of packets transmitted during the time interval.
As shown in Fig. 13, JRC versions allow a higher number of packet
transmissions due to smaller packet sizes and fewer beam alignments compared
to the standard. The overall communication throughput is calculated based on

$Throughput=\left(1-\frac{\sum_{i=1}^{N_{p}}BER_{i}}{N_{p}}\right).\frac{(D)(N_{p})}{T_{d}}$
(20)

where, $N_{p}$ is the number of packets transmitted, $T_{d}$ is the total
duration and $D$ is the number of data bits transmitted in each packet which
is kept fixed. The overall throughput in Gigabits per second (Gbps) for
standard, JRC _Version-1_ and JRC _Version-2_ are presented in Table.II.

TABLE II: Throughput Comparison Of Different Architectures | Frii’s free space | Rician
---|---|---
Values in Gbps | Standard | JRC _Version-1_ | JRC _Version-2_ | Standard | JRC _Version-1_ | JRC _Version-2_
Trajectory 1 (Translational) | 0.336 | 0.880 | 0.883 | 0.329 | 0.878 | 0.880
Trajectory 2 (Radial) | 0.840 | 0.883 | 0.883 | 0.839 | 0.881 | 0.883

The results show that the standard shows a much poorer throughput under both
Frii’s free space and Rician channel conditions for both trajectories when
compared to both versions of the JRC for the first trajectory which required
more frequent beam alignments. Even for the second trajectory, the standard
has poorer throughput due to the longer beam alignment duration. The
throughputs for the two JRC versions are comparable.

##  VI Summary

We provide a complete architectural framework of an IEEE 802.11ad-based JRC
wireless transceiver for enabling mmW communications between BS and fast-
moving users. The radar functionality within the JRC enables the detection of
point and extended mobile user targets and provides accurate estimates of
their angular positions through range, Doppler, and azimuth processing. This
information enables rapid beam alignment of the communication beams at the BS
when compared to the lengthy beam training procedure adopted by the standard
protocol. A complete end-to-end software prototype implementation on MATLAB is
provided with transceiver design details, radar waveform, transmission signal
models, and the corresponding signal processing algorithms. For an example
case of a system with 32 beams in the BS and 4 beams in the MU, we demonstrate
an improvement in the beam alignment timing by a factor of 4 and a significant
improvement in the overall communication throughput for the JRC with respect
to the standard. The main advantages offered by the JRC are the reduction in
the packet lengths and number due to the omission of the beam training fields
overhead; and the overall lower BER due to the precise estimate of the MU’s
angular position by the radar within the BS when compared to the standard’s
use of pre-determined beams. Further improvements in the JRC timing are
anticipated for a higher number of MUs and hardware acceleration of the radar
signal processing. This is the focus of our future work.

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# Editorial on Research Topic: High-Tc Superconductivity in Electron-Doped
Iron Selenide and Related Compounds

Jose P. Rodriguez 1,∗, Dmytro S. Inosov 2 and Jun Zhao 3

Iron-selenide superconductors comprise a particularly interesting group of
materials inside the family of iron-based superconductors. The simplest member
of the group is bulk FeSe, which has a modest critical temperature of
$T_{c}=9$ K. Like iron-pnictide superconductors, bulk FeSe shows a structural
transition at $T_{s}=90$ K from a tetragonal to an orthorhombic phase driven
by nematic ordering of the electronic degrees of freedom. Angle-resolved
photoemission spectroscopy (ARPES), for example, reveals a small hole Fermi
surface pocket at the center of the Brillouin zone and two electron Fermi
surface pockets at the corner of the Brillouin zone, each with unequal
$d_{xz}/d_{yz}$-orbital character. Unlike in iron-pnictide superconductors,
however, no magnetic order coexists with the nematic order at temperatures
below the structural transition. Inelastic neutron scattering (INS)
spectroscopy finds a spin resonance inside the energy gap of the
superconducting phase in bulk FeSe, however, at wavevectors corresponding to a
stripe spin-density wave (SDW)[1]. It strongly suggests $s^{+-}$
superconductivity across the hole and electron Fermi surface pockets driven by
associated antiferromagnetic spin fluctuations. INS also finds spin
fluctuations at the Néel wavevector $(\pi,\pi)$ above the superconducting
energy gap[2]. This suggests that superconductivity, nematic order, stripe-SDW
order, and some type of Néel antiferromagnetic order compete at low
temperature in bulk FeSe. One of the editors of the research topic has
proposed that the latter is hidden Néel order[3, 4].

The superconducting critical temperature increases dramatically to $30$-$40$ K
and above upon doping iron selenide with electrons. The latter has been
achieved in various ways; for example, by alkali-metal intercalation, by
placing a monolayer of FeSe on a substrate, and by organic-molecule
intercalation. ARPES finds that the hole bands at the center of the Brillouin
zone lie buried below the Fermi level. INS finds a spin resonance inside the
superconducting energy gap, but it lies midway between the SDW and Néel
wavenumbers[5]. INS also finds peaks and rings of low-energy spin excitations
above the energy gap around the Néel wavevector[6, 7]. ARPES and scanning
tunneling microscopy (STM) find a non-zero superconducting energy gap. The
situation with electron-doped FeSe is rather puzzling then, with high-$T_{c}$
superconductivity existing over electron Fermi surface pockets alone! This is
not expected in iron-selenide superconductors, where electron-electron
repulsion is strong[8]. The latter requires that the sign of the pair
wavefunction oscillates over the Brillouin zone[4].

It is our pleasure to introduce eight articles from the Research Topic that
address many of the unsolved problems that have emerged in the field of iron-
selenide superconductors, some of which we have listed above. The
contributions to the Research Topic contain articles on both theory and
experiment, with four papers reporting on original research, and with four
review papers. Tong Chen, Min Yi and Pengcheng Dai review how nematicity in
bulk iron selenide can be scrutinized by exploiting detwinning techniques[9],
while Amalia Coldea reviews the series of nematic superconductors
FeSe1-xSx[10]. Both articles tackle the interplay between nematicity and
superconductivity that exists in bulk FeSe, with or without chemical
substitutions. Maw-Kuen Wu and collaborators show that insulating Fe4Se5
becomes a superconductor with $T_{c}=8$ K after proper annealing[11]. They
thereby argue that Fe4Se5 is the insulating parent compound for iron-selenide
superconductors. It would clearly be useful to compare future studies of the
low-energy spin excitations in Fe4Se5 with those of its electron-doped
counterpart Rb2Fe4Se5 [5, 6]. Finally, Xiaoli Dong, Fang Zhou and Zhongxian
Zhao review a new soft-chemical technique to grow high-quality single crystals
of organic-molecule intercalated FeSe[12]. Their samples have critical
temperatures of $T_{c}=42$ K, and they notably show record critical currents.

On the theory side, Rong Yu, Qimiao Si and collaborators review $3d$-orbital-
selective physics in iron superconductors[13]. They point out how the $d_{xy}$
orbital is the one most susceptible to Mott localization in iron-selenide
superconductors[8]. They also emphasize how the relatively small energy
splitting between the $d_{xz}/d_{yz}$ orbitals that is seen by ARPES in the
nematic phase of bulk FeSe, $\Delta E_{\Gamma}$ and $\Delta E_{M}<50$ meV, can
be reconciled with the large orbitally-dependent wavefunction renormalizations
seen by STM in the same phase, $Z(d_{yz})/Z(d_{xz})=4$. Maxim Dzero and Maxim
Khodas study the effect of point disorder on the stripe SDW state by
exploiting a quasi-classical Green’s function technique[14]. They find that
the tetragonally symmetric stripe SDW state is more robust with respect to
disorder than the orthorhombically symmetric one. This result could have
bearing on the absence of magnetic order in the nematic phase of bulk FeSe,
for example. Last, Andrzej Ptok, Konrad Kapcia and Przemysław Piekarz study a
two-band model for iron superconductors that includes intra-band and inter-
band coupling between Cooper pairs[15]. They notably find Cooper pair states
in relative orbitals of mixed symmetry. Finally, Rustem Khasanov and
collaborators applied muon-spin rotation/relaxation ($\mu$SR) on the iron-
pnictide superconductor NdFeAsO0.65F0.35, thereby obtaining London penetration
lengths[16]. Interestingly, a two-band analysis of their data yields only weak
inter-band coupling of the Cooper pairs.

The brief survey above of the author contributions to the Research Topic
conveys the richness of the field of iron-selenide superconductivity and
related materials. We believe that you will enjoy reading the Research Topic.

Yours sincerely, Jose Rodriguez, Dmytro Inosov and Jun Zhao, February 28,
2022.

## References

  * [1] Wang Q, Shen Y, Pan B, Hao Y, Ma M, Zhou F, Steffens P, Schmalzl K, Forrest TR, Abdel-Hafiez M, Chareev DA, Vasiliev AN, Bourges P, Sidis Y, Cao H, and Zhao J, “Interplay between stripe spin fluctuations, nematicity and superconductivity in FeSe”. Nat Mater. (2016) 15:159-163. doi:10.1038/nmat4535
  * [2] Wang Q, Shen Y, Pan B, Zhang X, Ikeuchi K, Iida K, Christianson AD, Walker HC, Adroja DT, Abdel-Hafiez M, Chen X, Chareev DA, Vasiliev AN, and Zhao J, “Magnetic ground state of FeSe”. Nat Commun. (2016) 7:1–7. doi: 10.1038/ncomms12182
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