# Design and Implementation of Low Complexity Reconfigurable Filtered-OFDM
based LDACS

Niharika Agrawal, Abhishek Ambede, S. J. Darak, A. P. Vinod, and A. S.
Madhukumar Niharika Agrawal and Abhishek Ambede are joint first-
authors.Niharika Agrawal and S. J. Darak are with ECE Department, IIIT-Delhi,
India 110020, e-mail: {niharikaa<EMAIL_ADDRESS>Ambede and A. S.
Madhukumar are with SCSE, NTU, Singapore 639798, e-mail:
<EMAIL_ADDRESS><EMAIL_ADDRESS>P. Vinod is with EE
Department, IIT-Palakkad, India 678557, e-mail<EMAIL_ADDRESS>
###### Abstract

$L$-band Digital Aeronautical Communication System (LDACS) aims to exploit
vacant spectrum in $L$-band via spectrum sharing, and orthogonal frequency
division multiplexing (OFDM) is the currently accepted LDACS waveform.
Recently, various works dealing with improving the spectrum utilization of
LDACS via filtering/windowing are being explored. In this direction, we
propose an improved and low complexity reconfigurable filtered OFDM (LRef-
OFDM) based LDACS using novel interpolation and masking based multi-stage
digital filter. The proposed filter is designed to meet the stringent non-
uniform spectral attenuation requirements of LDACS standard. It offers
significantly lower complexity as well as higher transmission bandwidth than
state-of-the-art approaches. We also integrate the proposed filter in our end-
to-end LDACS testbed realized using Zynq System on Chip and analyze the
performance in the presence of $L$-band legacy user interference as well as
LDACS specific wireless channels. Via extensive experimental results, we
demonstrate the superiority of the proposed LRef-OFDM over OFDM and Filtered-
OFDM based LDACS in terms of power spectral density, bit error rate,
implementation complexity, and group delay parameters.

###### Index Terms:

Air-ground communication, filtered OFDM, LDACS, low complexity, spectrum
sharing, variable digital filter.

##  I Introduction

The global air traffic has increased tremendously over the past few decades
and numerous studies and statistical forecasts predict its rapid growth in the
future as well [1, 2]. The consequent massive growth in the air-ground
communication traffic has led to congestion in currently used very high
frequency (VHF) aeronautical communication band (118-137 MHz). To ensure
reliable communications with the desired quality-of-service and to support the
growing need of multimedia communications that demand high bandwidth (BW), a
new L-band (960-1164 MHz) Digital Aeronautical Communications System (LDACS)
[3] is under development. In this paper, we focus on the physical layer (PHY)
of LDACS.

The aeronautical $L$-band is already occupied by multiple legacy systems, most
prominently by the distance measuring equipment (DME), which operates in the
range 962–1213 MHz. LDACS is proposed to exploit the 1 MHz vacant band(s)
between adjacent DME users via inlay based spectrum sharing approach.
Orthogonal frequency division multiplexing (OFDM), is widely used in cellular
and WiFi standards, is the preferred choice for LDACS PHY waveform. However,
LDACS environment has always-ON legacy DME signals, and high out-of-band
attenuation (OOBA) of OFDM limits the transmission BW to only 498 kHz out of
the available 1 MHz spectrum (50% spectral utilization) [3]. In this
direction, we proposed filtered-OFDM (FOFDM) based LDACS to improve the OOBA,
thereby allowing higher transmission BWs of up to 732 kHz without compromising
on bit-error-rate (BER), and our frame structure is compatible with legacy
LDACS [11, 5].

In this paper, we focus on the complexity aspect of FOFDM based LDACS
transceivers especially for deployment on-board aircrafts, along with in-depth
performance analysis of end-to-end LDACS transceiver on heterogeneous Zynq
System on Chip (ZSoC) platform consisting of FPGA and ARM processor. As on-
board aircraft systems are battery-powered, reducing the LDACS PHY complexity
is an essential step towards extending the battery life. Specifically, we
propose a novel interpolation and masking based multi-stage digital finite
impulse response (FIR) filter that when integrated with LDACS transceiver, not
only meets the stringent non-uniform spectral attenuation requirements of
LDACS standard but also allows variable transmission BWs up to 732 kHz.
Compared to our previous works, we offer significant savings in the area
(12.78 % in DSP48 units) and power consumption (14.14 %) at the transceiver
level, along with more than 50% fewer multipliers over conventional single-
stage filtering approaches. Hereafter, the proposed solution is referred to as
low complexity reconfigurable filtered OFDM (LRef-OFDM) based LDACS. Various
LDACS transceivers are implemented on the ZSoC platform and integrated with
analog front-end (AFE) for experimental evaluation in the presence of LDACS
specific wireless signals and DME interference. Via extensive experimental
results, we demonstrate the superiority of the LRef-OFDM over OFDM and
Filtered-OFDM (FOFDM) based LDACS in terms of power spectral density (PSD),
BER, implementation complexity and group delay parameters for a wide range of
signal-to-noise ratios (SNRs) and word-lengths (WLs). We begin with the design
of the proposed filter in the next section.

Figure 1: Building blocks of the proposed LRef-OFDM based LDACS transceiver
along with end-to-end testbed.

##  II Proposed Filter Design

An end-to-end LRef-OFDM based LDACS transceiver is shown in Fig. 1, and it is
based on the standardized LDACS transceiver [3, 5] in terms of frame,
protocol, and building blocks. In this section, we focus on the design of the
low complexity BW-reconfigurable digital FIR filter in Fig. 1 and the aim is
to meet the OOBA specifications of LDACS standard for a wide range of
transmission BWs. Please refer to supplementary material in [11] and Section
III herein for design details of other baseband blocks of the transceiver and
the ZSoC testbed, respectively.

The proposed filter employs the interpolation operation [6, 7, 8] to reduce
the complexity. In this operation, if the coefficients of a lowpass prototype
filter are interpolated by a factor $M$, every unit delay in the filter is
replaced by $M$ delays. This results in a multi-band frequency response with
sub-bands located at even multiples of $\frac{\pi}{M}$, each having its
passband and transition BW $\frac{1}{M}$ times that of the prototype filter.
The interpolated frequency response can be given by:

$\vspace{-0.1cm}H_{Ip}(z)=\sum_{n=0}^{\frac{N}{2}-1}h_{n}[z^{-Mn}+z^{-M(N-n)}]+h_{\frac{N}{2}}z^{\frac{-Mn}{2}}\vspace{-0.1cm}$
(1)

where, $h_{0},h_{1}$ …$h_{\frac{N}{2}}$ are the unique filter coefficients of
an $N^{th}$ order FIR filter.

In proposed filter design approach, three sub-filters denoted as Filter I,
Filter II, and Filter III are cascadedand illustrative frequency responses are
shown in Fig. 2. If $H_{I}(z)$, $H_{II}(z)$, $H_{III}(z)$ denote the z-domain
representations of sub-filters, the resultant filter is given as,

$H(z)=H_{I}(z).H_{II}(z).H_{III}(z)$ (2)

The LDACS signal is over-sampled by a factor of four to assist in interference
reduction [3]. Therefore, as the standardized LDACS BW is approximately 500
kHz, the sampling frequency for our filter is chosen as 4 MHz. Fig. 2 shows
the frequency responses of three sub-filters designed for a transmission
bandwidth of 498 kHz on the frequency scale normalized with respect to Nyquist
frequency, i.e., half of sampling frequency. The sub-filter design is
explained below:

  1. 1.

Filter I: The stage I filter is designed with minimum order $(N=26)$
satisfying the stringent spectral mask, and has passband edge ($Fp_{1}$) as
$M(=4)$ times of the passband edge of the LDACS signal ($Fp_{s}$) based on its
transmission BW, i.e, $Fp_{1}=4*Fp_{s}$. Similarly the stopband edge
($Fs_{1}$) is $4*Fs_{s}$, where $Fs_{s}$ is the stopband edge of the LDACS
signal. As the most relaxed required attenuation level is adjacent to the
passband, this sub-filter is designed with the most relaxed attenuation
specification.The filter response for this stage I filter $H_{I}(z)$ is
obtained by substituting the value of I and N in (6),

$\vspace{-0.1cm}H_{I}(z)=\sum_{n=0}^{12}h_{n}[z^{-4n}+z^{-4(26-n)}]+h_{13}z^{-2n}\vspace{-0.1cm}$
(3)

  2. 2.

Filter II: This sub-filter removes the unwanted central subband from the
frequency response of interpolated Filter I. This filter is designed with
order $26$ having interpolation factor $(M)$ of 2, and the filter response
$H_{II}(z)$ can be expressed as,

$\vspace{-0.2cm}H_{II}(z)=\sum_{n=0}^{12}h_{n}[z^{-2n}+z^{-2(26-n)}]+h_{13}z^{-n}$
(4)

The passband and stopband edge frequencies of Filter II are based on the
resultant edge frequencies in the interpolated frequency response of Filter I
and can be represented as $Fp_{2}=\frac{F_{m}}{2}$ and $Fs_{2}=1-Fp_{2}$
respectively, where $F_{m}$ is a reference frequency whose value is chosen
based on the supported transmission BWs.

  3. 3.

Filter III: This sub-filter removes the unwanted highpass subband from the
cascaded frequency response of Filter I and Filter II, i.e.,
$H_{I}(z).H_{II}(z)$. It’s edge frequencies are based on the resultant edge
frequencies in the cascaded frequency response. The passband and stopband edge
frequencies for Filter III can be represented as $Fp_{3}=\frac{F_{m}}{4}$ and
$Fs_{3}=1-Fp_{3}$ respectively. It has the most relaxed transition BW and the
most stringent stopband attenuation specification among the three sub-filters.
The frequency response of this filter $H_{III}(z)$ can be represented as,

$H_{III}(z)=\sum_{n=0}^{6}h_{n}[z^{-n}+z^{-(14-n)}]+h_{7}z^{\frac{-n}{2}}\vspace{-0.1cm}$
(5)

Figure 2: Frequency responses of sub-filters $H_{I}(z)$, $H_{II}(z)$,
$H_{III}(z)$ and the resultant filter $H(z)$ for 498 kHz LDACS transmission
BW.

Here, we mainly focuses on the filter design, and the details regarding
complete transceiver in included in the appendix as supplementary material [9]

In [11, 5], we showed that LDACS can have additional bandwidths of 342 kHz,
654 kHz, 732 kHz by maintaining compatibility with the standardized frame
structure of 498 kHz. To realize a BW reconfigurable transceiver, we store the
unique filter coefficients corresponding to all four BWs in memory. We can
thus support different transmission BWs on the fly by just selecting
appropriate filter coefficients from memory at run-time. This would require a
memory component with storage capacity of 144 coefficients: 14*4 (Filter I
with order 26) + 14*4 (masking Filter II with order 26) + 8*4 (masking Filter
III with order 14). However, to reduce this requirement, we design and use the
same masking filters (Filter II and III) for all the BWs, and they are
designed as halfband FIR filters to minimize the number of distinct non-zero
coefficients. Based on the design of Filter I, a reference frequency $F_{m}$
is computed and the passband and stopband edge frequencies of Filter II and
Filter III are chosen based on $F_{m}$. The reference frequency $F_{m}$ is
selected based on the supported transmission BWs and is chosen to be the
stopband edge frequency of Filter I corresponding to the widest supported
transmission BW. As a result, we can use the same masking filters II and III
for all BWs and the total required memory storage capacity is just 67
coefficients: 14*4 (Filter I with order 26) + 7 (halfband masking Filter II
with order 26) + 4 (halfband masking Filter III with order 14). The overall
filter responses for all four transmission BWs satisfying the corresponding
LDACS spectral masks are shown in Fig. 3. Note that the standardized LDACS
spectral mask in [3] is considered for BWs 342 kHz and 498 kHz, and an
appropriately modified version is considered for other BWs.

(a)

(b)

(c)

(d)

Figure 3: Overall frequency response characteristics of the proposed filter
for the bandwidths: (a) 342 kHz (a) 498 kHz (a) 654 kHz (a) 732 kHz

It is empirically computed that among the different possible combinations of
interpolation factors [9], the lowest overall filter complexity (in terms of
total number of unique multipliers) is obtained using the interpolation
factors 4, 2, 1 respectively for the three sub-filters. The design parameters
of the three sub-filters for the different transmission BWs are listed in
Table I (normalized with respect to Nyquist frequency). Except for the
$Fp_{1}$ and $Fs_{1}$, which are set according to the transmission BW, all
other filter design specifications are identical for all the BWs. The
coefficients of the three sub-filters corresponding to the design parameters
listed in Table I are obtained using MATLAB.

TABLE I: Filter design specifications for different LDACS transmission BWs. Parameters | Filter I |  Filter II |  Filter III
---|---|---|---
342 kHz |  498 kHz |  654 kHz |  732 kHz
Order $(N)$ |  26 |  26 |  26 |  26 |  26 |  14
Passband Freq. |  0.3418 |  0.498 |  0.6543 |  0.7324 |  0.3975 |  0.1988
Stopband Freq. |  0.6724 |  0.6724 |  0.795 |  0.795 |  0.6025 |  0.8013
Attenuation (dB) |  -70.5 |  -37.9 |  -31.5 |  -14.5 |  -43.1 |  -81.8
Interpolation $M$ |  4 |  4 |  4 |  4 |  2 |  1

From Table I, Fig. 2, and Fig. 3, it can be noted that although the
attenuation specifications of the different sub-filters are relaxed, the
overall cascaded non-uniform frequency responses satisfy the stringent LDACS
spectral masks for each transmission BW. This idea of using sub-filters with
different relaxed attenuation specifications and thus, lower complexity is a
unique feature of this work.

Satisfying the stringent spectral mask specifications [10] should not come at
the cost of large delay and high implementation complexity that will also
affect the overall power consumption. To understand the filtering complexity,
we compare the multiplication complexity (total number of multiplier units)
and group delay of the proposed filter with the filters designed for 498 kHz
BW using various state-of-the-art approaches: 1) Parks-McClellan (PM)
algorithm [11, 11], 2) Least squares (LS) technique [11], 3) Traditional
interpolated FIR (IFIR) technique (wherein two sub-filters are cascaded with
only the first subject to interpolation) [6] and 4) Generalized IFIR technique
(wherein more than two sub-filters can be cascaded with multiple out of those
subject to interpolation) [12].

The total number of multipliers involved in the proposed filter is the sum of
the multipliers required to implement the three sub-filters. It can be noted
that while implementing the FIR sub-filters, the symmetry of their
coefficients can be exploited such that only half of the coefficients need to
be implemented, using the transposed direct-form FIR filter architecture [13].
Also, for halfband FIR filters (sub-filters II and III in our case), every
alternate coefficient is zero, and the central coefficient is always 0.5,
which can be implemented simply with a logical shift operation. Exploiting
these properties, sub-filters I, II, and III in the proposed LRef-OFDM based
LDACS can be implemented using 14, 7, and 4 multipliers respectively and the
total number of multipliers required is thus 25. As the three sub-filters are
cascaded, the group delay of the proposed filter is the sum of the group
delays of sub-filters I, II, and III. The total group delay of the proposed
filter is thus (13x4) + (13x2) + (7x1) = 85 samples. In units of time, this
corresponds to 21.25 $\mu$s as the sampling frequency is 4 MHz. The total
number of required multipliers and group delays are similarly calculated for
different state-of-the-art filters that can be used in the FOFDM based LDACS,
and the comparative analysis is presented in the Table II.

TABLE II: Complexity and Group Delay Comparison Filters based on |  Number of Multipliers | Group Delay
---|---|---
In samples |  In $\mu$s
PM algorithm [11, 11] |  101 |  100 |  25
LS technique [11] |  75 |  74 |  18.5
Traditional IFIR [6] |  46 |  110.5 |  27.625
Generalized IFIR [12] |  38 |  131 |  32.75
| Proposed Filter
---
25 |  85 |  21.25

We can observe from Table II, that the proposed filter offers 75.25%, 45.65%,
34.21% and 66.67% reductions in multiplication complexity and 15%, 23.08%,
35.11% lower and 14.87% higher group delay when compared to the filters
designed using the PM algorithm, traditional IFIR technique, generalized IFIR
technique, and LS technique respectively.

A detailed comparison analysis of end-to-end LDACS transceivers in terms of
PSD, BER, and hardware resource utilization is presented in the next section.

##  III Performance Analysis on ZSoC Testbed

For performance analysis, the proposed filter is integrated with our end-to-
end LDACS transceiver realized on the Xilinx Zynq ZSoC ZC706 platform, and the
sample rate is set to 4 MHz. This is accomplished using MATLAB HDL Coder and
Verifier Toolboxes. Please refer to [11] for additional implementation
details. Next, the transceiver is integrated with RF front-end for performance
analysis in the real-radio environment. The RF front-end is designed using
building blocks of the MATLAB RF Toolbox. At the transmitter, RF front-end
consists of digital up-converter, analog filtering, power amplifier, followed
by the RF transmission. The transmission frequency can be set to anywhere in
the $L$-band (960-1164 MHz) and it is set to 985 MHZ for the results discussed
here. At the receiver, we need low-noise amplifier, analog filtering, and
digital down-converter to get the desired baseband signal. Since RF front-end
introduces phase noise, additional pilot reference signal based phase
correction is added. The output of the phase correction block is passed to the
proposed filter followed by baseband signal processing, as shown in Fig. 1.

###  III-A Power Spectral Density (PSD) Comparison

In Fig. 4, we present the PSD comparison of OFDM, FOFDM, and LRef-OFDM based
LDACS transceivers implemented using 16 bit WL. The LRef-OFDM and FOFDM based
LDACS offer higher OOBA than standardized OFDM based LDACS. Higher OOBA leads
to lower interference to legacy DME signals as well as enables wider
transmission BW of up to 732 kHz compared to only 498 kHz in existing LDACS.
This results in around 50% improvement in the spectrum utilization.

(a)

(b)

Figure 4: The PSD comparison of various waveforms for two different signal
BWs, (a) 732 kHz, and (b) 498 kHz and three different channels.

Next, we study the effect of WL on the PSD. To understand the impact of
varying WL settings for the filter as well as the complete transceiver, we
consider two scenarios: (1) Proposed filter with WL of {8,16,32} bits and rest
of the transceiver blocks with WL of 16 bits, and (2) Complete transceiver
with the WL of {8,16,32} bits. Due to space constraints and to avoid
repetitive results, we consider only LRef-OFDM based LDACS in Fig. 5a and Fig.
5b. In both scenarios, it can be observed that the PSD is almost identical for
WL of 16 and 32 bits. However, the PSD degrades substantially when the WL of
the entire transceiver is reduced to 8 bits, as shown in Fig. 5b. The
interpretation of these results can be stated as the LRef-OFDM based LDACS
system can even be implemented with lower filter WL to meet the application-
specific complexity constraints. Similar results are also observed for FOFDM
based LDACS, while the OFDM based LDACS needs minimum WL of 16 bits for a
complete transceiver.

(a)

(b)

Figure 5: PSD comparison of different WLs in LRef-OFDM based LDACS. Note: TR
and F in the legends refer to transceiver and filter respectively.

###  III-B Bit Error Rate (BER) Comparison

Next, we analyze the BER performance in the presence of three LDACS specific
wireless channels: enrouting (ENR), airport/taxi (APT), and terminal
maneuvering area (TMA). Compared to simulation-based BER discussed in
literature [5], our analysis considers the effect of interference from legacy
DME signals, impairments due to RF front-end, and different WLs. The BER
analysis is done for two different signals BWs, 732 kHz and 498 kHz, and
corresponding plots are shown in Fig. 6a and Fig. 6b respectively. It can be
observed that LRef-OFDM based LDACS does not have any significant degradation
in BER when compared with FOFDM based LDACS as both employ filtering to
improve OOBA and to reduce the interference from DME. The errors due to RF
front-end are mitigated via a phase correction block. As expected, BER of OFDM
based LDACS suffers due to severe interference from DME, and its transmission
BW has thus been limited to 498 kHz by the standardization committee.

(a)

(b)

Figure 6: The BER comparison of transceivers for three different LDACS
channels and two different signal BWs, (a) 732 kHz, and (b) 498 kHz.

In Fig. 7, we study the effect of WL on the BER performance of the LDACS
transceiver. Similar to the PSD analysis, we consider two scenarios. With the
decrease in WL of the filter and transceiver, the BER degrades. It can be
observed that the WL of 8-bit may not be a good choice for the transceiver.
However, we can have 16-bit transceiver with 8-bit filter, which also offers
desired PSD performance. A similar analysis can be performed for each
transceiver block, thereby reducing the complexity significantly without
compromising on the BER and PSD. Thus, experimental BER analysis on ZSoC
offers insights on the performance in real radio environment, which is
otherwise not possible in simulation-based analysis.

Figure 7: The BER comparison of various LDACS transceiver implementations for
different fixed-point word lengths

The LRef-OFDM based LDACS thus offers better PSD and BER performance than
standardized OFDM based LDACS. It provides higher spectrum utilization due to
wider transmission BW, and support for various BWs can enable LDACS to offer
multiple services ranging from text, audio, to multimedia. When compared to
FOFDM based LDACS, proposed LRef-OFDM based LDACS offers identical
performance. Next, we compare the complexity of the LDACS transceivers.

###  III-C Resource Utilization and Power Consumption Comparison

In this subsection, we compare the resource utilization and power consumption
of the proposed filter and the PM approach based filter implemented on the
ZC706. We also compare the same for one variant of the OFDM, FOFDM, and LRef-
OFDM based LDACS transceiver. For a detailed comparison of all the nine
transceiver configurations one can refer to [9]. The resource utilization
comparison is presented in the Table III. We can observe from the Table III
that the proposed filter utilizes fewer resources than the PM based filter of
WL 16 bit, and hence the proposed LRef-OFDM based LDACS transceiver has lower
area requirement than FOFDM based LDACS transceiver. Also, as expected, the
OFDM based LDACS transceiver shows the least resource utilization due to lack
of an extra filtering module.

TABLE III: Resource Utilization Comparison on ZC706 LDACS Transceiver Type | Resources utilized
---|---
| No. of
---
Flip - Flops
| No. of
---
DSP48
| No. of LUT
---
as memory
| No. of LUT
---
as logic
PM filter |  | 10100
---
(2.31 %)
| 296
---
(32.89 %)
| 64
---
(0.09 %)
| 5350
---
(2.45 %)
Proposed filter |  | 8921
---
(2.04 %)
| 181
---
(20.11 %)
| 50
---
(0.073 %)
| 4114
---
(1.89 %)
| OFDM based
---
LDACS transceiver
| 39501
---
(9.03 %)
| 570
---
(63.33 %)
| 994
---
(1.35 %)
| 37541
---
(17.23 %)
| FOFDM based
---
LDACS transceiver
| 47653
---
(10.89 %)
| 812
---
(90.22 %)
| 1021
---
(1.44 %)
| 43439
---
(19.93 %)
| LRef-OFDM based
---
LDACS transceiver
| 46394
---
(9.82 %)
| 697
---
(77.44 %)
| 1009
---
(1.42 %)
| 41552
---
(19.07 %)

We also compare the dynamic power and critical path delay for all the
transceivers. Though, LRef-OFDM based LDACS (0.437 W) consumes 30.43% more
power than OFDM based LDACS (0.304 W), it consumes 14.14 % less power than
FOFDM based LDACS (0.509 W) due to proposed filter design. Also, the critical
path delay of the LRef-OFDM based LDACS is 12.1 ns compared to the 12.5 ns for
FOFDM based LDACS, which means that the throughput of the LRef-OFDM is higher
than FOFDM. Additionally, we compare the complexity for different WLs of OFDM
and Ref-OFDM based LDACS transceiver in Table. IV. We observed that resource
utilization and power consumption increases with the increase in the WL. To
summarize, LRef-OFDM based LDACS offers better OOBA and BER performance, along
with lower implementation complexity and power consumption. This makes it an
attractive alternative to the existing OFDM based LDACS for future air-ground
communications.

TABLE IV: Resource Utilization Comparison for Transceiver’s different Word Lengths on ZSoC ZC706 Resources Utilized | OFDM LDACS | LRef-OFDM LDACS
---|---|---
8-bit WL | 32-bit WL | 8-bit WL | 32-bit WL
| No. of
---
Flip-Flops
| 33514
---
(7.66 %)
| 51254
---
(11.72 %)
| 38421
---
(8.79 %)
| 58624
---
(13.40 %)
| No. of LUT
---
as logic
| 31421
---
(14.42 %)
| 47264
---
(21.69 %)
| 36283
---
(16.65 %)
| 53234
---
(24.43 %)

##  IV Conclusion

In this paper, we presented LRef-OFDM based LDACS using low complexity
reconfigurable filter design approach. With extensive experimental results on
hardware testbed, we validated its superiority over OFDM based LDACS in terms
of PSD and BER along with tunable bandwidth. It also offers a lower area and
power complexity than FOFDM based LDACS. Proposed work considers in-depth
experimental analysis via different world lengths, RF impairments, and LDACS
channel compared to existing simulation-based studies.

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## Appendix

In this appendix, firstly we will give an idea about some recent state of the
art filters mainly based on interpolation method. Then we provide the design
details for the proposed low complexity reconfigurable filter followed by the
mathematical analysis for the proposed LRef-OFDM based LDACS transceiver. In
the end we also present some additional resource and power utilization results
for various transceiver configurations based on PS/PL boundary.

## Literature Review

Numerous filter design approaches employing the interpolation technique have
been proposed to obtain low complexity FIR filters. For example, a
computationally efficient digital filter based on interpolation and frequency-
response-masking (FRM) technique is presented in [1]. In this paper, the
designed filter is optimized in minimax sense by jointly optimizing the
subfilters involved using a convex-concave procedure (CCP). Authors also
extend the work to the design of FRM filters that simultaneously promotes
sparsity of the filter coefficients to reduce implementation complexity.

Similarly, interpolation based narrow-band sparse FIR filters and
centrosymmetric bandpass filters are designed in [2]. The design method is
realized by cascading a model filter with a sparse masking filter. In this
technique, the model filter is first designed and then interpolated to
generate the desired impulse response replica. A sparse masking filter is used
to mask the extra unwanted passbands.

A low complexity 17-band non-uniform IFIR filter bank for digital hearing aid
applications is designed in [4]. In this filter, different levels of
interpolations are done on these filters, to create various bands.

The filtered OFDM can be applied in several other communication environments
suitable for next generation wireless communication system. Such as, to
achieve better spectrum leakage performance in 5G wireless communication,
authors in [6] have proposed a Nuttall’s Blackman-Harris windowed F-OFDM
system, and analyzes the performance of different window functions in the
F-OFDM. They have also compared the proposed filter’s performance with the
hamming windowed filter and claims to achieve better PSD and BER performance
with the proposed filter.

Similarly, a winnowed sync filter for filtered OFDM to reduce the out-of-band
emission is discussed in [7]. Authors have proposed an optimal filter choice
by analysing the system performance by employing six windowing functions such
as: Hann, Hamming, Kaiser, Barlett, Blackman, Flat-top. They further study the
performance of a two-user uplink scenario where the two uplink users pass the
respective OFDM modulated data through time domain filters of appropriate
bandwidths. According to the author’s analysis Kaiser Window gives the best
performance in terms of BER and OOB reduction.

Further, a novel resource block (RB) filtered OFDM (RBF-OFDM) is proposed in
[8], that segregates the entire available spectrum into different blocks (RBs)
and filters individual signal transmitted on each block. The performance of RB
F-OFDM is similar to filtered OFDM with the additional support for non-
contiguous spectrum under channels with moderate delay spread and adjacent
channel interference (ACI).

An interpolated band-pass method (IBM) based narrow-band finite impulse
response (FIR) filter for 5G cellular network is proposed in [9]. The proposed
filter consists of different sub-filters such as prototype filter,
$H_{a}(e^{j\omega})$, complementary prototype filter $H_{c}(e^{j\omega})$. The
approach considers a band-pass filter (BPF), $H_{bp}(e^{j\omega})$ placed in
between prototype and complementary prototype filter pair. Authors in this
paper claims that the proposed IBM based narrow-band filter accomplishes
shorter out-of-band emission (OOBE) without affecting the BER performance
while compared to the other narrow-band filters.

Authors in paper [10], proposed filters constructed by filter banks to
transmit and receive F-OFDM signals to adapt the flexible numerology of 5G
communication. The proposed filter bank supports multiple sub-bands and
consists an analysis filter bank (AFB) and a synthesis filter bank (SFB). Each
filter bank is composed of a set of modulated filters. Further the sub-band
filters are implemented by using the poly-phase structure to reduce the
computational complexity.

Next, we present the design details of the proposed low complexity
reconfigurable filter.

## Low Complexity Reconfigurable Filter Design

The proposed filter is a interpolation based multi-stage filter. The type and
parameters of every stage of the proposed filters is designed to shape the
transmission spectrum so as it meets the stringent LDACS spectral mask, BER
and PSD requirements. At the same time, overall filter complexity (in terms of
total number of unique multipliers) and group delay should be as small as
possible.

In an interpolation based multi-stage filter design approach like the one
followed in our work, three parameters are interlinked – (1) number of
cascaded filter stages, (2) interpolation factors for every filter stage, and
(3) the prototype filter orders for every filter stage. The overall filter
complexity (in terms of total number of unique multipliers) of a multi-stage
filter is dependent on the number of stages and interpolation factor for each
stage. The interdependence between these parameters can be described as –

  * •

If number of cascaded filter stages is kept fixed, then choosing a higher
interpolation factor for the first stage filter (thus lower order and lesser
multipliers for corresponding prototype filter) results in the requirement of
higher order masking filters for the subsequent stages (due to more stringent
masking requirements to remove the unwanted subbands that are more in number
and closer together). Conversely, choosing a lower interpolation factor for
the first stage filter can help to lower the filter order for the subsequent
stages’ masking filters (due to relatively relaxed masking requirements to
remove the unwanted subbands that are lesser in number and farther away), but
this choice requires a relatively higher filter order and thus more
multipliers for the prototype filter in the first stage itself. The overall
filter complexity in terms of the total required number of multipliers thus
needs to be minimized by considering the full set of interpolation factors in
all the stages appropriately.

  * •

In the LDACS scenario, the spectrum mask mandates varying attenuation levels
for different frequencies wherein highest attenuation levels are required
furthest away from the LDACS signal. In our design approach, we use three
cascaded filter stages so that we can achieve the different attenuation levels
using aggregation of attenuations provided by the individual filters. This
helps to keep the filter orders (and thus required number of multipliers) low
in every stage while ensuring that the overall filter frequency response
satisfies the LDACS spectral mask requirements.

  * •

Meanwhile, when deciding the interpolation factors, it is to be noted that the
maximum interpolation factor $I_{max}$ that can be chosen for a filter stage
with final desired normalized stopband edge frequency Fstop of the desired
subband in the interpolated frequency response is given by
$I_{max}=\left\lfloor\frac{1}{F_{stop}}\right\rfloor$. This upper limit
ensures that the prototype filter design corresponding to the chosen
interpolation factor for that stage is feasible, i.e., stopband edge frequency
specification of the protype filter is less than 1. In our filter design, the
maximum possible interpolation factor for the first stage filter is obtained
as 4 by considering the frequency edge specifications corresponding to the
widest supported LDACS signal bandwidth, i.e., 732 kHz.

By considering the above points in our work, we concluded to design a three
stage filter with interpolation factors 4, 2, 1 having the filter order as 26,
26, 14 provides the lowest overall filter complexity.

To explain further using a specific example, table provides a comparison of
few of the possible multi-stage filter designs for our variable bandwidth
LDACS system. It can be noted how the lowest overall filter complexity in
terms of total number of multipliers required is achieved by Option 4 which is
our final choice of design discussed in the paper. Note that the LDACS
spectrum mask mentioned in LDACS standard provides the desired attenuation
levels for various values of frequency difference with respect to carrier
frequency. Since the spectrum mask only provides numerical values without any
mathematical model, interpolation factors, number of stages and filter order
are selected empirically to meet the desired attenuation constraints and
minimize the computational complexity.

Option |  | Number of
---
stages
| Interpolation
---
factor for
each stage
| Filter
---
order for
every stage
| Type of
---
filters in
every stage
| Overall filter
---
order
| Total number of
---
unique multipliers
required for
implementation
1 | 2 | {4, 1} | {26, 50} | {FIR, FIR} | (26x4) + 50 = 154 | 14+26 = 40
2 | 2 | {3, 1} | {44, 24} | {FIR, FIR} | (44x3) + 24 = 156 | 23+13 = 36
3 | 2 | {2, 1} | {104, 14} | {FIR, FIR halfband} | (104x2) + 14 = 222 | 53+4 = 57
| 4
---
(Final)
3 | {4, 2, 1} | {26, 26, 14} |  | {FIR, FIR halfband,
---
FIR halfband}
| (26x4) + (26x2)
---
\+ 14 = 170
14+7+4 = 25

The interpolated frequency response can be given by:

$H_{Ip}(z)=\sum_{n=0}^{\frac{N}{2}-1}h_{n}[z^{-Mn}+z^{-M(N-n)}]+h_{\frac{N}{2}}z^{\frac{-Mn}{2}}$
(6)

where, $M$ is the interpolation factor, $N$ is the filter order, $h_{0},h_{1}$
…$h_{\frac{N}{2}}$ are the unique filter coefficients of an $N^{th}$ order FIR
filter.

The lowpass prototype filter I (stage 1) are interpolated by a factor 4 and
has the passband edge ($Fp_{1}$) as four times that of the passband edge of
the signal ($Fp_{s}$) to be filtered $Fp_{1}=4*Fp_{s}$. Similarly, the
stopband edge ($Fs_{1}$) of Filter I is selected as $4*Fs_{s}$ (stopband edge
of the signal to be filtered). The interpolated multi-band frequency response
is shown in Fig. 8 (a) and can be given by:

$H_{I}(z)=\sum_{n=0}^{12}h_{n}[z^{-4n}+z^{-4(26-n)}]+h_{13}z^{-2n}$ (7)

The Filter II (stage II) and III (stage III) are used as masking filters to
remove the unwanted subbands and are designed by employing interpolation
factor 2 and 1 (interpolation factor 1 signifies no interpolation operation)
respectively. Based on the design of Filter I, a reference frequency ($F_{m}$)
is computed and the passband and stopband edge frequencies of Filter II and
Filter III are chosen based on $F_{m}$. The reference frequency $F_{m}$ is
selected based on the supported transmission BWs and is chosen to be the
stopband edge frequency of Filter I corresponding to the widest supported
transmission BW. Once this reference frequency is selected, we define the
passband edge frequency for Filter II and Filter III as
$Fp_{2}=\frac{F_{m}}{2}$ and $Fp_{3}=\frac{F_{m}}{4}$ respectively.
Furthermore, to obtain both these masking filters as halfband filters, the
stopband edge frequency is chosen as $Fs_{2}=1-Fp_{2}$ and $Fs_{3}=1-Fp_{3}$
for Filter II and Filter III respectively and the frequency responses
($H_{II}(z),H_{III}(z)$) are illustrated in Fig. 8 (b) and (d) respectively
and can be represented as :

$H_{II}(z)=\sum_{n=0}^{12}h_{n}[z^{-2n}+z^{-2(26-n)}]+h_{13}z^{-n}$ (8)

$H_{III}(z)=\sum_{n=0}^{6}h_{n}[z^{-n}+z^{-(14-n)}]+h_{7}z^{\frac{-n}{2}}$ (9)

The output of the stage II filter $H_{I}(z).H_{II}(z)$ is shown in Fig. 8 (c).

Figure 8: Frequency response of (a) first stage filter (b) second-stage filter
(c) output of second stage filter ($H_{I}(z).H_{II}(z)$) (d) third stage
filter (e) Output of third stage filter ($H_{I}(z).H_{II}(z).H_{III}(z)$)

Furthermore, the masking filter stage of the proposed approach are fixed and
independent of the transmission bandwidth. This is done by considering the
worst-case passband edge and stopband edge specifications of the masking
filters (Filter II and III). The text in Section II on page 2 explaining the
sub-filter design has been updated in the reviewed manuscript accordingly.

To support above explanation, we have included Fig. 9 which shows the
frequency response for the different transmission bandwidths : 342 kHz, 498
kHz, 654 kHz, 732 kHz. The multi-band frequency response for filter I
(interpolated by 4) and filter II (interpolated by 2) is shown in Fig. 9 (a)
and (b) respectively. Fig. 9 (c) shows the output obtained at the stage II by
cascading the Filter I ($H_{I}(z)$) and Filter II ($H_{II}(z)$). The output of
the stage II filter is then cascaded with the stage III filter (as shown in
Fig. 9 (d)) to obtain the resultant filter as shown in Fig. 9 (e).

Figure 9: Variable BW frequency response of (a) first stage filter (b) second-
stage filter (c) cascaded output of second stage filter ($H_{I}(z).H_{II}(z)$)
(d) third stage filter (e) cascaded output of third stage filter
($H_{I}(z).H_{II}(z).H_{III}(z)$)

Next, we present the mathematical model for the proposed LRef-OFDM based LDACS
transceiver.

## Mathematical illustration for LRef-OFDM based LDACS transceiver

###  IV-A LRef-OFDM based LDACS Transmitter

A brief analysis for the transmitter is given as follows: The discrete time
domain OFDM signal corresponding to the kth subcarrier can be given as

$x[n]=\frac{1}{K}\sum\limits_{k=0}^{K-1}X_{k}e^{\frac{j2\pi kn}{K}}$ (10)

where, $K$ is the IFFT size, $n$ is the discrete time index and $X_{k}$ is
frequency domain response of the transmitted signal at the $k^{th}$ sub-
carrier. It is given by

$X_{k}=\sum\limits_{n=0}^{K-1}x[n]e^{\frac{-j2\pi kn}{K}}$ (11)

The transmitted signal $x^{\prime}[n]$ is the convolution ($\ast$) of $x[n]$
and the filter $h[n]$ and can be expressed as,

$x^{\prime}[n]=h[n]\ast x[n]$ (12)

The transmitted signal then passes through the LDACS wireless channel with
impulse response $c^{L}[n]$, and a DME interference signal passes through the
LDACS wireless channel with impulse response $c^{D}[n]$.

###  IV-B LRef-OFDM based LDACS Receiver

The signal received at the input of the receiver r[n] can be expressed as,

$r[n]=c^{L}[n]\ast x^{\prime}[n]+c^{D}[n]\ast s[n]+\tilde{n_{0}}[n]$ (13)

where, $x^{\prime}[n]$ is the transmitted signal, $s[n]$ is the DME signal,
and $\tilde{n_{0}}[n]$ is the zero-mean additive white Gaussian noise.

In LDACS environment, both channels $c^{L}[n]$ and $c^{D}[n]$ assumed to have
identical statistics such that

$c^{L}[n]=\sum_{l=1}^{L}c^{L}_{l}\delta[n-l]~{}and~{}c^{D}[n]=\sum_{l=1}^{L}c^{D}_{l}\delta[n-l]$
(14)

Where $L$ is the total number of channel taps, $c^{L}_{l}$ and $c^{D}_{l}$ are
the impulse responses of the channel faced by LDACS and DME signal of the
$l^{th}$ path, respectively. The channels are assumed to be time-invariant for
each transmitted OFDM symbol.

$r^{\prime}[n]=h[n]\ast c^{L}[n]\ast h[n]\ast x[n]+c[n]\ast c^{D}[n]\ast
s[n]+c[n]\ast\tilde{n_{0}}[n]$ (15)

After doing FFT, the received signal $r^{\prime}[n]$ is converted into the
frequency domain and can be represented as $R^{\prime}_{k}$ at $k^{th}$
subcarrier:

$R^{\prime}_{k}=H_{k}C_{k}H_{k}X_{k}+H_{k}C_{d_{k}}S_{k}+H_{k}\tilde{N_{0}}{k}$
(16)

where, $C_{k}$ , $C_{d_{k}}$ are the LDACS and DME channel frequency responses
at the $k^{th}$ subcarrier respectively can be given as

$C_{k}=\sum_{l=1}^{L}c^{L}_{l}e^{\frac{-j2\pi
kl}{N}}~{}and~{}C_{d_{k}}=\sum_{l=1}^{L}c^{D}_{l}e^{\frac{-j2\pi kl}{N}}$ (17)

we obtain $H_{k}$ by taking K-point FFT of the zero padded filter impulse
response where

$H_{k}=W^{H}.[h[n]]$ (18)

Here, $W$ is the $K$-point FFT matrix.

The impulse response of the proposed filter $h[n]$ can be calculated by taking
Inverse ZT of the resultant cascaded filter $H(z)$.

$h[n]=\text{\ooalign{\raisebox{1.03331pt}{--}\cr$Z$\cr}}^{-1}[H(z)]$ (19)

where, the proposed LRef filter response $H(z)$ can be given as,

$H(z)=H_{I}(z).H_{II}(z).H_{III}(z)$ (20)

$H_{I}(z),H_{II}(z),H_{III}(z)$ are as given in eq. 7, 8, 9

We finally realize the BER performance of the $k^{th}$ received symbol for
M-QAM can be expressed as,

$P_{e_{MQAM}}^{\lambda,\lambda_{d}}(k)\cong\frac{4}{log_{2}M}\left(1-\frac{1}{\sqrt{M}}\right)\sum_{i=1}^{\sqrt{M}/2}Q(2i-1)\times\sqrt{\frac{3log_{2}MH_{k}^{2}\lambda_{k}P}{\left(M-1\right)\left(P_{\tilde{N_{0}}}+\lambda_{d_{k}}P_{DME}\right)}}$
(21)

where $P$ is the transmitted signal power, $P_{DME}$ is the DME signal power.
A detailed derivation for $P_{DME}$ is given in [5]. erfc(.) is a complex
error function, therefore, BER averaged across the fading channel can be
expressed as,

$P_{e_{MQAM}}(k)=E[P_{e_{MQAM}}^{\lambda,\lambda_{d}}(k)]\cong\int_{0}^{\infty}\int_{0}^{\infty}P_{e_{MQAM}}^{\lambda_{1},\lambda_{2}}(k)~{}\times
p_{\lambda}(\lambda)d\lambda~{}p_{\lambda_{d}}(\lambda_{d})d\lambda_{d}$

The average BER across all the subcarriers is given by

$P_{e_{MQAM}}=\frac{1}{K}\sum_{k=0}^{K-1}P_{e_{MQAM}}(k)$ (22)

Next, we present the additional results comparing various transceiver
configurations corresponding to different boundary between PS and PL.

## Experimental Results: Resource Utilization and Power Consumption Comparison

Here, we present the resource utilization and power consumption results for
the nine different configurations implemented via hardware software co-design
approach [11]. The comparison is done for OFDM, FOFDM (PM based filtered
OFDM), and the proposed LRef-OFDM based LDACS transceivers. Here, we consider
16 bit word length and the highest bandwidth possible 732 kHz for the
comparison. All results are obtained after realizing the transceiver on ZC706
from Xilinx. Since V1 configuration is realized completely in PS, PL resource
utilization results are omitted. In V2, FOFDM and LRef-OFDM resource
utilization is due to the filtering block realized in PL. Later, one by one
block is transferred to the PL in the subsequent configurations.

We can observe from the Table V that the proposed LRef-OFDM based LDACS
transceiver has lower area and power requirement than FOFDM based LDACS
transceiver. Also, as expected, the OFDM based LDACS transceiver shows the
least resource utilization and dynamic power due to lack of an extra filtering
module.

TABLE V: Resource Utilization and Power Consumption of Transceiver on ZSoC Parameter |  Waveform |  V2 |  V3 |  V4 |  V5 |  V6 |  V7 |  V8 |  V9
---|---|---|---|---|---|---|---|---|---
No. of Flip-Flops |  OFDM |  N/A |  14851 (3.39%) |  31891 (7.29%) |  32385 (7.41%) |  32981 (7.54%) |  34351 (7.86%) |  38127 (8.72%) |  39501 (9.03%)
|  FOFDM |  10100 (2.31%) |  30124 (6.89%) |  37912 (8.67%) |  40174 (9.19%) |  40927 (9.36%) |  42129 (9.63%) |  44852 (10.26%) |  47653 (10.89%)
|  LRef-OFDM |  8921 (2.04%) |  27521 (6.29%) |  33874 (7.75%) |  36981 (8.46%) |  38121 (8.72%) |  39984 (9.15%) |  42191 (9.65%) |  46394 (10.61%)
No. of DSP48 |  OFDM |  N/A |  534 (59.33%) |  570 (63.33%) |  570 (63.33%) |  570 (63.33%) |  570 (63.33%) |  570 (63.33%) |  570 (63.33)
|  FOFDM |  296 (32.89%) |  785 (87.22%) |  812 (90.22%) |  812 (90.22%) |  812 (90.22%) |  812 (90.22%) |  812 (90.22%) |  812 (90.22%)
|  LRef-OFDM |  181 (20.11) |  668 (74.22%) |  697 (77.44%) |  697 (77.44%) |  697 (77.44%) |  697 (77.44%) |  697 (77.44%) |  697 (77.44%)
No. of LUT as Memory |  OFDM |  N/A |  396 (0.56%) |  865 (1.23%) |  881 (1.25%) |  918 (1.30%) |  922 (1.31%) |  941 (1.34%) |  994 (1.35%)
|  FOFDM |  64 (0.09%) |  411 (0.583%) |  894 (1.27%) |  913 (1.29%) |  936 (1.32%) |  943 (1.34%) |  964 (1.37%) |  1021 (1.44%)
|  LRef-OFDM |  50 (0.073%) |  392 (0.55%) |  871 (1.23%) |  898 (1.26%) |  913 (1.28%) |  931 (1.31%) |  946 (1.33%) |  1009 (1.42%)
No. of LUT as Logic |  OFDM |  N/A |  23124 (10.58%) |  32185 (14.72%) |  32912 (15.06 %) |  33842 (15.48%) |  34251 (15.67%) |  35921 (16.43%) |  37541 (17.23%)
|  FOFDM |  5350 (2.45%) |  26571 (12.16%) |  33125 (15.15%) |  34981 (16.01%) |  36521 (16.71%) |  37852 (17.32%) |  41146 (18.82%) |  43439 (19.07%)
|  LRef-OFDM |  4114 (1.89%) |  25124 (11.49%) |  32742 (14.98%) |  33521 (15.33%) |  35215 (16.11%) |  36259 (16.59 %) |  40212 (18.55%) |  41552 (19.07%)
No. of |  OFDM |  N/A |  35 |  683 |  745 |  1144 |  1217 |  1882 |  1930
MUXes |  FOFDM |  25 |  57 |  835 |  1152 |  1401 |  1523 |  1985 |  2102
|  LRef-OFDM |  19 |  47 |  742 |  951 |  1261 |  1394 |  1885 |  2041
Dynamic |  OFDM |  N/A |  0.045 |  0.285 |  0.295 |  0.297 |  0.299 |  0.301 |  0.304
Power |  FOFDM |  0.112 |  0.205 |  0.434 |  0.493 |  0.494 |  0.496 |  0.500 |  0.509
in Watt |  LRef-OFDM |  0.072 |  0.134 |  0.375 |  0.401 |  0.421 |  0.429 |  0.434 |  0.437

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