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ArticlesA Flexible Multiband Multicarrier Signal Design for Broadband Channel Sounding Applications
• Asif Iqbal1,*, Micheal Drieberg1, Varun Jeoti2, Azrina Binti Abd Aziz1, Goran M. Stojanović2, Mitar Simić2, and Nazabat Hussain3

Human-centric Computing and Information Sciences volume 12, Article number: 19 (2022)
https://doi.org/10.22967/HCIS.2022.12.019

Abstract

Radio frequency radars have garnered considerable attention in contactless sensing. The congestion in frequency bands and ultra-wideband (UWB) sensing requirements pose challenges to the design of the radars. RF radars can be alternatively considered as channel sounders, which too are facing new channel characterization and modeling challenges owing to new frequency bands in 5th generation (5G) and 6th generation (6G) cellular networks. Various sounding systems were developed to meet the frequency and system bandwidth requirements. However, most offer limited system bandwidth and cannot be easily tuned for different applications. This work aims to address these challenges, by providing a new multiband multicarrier architecture and flexible signal design for channel sounding. Firstly, a channel sounder architecture is developed using commercial software-defined radios (SDRs). Secondly, a new phase-modulated multiband orthogonal frequency division multiplexing (MB-OFDM) waveform, which is designed to provide a flexible frame structure with a low peak-to-average power ratio (PAPR), is proposed to optimize the pulse repetition period for the sounding system by maintaining all the valuable properties of OFDM. The overall system is implemented in a simulated environment, and the results show an improved PAPR performance of the MB-OFDM signal design. In addition, the overall system is tested for different channel conditions and validated against theoretical data. The numerical experiments show that the proposed system is a viable option for UWB channel sounding for a wide range of applications.

Keywords

Radars Sensing, Passive Sensing, Channel Sounder, PAPR, Channel Impulse Response, Channel Characteristics, 5G/6G, OFDM, MB-OFDM

Introduction

Radar sensing has already proved its usefulness and significance in defense applications. Recently, radar sensing has been prominently showcased in various domains, such as passive sensing, healthcare, and autonomous vehicles [1, 2]. Contactless sensing of various parameters makes radars an alternative to direct sensing technologies [3]. Lately, transduction-based electromagnetic sensors have been introduced for remote sensing [46]. In the same way, the backscattering radar principle is used for passive radio frequency identification (RFID) localization and battery-free surface acoustic wave (SAW) based sensors [7, 8]. The emerging application of battery-free passive sensors is posing new challenges in combating frequency congestion problems. In addition, the demand for new frequency bands is increasing to meet future consumer and industry needs. The envisioned 5G and 6G of cellular networks are focused on enhanced mobile broadband, massive machine-type communication, and ultra-reliable and low latency communications. The 5G network utilizes new frequency spectrums below 60 GHz, while 6G targets to use frequency bands beyond 95 GHz [9, 10], with below 6 GHz having well-understood propagation conditions. However, the propagation behavior of radio waves in new frequency bands needs more study. Generally, each frequency band behaves very differently in a similar propagation environment. Especially in the millimeter wave (mm-Wave) domain, the attenuation factor is very dominant due to oxygen, humidity, and rain. An extensive channel measurement data is required to develop a channel model, and these channel models are then used to design robust modulation schemes for a reliable communication system.
Primarily, radio frequency radar interrogators for passive sensing and channel sounders are similar, and both of them output a channel impulse response (CIR) at the receiver. In brief, sounding the channel with radio signals, acquiring knowledge of propagation phenomenon in specific channels, extraction of model parameters from measurement data, and channel model development are a few of the main objectives of channel sounding. The developed channel models are then used to design and test reliable communication systems. In comparison, radar sensing must similarly first learn the channel characteristics, thus it can accurately decipher the sensing variable by eliminating the effects of the channel. In this work, a more flexible channel sounder design framework is proposed to support various applications.
Sliding correlation is a well-known time domain technique for wideband CIR measurements [1115]. Various dedicated sliding correlator sounders were proposed to meet the needs for wideband channel measurements [1620]. Generally, the sliding correlator sounding system transmits pseudo-random noise (PN) sequences and performs a correlation at the receiver with a slightly slower rate identical copy of the PN sequence. Due to the efficient correlation properties of PN, this system can achieve high processing gain, better dynamic range, and fine resolutions [13, 15, 21, 22]. Sliding correlator sounders also have the advantages of low peak-to-average power ratio (PAPR) and efficient data compression for real-time recording. However, this system requires a complex and dedicated hardware system, and the choice of parameters, such as PN sequence length and chip rate, are also critical to optimize this system’s performance.
Frequency sweep is another well-known technique among channel sounding techniques. A frequency swept system utilizes a vector network analyzer (VNA) to perform channel sounding [2326]. The VNA sweeps a set of discrete frequencies within the required bandwidth, and a complex channel frequency transfer function or S-parameter S21 is then recorded in the acquisition systems. Afterward, inverse discrete Fourier transform (IDFT) is performed to compute the CIR. While straightforward, there are a few practical limitations of the VNA-based sounding system. Firstly, the system is only suitable for a static environment because of its long sweep time. Secondly, the transmitter and receiver must be co-located due to cable length limitations.
To mitigate the limitations of sliding correlation and VNA-based sounders, multicarrier or orthogonal frequency division multiplexing (OFDM)-based sounding systems are developed to perform frequency domain channel sounding [2735]. In the OFDM sounding system, the probing signal is synthesized in the frequency domain, while IDFT is performed before transmitting into the air. At the receiver, the matched filter operation is performed in digital baseband processors. However, the major problem of multicarrier channel sounder is the high PAPR. In this regard, various sequences have been proposed to reduce the PAPR. OFDM systems are usually implemented on software-defined radio (SDR). Accordingly, simple hardware implementation and faster computation make this technique a strong candidate for channel sounding.
The time resolution of the channel sounder depends on the system’s bandwidth. As a result, custom hardware is required for larger instantaneous bandwidth systems, and the overall solution is usually not affordable for many institutes and organizations. Recently, inspired by a VNA, new multiband sweep techniques have been proposed to perform faster and wider bandwidth channel sounding using low-cost commercial off-the-shelf (COTS) equipment. In [36], the authors have proposed a 60-GHz PN sequence-based wideband channel sounder using a heterodyne transmitter and receiver based on an arbitrary waveform generator (AWG), digitizers, and data storage device. To increase the system bandwidth, ten sequential measurements are performed with a 500-MHz frequency step to cover the full 5 GHz. After calibration, the channel transfer function (CTF) of all sub-bands are concatenated in the frequency domain, and IDFT is used to obtain the CIR of the complete 5 GHz channel bandwidth. This system has the advantage of constant envelope (CE) transmission. However, this system can only be used for indoor channel measurements.Bas et al. [37] have proposed another multiband sounding technique based on direct up/down conversion transceivers using AWG, an in-phase and quadrature (IQ) mixer, digitizer, frequency synthesizer, and high-speed data recorder of a redundant array of independent disks (RAID) storage. This system has an instantaneous bandwidth of 1 GHz, and operates from 3 GHz to 18 GHz. A fast-switching system is used to sweep the complete 15 GHz with overlapping frequency sub-bands. The proposed configuration of the system has a maximum delay spread of 2 μs, which limits it to urban and outdoor measurement scenarios, and the overall solution is also not very cost-effective. In [38], the authors have proposed a similar technique to develop a multiband multitone channel sounder. The proposed system is based on low-cost SDR and an open-source software named GNU radio [39]. The SDR can be tuned from a 300 MHz to 3.8 GHz RF frequency range with a maximum of 28 MHz instantaneous bandwidth. Channel sounding is performed in multiple sub-bands, and in each sub-band, 8 multitone are transmitted with phase randomization to reduce PAPR. Due to the latency between PC and SDR communication, this system is only used for the static environment. Li et al. [40] have proposed a frequency domain technique using a multiband (MB) OFDM signal. This sounder is based on superheterodyne SDR with 20 MHz instantaneous bandwidth, and measures 10 continuous sub-bands to cover 200 MHz in 3 ms, while a guard time is used to handle the switching time of hardware. A shared global positioning system (GPS) reference clock is used to synchronize a transmitter (TX) and receiver (RX). This system uses the IEEE Standard 802.11, a frame structure for sounding purposes that consists of the training sequence and data sections. The training section is used for frame and symbol synchronization. Although this system is very cost-effective in terms of hardware implementation, this system uses a shared clock between TX and RX, limiting it to perform channel sounding in an indoor environment. This system also has an inherent problem of the OFDM system, namely poor dynamic range and PAPR. Recently, in [41], the authors have proposed a flexible SDR-based multiband sounder for real-time channel measurement. In their work, a standard OFDM waveform is used as a probing signal. However, the PAPR problem is not addressed for optimal OFDM sounding.
Based on the limitations of the previous MB system, this work has contributed to defining an improved and flexible MB-OFDM-sounding architecture based on COTS SDRs. Particularly, due to the fact that most hardware systems are not suitable for UWB signal, MB-OFDM allows for combining one narrowband hardware into time-interleaved narrowband hardware that mimics MB UWB hardware. OFDM provides a flexible digital implementation of the UWB signal waveform. Nevertheless, the major problem in MB-OFDM signal design is the high PAPR. CE OFDM waveforms are highly encouraged to optimize transmitter performance. In this regard, various techniques have been proposed to reduce PAPR in the OFDM system [42]. Based on the previous limitations, there is a need to design an optimum MB-OFDM signal design. Accordingly, it is hypothesized that the constant amplitude zero autocorrelation (CAZAC) family sequence can provide a low PAPR MB-OFDM spectrum constraint waveform. A new Chu phasing scheme has been introduced in this work to produce a low PAPR probing signal, and an MB-OFDM signal design is developed for channel sounding. In addition, flexible sounding architecture is developed to perform sounding in different environmental conditions.
In order to develop a new OFDM sounding system, a brief introduction to the overall system architecture is needed. Accordingly, Section 2 first introduces a general architecture of an MB-OFDM sounding system. Afterward, in Section 3, a detailed formulation and numerical implementation of the MB-OFDM signal design is presented, and the probing signal is shown to meet all design requirements. Section 4 provides a brief formulation for CIR estimation. In Section 5, a discussion on the procedure to evaluate the methods’ performance and its validation against those in the literature is presented.A conclusion of the study is presented in Section 6.

Proposed Multiband Sounder Design

Conventionally, the hardware of radios is implemented on a component level, and most of the functionality is achieved using analog circuitry, while a fixed hardware platform limits the use of radios to a few specific applications. On the other hand, the SDR approach provides a versatile platform for re-programmable applications, and divides the radio functionality into two parts, a programmable digital platform and wideband analog frontend. The digital platform of SDR is built using a digital processor (DP) and field-programmable gate array (FPGA). The analog front is designed for a wide range of tunable RF frequencies, so that this makes SDR a highly desirable tool for R&D and implementation of new communication systems. This architecture also offers another advantage of using high-level programming languages for faster prototyping.
Given the hardware specification of SDRs, it is noted that almost all COTS SDRs offer only a few MHz of baseband signal bandwidth. Due to limited signal bandwidth, the available SDR systems cannot perform UWB channel sounding for finer time resolution. In this work, a multiband approach has been adapted for UWB communication making use of the IEEE 802.15.3a standard [43]. However, the proposed multiband sounder approach is different in several aspects (e.g. the signal bandwidth for the channel sounder is not fixed). Similarly, the physical layer is highly flexible to meet the sounding requirements.

Multiband OFDM Probing Signal Design Concept
In a multiband-sounding approach, various narrow bandwidth sub-bands are concatenated together to form a UWB frequency band. Each sub-band occupies a signal bandwidth per hardware specifications. In this regard,this approach offers the advantage of utilizing the standard SDR for UWB sounding, and the use of OFDM modulation provides spectral flexibility and control over the transmit power. In addition, the processing requirement is also very small since a much smaller bandwidth needs to be processed at one time.
Consider a UWB system built by concatenating S sub-bands as shown in Fig. 1. Each sub-band occupies a baseband signal bandwidth (BW), where the signal BW is defined by SDR hardware specifications. Each sub-band is further divided into N orthogonal subcarriers. An OFDM symbol in the time domain, x(n), is constructed using inverse fast Fourier transform (IFFT) of complex numbers corresponding desired pilots at the N frequency bins. The resulting timedomain samples of OFDM symbol, x_m (n), for mth period can be written as [44],

$x_m(n)= \displaystyle\sum_{k=0}^{N-1} s_m(k) exp⁡(j2πnk/N),$(1)

where $s_m(k)$ represents a complex modulated symbol to be transmitted in subcarrier k. The frequency spacing between adjacent subcarriers is $∆f=BW⁄N$. The resulting time-domain waveform has a duration of $T_b=1⁄∆f$. Let $T_c$ be the duration of a cyclic prefix, which is created by copying the last $N_c$ samples of IFFT and concatenating them to the front of the symbol. This gives a continuous waveform where the symbol and cyclic prefix are joined together to provide sufficient time for the longest significant path of the CIR. A guard time, $T_g$ is also added at the end of the symbol to prevent a windowing effect from attenuating the sample within $T_b$ period. It can also be used to cater to the switching time between carrier frequencies. Thus, the total duration of an individual OFDM symbol is

$T_{sym}=T_b+T_c+T_g.$(2)

Fig. 1. UWB multiband OFDM spectrum.

The coherencetime & bandwidth of the channel define the requirement for the maximum T_sym. It is carefully crucial to select the symbol length according to the channel condition. Since the switching time between carrier frequencies T_g depends on the hardware specification and is usually expressed in nanoseconds, T_b and T_c are used to control the overall symbol duration.
As described before, the UWB band is divided into S sub-bands, with the center frequency f_c for each sub-band with baseband BW calculatedwith the equation shown below:

$f_c= f_o+BW×s,$(3)

where $f_o$ is the center frequency for first sub-band and $s=1,2,…,S$.
In a multiband sounder, channelization is based on time-frequency codes and the number of transmitting streams, which is considered as different users. Each user has a unique code, each of which defines the center frequency of allocated sub-bands to one user and is generated for each user to cover the full bandwidth in the shortest possible time. Ideally, a larger separation of the band for each time window is advisable. However, for sounding application, the minimum separation kept is one, and there is no collision between multiple transmit streams. For example, for only one transmit stream, the code generated has a length of $s=1,2,…,S$. However, if we have two transmit streams, the code length will become half of $s$, and the subsets will not have common bands. Let us consider the same example given above where $S=6$. If a hardware resource has only one transmitter, the code generated is {1,2,3,4,5,6}. However, if two transmitters are available, the code for the first transmitter can be {1,3,5} while the second transmitter will have a code of {2,4,6}. Fig. 2(a) and2(b) illustrate the time-frequency code for one transmit stream and two transmit streams, respectively. For sounding applications, the code can also be shuffled as long as it covers a whole sounding frequency band. In other words, the proposed multiband sounding system has a similarity to VNA, where a single carrier is swept through a required frequency band. In the proposed method, the wideband signal is swept to provide a frequency response of UWB. Another advantage of this technique is that the sounding can also be performed in a cognitive model to avoid any interference between sounding and existing users.

Fig. 2. Time-frequency representation of a multi-band OFDM signal: (a) one transmitter code {1,2,3,4,5,6} and (b) two transmitters code 〖Tx〗_1={1,3,5} and 〖Tx〗_2={2,4,6}.

The multiband OFDM sounder uses standard OFDM block sets to build a physical layer as shown in Fig. 3. Since the focus of this work is to evaluate the performance of multiband OFDM soundings signal design and channel estimation block set, it is also assumed that the transmitter and receiver are perfectly synchronized. The block sets, such as a scrambler & de-scrambler, convolutional encoder & Viterbi decoder, and bit interleaver& de-interleaver, as well as synchronization are not discussed in this work. The reader may find additional information about these block sets in [44].

Fig. 3. OFDM system transmitter and receiver architecture.

OFDM Subcarrier Frequency Allocation
In the OFDM sounding system, the fundamental sampling of discrete tones is defined by the FFT size N. Among N subcarriers, N_d data tones are used for data transmission, and N_p pilot tones are used for training. The number of guard subcarriers at the lower band edge is N_gl, and the number of guard subcarriers at the upper band edge is N_gu. In total, N_g=N_gl+N_guare kept as guard subcarriers. The DC sub-carrier, N_dc=N/2+1, is not available to avoid error build-up at DC due to receiver imperfections. The number of useable carriers, N_u for link signaling and carrying payload data are as follows:

$N_u=N_d+N_p-1, where N_u<N-N_g$(4)

For sounding mode, N_d=0 and N_p=N-N_g-1. The pilot tones q_(k_p ) for mth symbol are assigned from a complex-valued p_u sequence expressed as:

$q_{m,k_p}=p_{m,u},$(5)

where, $k_p=N_{gl}+1,N_{gl}+2,…,N_{gl}+N/2,N_{gl}+N/2+2,…,N_{gl}+N_p,m=0,1,2,…,M_{sym}-1, u=0,1,2,…,N_p-1,$ and $M_{sym}$ is the $M^{th}$ symbol. In (5), $p_u$ is either BPSK or polyphase modulated sequence. The guard subcarriers $g_{m,k}$ takes the location expressed as:

$g_(m,k_g )=0,$(6)

where $k_g=1,2,3,… N_{gl},N_{gl}+N_p+1,N_{gl}+N_p+2,N$.
For a hybrid mode, the complex data symbols, d is grouped in N_d size. For mth symbol, d is the assigned to carriers c_(k_d )expressed as:

$c_{m,k_d}=d_{u_d+N_d m},$(7)

where,$u_d=0,1,2,…,N_d-1, m=0,1,2,…,M_{sym}-1,$ and $k_d$ indexes are computed as follows:
$Let A_{sub}={1,2,3,…,N},$ is a set which contains all available frequency bin indices and $B_g$ is a subset of $A_{sub}$ for guard subcarriers indices, $B_g={1,2,3,… N_{gl},N- N_{gu}+1,N- N_{gu}+2,N}$. The DC sub-carrier element is $B_{dc}={\frac{N}{2}+1}$. The useable subcarrier subset can be written as,

$A_u=A_{sub}\(B_g∪B_{dc})={N_{gl}+1,…,N⁄2,N⁄2+2 ,…,N-N_{gu} }.$(8)

If the OFDM symbol contains no pilot tones then $k_d⊆A_u$, otherwise $k_d⊂A_u$ and the number of elements of $k_d$ is equal to $N_d$. The pilot tones $q_{m,k_p}$ for mth symbol are assigned from a complex-valued, $p_{u_p}$, sequence as,

$q_{m,k_p}=p_{m,u_p},$(9)

where $k_p=A_u\k_d, u_p=0,1,2,…,N_p-1$ and $m=0,1,2,…,M_{sym}-1$.
Fig. 4 shows the hybrid mode subcarrier frequency allocation for 64-FFT size case. In this example, 10 guard carriers, 4 data carriers, and 49 pilots are used.

Fig. 4. Subcarrier frequency allocation for hybrid mode.

Sounding Subframes Structure
A frame-based transmission is used in the proposed multiband sounder. The OFDM symbols are concatenated to form subframes. A frame comprises two major components, a training sequence and a data section, as shown in Fig. 5. The primary objective of the training sequence is synchronization and the retrieval of a coherent data sample. A data section consists of multiple OFDM-sounding symbols. Suppose the cyclic prefix is set to zero. In that case, a minimum of three identical OFDM sounding symbols are required for an unambiguous CIR estimation, and CIR length will be equal to the duration of the symbol. However, if the cyclic prefix length is set to the fraction of the OFDM symbol length, the minimum number of symbols required is only one. Ideally, more than 2 data symbols are transmitted to provide better estimation performance. The number of data symbols, $N_{sym}^{data}$ and the number of training symbol, $N_{sym}^{training}$ are set to be flexible for sounder because it highly depends on the channel properties. The duration of the subframe containing $N_{sym}^{sub}=N_{sym}^{training} + N_{sym}^{data}$ symbols are:

$T_{subframe}=N_{sym}^{sub}×T_{sym}.$(10)

Fig. 5. Frame structure of OFDM sounding.

OFDM Pilot Sequence Design for Low PAPR

In a communication system, the preamble-sounding symbols are constructed in time-domain using CAZAC sequences. A CAZAC sequence provides constant envelope properties. However, it limits the use of symbols to only sounding, and no data can be transmitted during that time.
In this work, the sounding scheme is developed to provide flexibility for simultaneous sounding and data transmission. Although the data transmission is not a primary objective of a sounder, there are cases where TX and RX are not co-located, and there may be a need to exchange data between TX and RX. Hence, the proposed system has different challenges to meet the MB-OFDM sounding system requirement, and it has more similarities to OFDM data symbols where symbols are constructed in frequency-domain for better flexibility and control over data pilot subcarriers and spectrum shaping.

Phase Sequence for Pilot Tones
Let s_m (k)=c_m (k)+q_m (k), in (1), where c_m (k) and q_m (k) are complex-valued data and pilots tones transmitted in the kth subcarriers, respectively. Using (1), the time-domain samples of mth OFDM can be rewritten as,

$x_m(n)= \displaystyle\sum_{k=0}^{N-1} [c_m(k)+q_m(k)]exp(j2πnk/N).$ (11)

The crest factor of $x_m(n)$ is a critical parameter to optimize the PA performance. Multicarrier techniques are prone to the high PAPR because the phase of tones is dependent on the constellation of a random input data stream and pilot sequence. The instantaneous power can be written as,

$P(n)= |x(n) |^2.$(12)

The average power is given by,

$P_{avg} (n)=avg {|x(n) |^2 },$(13)

and PAPR is the ratio of maximum envelope power to average power. Thus,

$PAPR= \frac{max⁡{P(n)}}{P_avg (n)}.$(14)

The data tones, $c_m(k)$, are assigned from the QPSK or QAM constellations, whereas pilot tones, $q_m(k)$, are unity-gain phase-modulated tones that take values from sequences $p_m(u)$ as described below,

$p_m(u)=a_m(u) exp⁡j(θ_m(u)).$(15)

Here, $a_m(u)$ and $θ_m(u)$ are amplitude and phase associated with uth element of sequence for $m^{th}$ symbol, and $j=sqrt{-1}$ is an imaginary number. The crest factor of $x_m(n)$ caused by pilot sequence is dependent on the phase angle $θ_m(u)$. Each element of the pilot sequence $p_m(u)$ is assigned to dedicated tones in the frequency domain using (9). The choice of phase angle is very critical to the PAPR of the transmit signal. Having the same phase for all tones is the worst choice. Conventionally, pilot subcarriers are BPSK modulated with pseudo-random binary sequence (PRBS). PRBS is generated using linear feedback shift registers (LFSR). Though this is better than the same-phase case, the PAPR still grows as the number of tones increases. In[45], the author used PRBS sequence-based phase randomization with a recursive algorithm to reduce the PAPR. However, these recursive algorithms require very high computational effort, especially for a large number of carriers. On the other hand, there is another approach where researchers look for sequences that can provide a phasing scheme that achieves the desired low PAPR waveform without the need for recursive algorithms, precoding, or clipping methods [46].
In this work, a new phasing scheme based on the Zadaff-Chu (ZC) sequence is used [47]. In the proposed method, symbols are synthesized in the frequency domain, and phase randomization of pilot tones is performed using the phases from the ZC sequence. A ZC sequence is given by

$p_m^{Chu}(u)=a_m^{Chu}(u) exp⁡(θ_m^{Chu}(u)).$(16)

In (16), $a_m^{Chu}$ is the amplitude of sequence and $θ_m^{Chu}$ is the phase, described as

$θ_m^{Chu}(u)=-jπγu(u+c_"f" +2κ)/N_p ,$(17)

where, 0≤u<N_p, 0<u<N_p "and" gcd⁡〖(N_p,γ)=1〗, c_"f" =N_p "mod" 2, κ∈Z, N_p= length of the sequence.

Fig. 6. Comparison of PAPR for ZC, Newman, and PRBS phase.

The sounding pulse duration depends on the channel conditions, while frequency-selective channels may require a very large FFT size. Thus, the pilot sequence must have a low PAPR for large numbers of pilot tones. As a result, a detailed comparison of 64 up to 130k number of tones is presented in Fig. 6 for PRBS, Newman, and ZC phasing schemes. It can be observed that the ZC phasing scheme gives the lowest PAPR for a sufficiently large number of tones.

Sounding Signal PAPR in the Presence of Data Tones
In the previous section, it has been shown that the proposed ZC sequence-based phase randomization of pilot tones provides an optimum PAPR performance. However, for hybrid or data transmission cases, where data subcarriers are assigned from a complex-valued constellation, additional PAPR results, for which Monte Carlo simulations are performed to provide a complementary cumulative distribution function (CCDF) of PAPR in the presence of data tones for data transmission cases.
The results provide a comparison of different FFT sizes, and the 4-QAM modulation is used for all cases, with system BW being kept constant at 20MHz. An example of OFDM subcarrier mapping for 64-FFT size for data transmission cases is illustrated in Fig. 7(a), in which the y-axis represents the frequency bin, and the x-axis the number of symbols. The OFDM subcarrier mapping remained the same for all symbols. The color map is used to depict different types of subcarriers. The number of data subcarriers is approximately 50% of useable subcarriers for each FFT size case. Fig. 7(b) presents the PAPR for different sizes of FFT length, and the results are also compared with PRBS for 16-FFT size. For the data transmission case, the PAPR contribution of the data carrier is very dominant, and a larger FFT size has a PAPR close to 11 dB. A comparison between PRSB and ZC-based pilots is presented for the PRSB 16k-FFT size. Accordingly, it can be observed that the PRSB case has around 12.5 dB PAPR, and the ZC based scheme performs better than PRSB for similar system configurations, so that it can be concluded that the PAPR with the ZC pilot sequence is between 9 to 11 dB.

Fig. 7. (a) OFDM subcarrier mapping for data transmission mode. (b) PAPR comparison of different length ZC sequences and 16K PRBS for hybrid mode.

In the above examples, PAPR reduction techniques, e.g., precoding matrices clipping [46], are not used to provide a comparison of worst-case scenarios. If we employ PAPR reduction techniques for data subcarriers, the data transmission PAPR can be further reduced. Hybrid sounding systems, where data and probing signals are transmitted together, may be needed in radar sensing applications. The proposed phasing provides a superior performance compared to the conventional method in data transmission mode. Thus, it can be concluded that the designed probing signal provides the flexibility of configuration and meets the requirement for the sounding waveform of a low PAPR.

Channel Impulse Response Estimation

The impulse response of the multipath channel for an ideal Dirac pulse, δ(n), can be given from the equation:

$h(n)=\displaystyle\sum_{l=0}^{L-1}α_l e^{jθ_l} δ{n-τ_l},=\displaystyle\sum_{l=0}^{L-1}h_lδ(n-τ_l),$(18)

where L is the total number of multipath, $α_l$ is the amplitude, $τ_l$ is an additional time delay and $θ_l=2πf_c τ_l$ is the phase associated with the $l^th$ path. The transmitted signal, $x_m(n)$, goes through the multipath channel and a received baseband signal, $y_m(n)$, for mth symbol can be written as:

$y_m (n)=\displaystyle\sum_{l=0}^{L-1}h_{m,l} x_m (n-τ_l)+w_m(n),or$
$y_m (n)=h_m (n)*x_m (n)+w_m (n),$ (19)

where w(n) is additive white Gaussian noise (AWGN). As the cyclic prefix OFDM system is related to periodic convolution between the channel and OFDM symbols, (19) can be written as:

$y_m (n)=h_m (n)x_m (n)+w_m (n),$(20)

where operator ⊛ represents periodic convolution.
CIR, $h_m(n)$, estimation is a challenge in a time-varying environment. Generally, blind, non-blind, and semi-blind estimation techniques are used for channel estimation. However, non-blind methods perform better because known information is available at the receiver for the estimation of CIR, whilein non-blind schemes, pilots are commonly used. In this regard, different types of pilot arrangement, block, comb, and lattice, are proposed to optimize the pilot density and system performance in several kinds of channels [48]. The least-square (LS) and minimum mean-square error (MMSE) channel estimation techniques are well known for the pilot-assisted OFDM system, and whilethe LS technique is computationally efficient, it however suffers from poor accuracy. On the other hand, MMSE requires very high computation but provides better accuracy [48, 49]. Recently, time-domain correlation-based techniques such as frequency-domain pilots & time-domain correlation (FPTC) have been introduced to improve computational efficiency [5052].
Since, the objective of this work is to develop the signal design, conventional channel estimation techniques are used for performance measurement.

Results & Discussion

Extensive numerical experiments are performed to extend the validation of the proposed multiband channel sounders, and the proposed channel sounder is implemented in MATLAB. In this work, known CSI is used as a benchmark, and conventional techniques are also implemented such as LS, DFT-based LS, and FPTC in a similar MATLAB environment to evaluate the proposed sounder. The testing is performed to show that the particular implementation of the proposed CIR estimation techniques is valid and suitable for its intended purpose, respectively, within a reasonable bound of accuracy. For a detailed performance evaluation, mean-square error (MSE) is computed for each case with known CIR as a reference. The channel transfer function (CTF) is computed using FFT of CIR, with the formula used to calculate MSE given by [53]:

$MSE=E{|H(k)-H ̃(k)|^2 },$(21)

where $H(k)$ is the known CTF and $\tilde H(k)$ is the estimated CTF using proposed and conventional
techniques. An average MSE is computed based ona Monte Carlo simulation for different SNR scenarios in various environmental conditions.
It is assumed that two coherent and independent transmitter resources are available—each transmitter supports a 20 MHz of the system bandwidth. In addition, a multiband bandwidth of 200 MHz is considered, andthe total number of sub-bands is 10. As described in the previous section, a unique time-frequency code is used for each transmitter. Transmitter one has assigned code {1,3,5,7,9}, and transmitter two the code {2,4,6,8,10}. A resource mapping of multiband switching is shown in Fig. 8. Since we have two transmitter resources available, there are a total number of five switching time slots andswitching between two bands has a guard duration. Here,the system configurations of the spectrum constraint hybrid mode are used for the simulation. The FFT length of 64-point is used for each sub-band, and a cyclic prefix of ½ of FFT-size is used. The symbol duration without cyclic prefix and guard period is 3.2 μs. The 4-QAM data modulation order is used, andthe MSE results are compared with those from theoretical and conventional techniques, withthe summary of simulation parameters given in Table 1.

Fig. 8. Resource mapping of multiband OFDM sounder.

Table 1. Simulation parameters for multiband transmission in Rayleigh channel
System parameter Value
Data transmission mode
Number of pilot subcarriers 27
Number of data subcarriers 26
QAM order 4
Number of guard subcarriers  10
$∆f$ : subcarrier spacing (kHz) 312.5
$T_b$ : OFDM Symbol duration of sub-band (μs) 3.2
$T_c$ : Cyclic Prefix duration of sub-band (μs) 1.6
$T_g$ : Guard Interval duration (μs) 0.25
$T_{sym}$ : Symbol duration (μs) 5.05
Number of sub-bands 10
Number of transmitters 2
To evaluate the performance of the proposed sounder, a more challenging frequency selective Rayleigh channel is used. The power delay profile of the 6-tap channel is described in Table 2, and Fig. 9(a) shows the semi-logarithmic plot of MSE results from the Monte Carlo simulations for Eb/No values ranging from 0 until 30 dB. The results compare LS, LS-DFT, and FPTC at different iteration levels, andfrom the results, it is observed that LS and FPTC have similar performance. However, LS-DFT performed better than LS and FPTC for the frequency selective channel. In other words, for a fixed threshold of MSE at 〖10〗^(-3), LS and FPTC require 17 dB of Eb/No while LS-DFT can reach the threshold of performance at 15 dB, which is better against other techniques. In addition, it can also be observed that LS-DFT performs better for less than 15 dB Eb/No. However for higher Eb/No, there is no significant advantage of using LS-DFT due to the additional computation burden it brings for FFT operations.

Table 2. Power delay profile for a frequency selective Rayleigh channel
Path No. Delay (μs) Power (dB)
1 0 -3
2 0.002 -9
3 0.01 -3
4 0.05 -6
5 0.2 -9
6 0.3 -12

Fig. 9. (a) Comparison of MSE performance for conventional techniques in a frequency-selective Rayleigh channel. (b) Comparison of BER performance for conventional techniques in a frequency-selective Rayleigh channel.

As explained in the experiment setup above, a data transmission or hybrid system configuration is used to evaluate the sounders’ performance. Since data is also transmitted on approximately 50% of available subcarriers, Fig. 9(b) shows the comparison of BER results from LS, LS-DFT, and FPTC. A zoomed-in plot of BER for 15 to 21 dB of Eb/No is also provided for a detailed comparison and insight. As we have discussed, the MSE of LS-DFT only performs better for lower Eb/No values, and it is also apparent from the results that BER is higher for LS-DFT as compared to other techniques for high Eb/No values.
For further study, a comparison of an instantaneous CIR from simulations is presented for a 30 dB Eb/No in Fig. 10(a). The x-axis represents the time from 0 to 1.2 μs and y-axis represent the amplitude of each channel tap. As described in the simulation setup, we have assumed six tap Rayleigh channels to evaluate the proposed sounder’s performance. It can be observed from results that the proposed multiband can clearly identify a high-resolution impulse response. The CTF of Fig. 9(a) is computed to provide detailed insight, and a comparison of an instantaneous CTF between conventional techniques is presented for 30 dB Eb/No in Fig. 10(b). The x-axis represents the 40 MHz frequency channel, while the y-axis provides channel gain in dB. The CTF of the known CSI case does not include the noise artifact. However, theoretical results are computed with AWGN noise. Each sub-channel is 20 MHz wide and has spectrum constraints due to a guard band and DC subcarrier. For LS, the interpolation error can be seen at the edge of the sub-channels. Accordingly, to provide better visualization, the CTF of known CSI is compared with other techniques and 40 MHz around a DC carrier, which is illustrated in Fig. 10(b). From the results, it can be concluded that the proposed multiband sounder is suitable for higher resolution impulse response measurements.

Fig. 10. (a) Comparison of CIR performance for conventional techniques in a frequency-selective Rayleigh channel. (b) Comparison of CFR performance for conventional techniques in a frequency-selective Rayleigh channel.

Conclusion

In this work, a detailed design methodology of a flexible multiband OFDM sounding system has been presented. We have so far discussed the general architecture of a multiband OFDM sounding system. Subsequently, a detailed formulation and numerical implementation of the MB-OFDM signal design has been presented, while a low PAPR transmitter waveform was designed for MB-OFDM sounding, whose PAPR results were validated. Using the proposed sounding architecture and probing signal, a high-resolution CIR performance has been validated by comparing results from known CIR, LS, LS-DFT, and FPTC, the results of which in turn validate that a high-resolution impulse response can indeed be obtained through the broadband sounding technique proposed herein. Accordingly, the proposed flexible architecture has the capability to allow a vast range of use cases beyond channel sounding, such as those in radar sensing. Nevertheless, there are still gaps in the channel estimation techniques for a sounding application that will be further explored in a future work.

Author’s Contributions

Conceptualization, AI, VJ. Funding acquisition, GS, MS. Investigation and methodology, AI, VJ, NZ. Supervision, MD, AAA, VJ. Writing of the original draft, AI. Writing of the review and editing, VJ, MD, AAA, NZ, GS, MS. Formal analysis, AI.

Funding

This study has received funding for publication from the European Union’s Horizon 2020 research & innovation programme under grant agreement No. 854194.

Competing Interests

The authors declare that they have no competing interests.

Author_Biography

Asif Iqbal, received his M.Sc. degree in Electrical & ElectronicsEngineering from Universiti Teknologi PETRONAS,Malaysia in 2012. Currently, he is Ph.D. student atthe Department of Electrical and Electronics Engineering, UniversitiTeknologi PETRONAS, Malaysia. His research interestincludes fast and efficient numerical algorithms, radiopropagation, wireless channel characterization, and modeling.He is currently working on the channel sounder andemulators.

Micheal Drieberg (Member, IEEE) received the B.Eng. degree in electrical and electronics engineering from UniversitiSains Malaysia, Penang, Malaysia, in 2001, the M.Sc. degree in electrical and electronics engineering from Universiti Teknologi PETRONAS, Seri Iskandar, Malaysia, in 2005, and the Ph.D. degree in electrical and electronics engineering from Victoria University, Melbourne, Australia, in 2011. He is currently a Senior Lecturer with the Department of Electrical and Electronics Engineering, Universiti Teknologi PETRONAS. He has made several contributions to the Wireless Broadband Standards Group. He has published and served as a reviewer for several high impact journals and flagship conferences. His research interests include radio resource management, medium access control protocols, energy harvesting communications, and performance analysis for wireless and sensor networks.

Varun Jeoti, (SM’13) received his Ph.D. degree from Indian Institute of Technology, Delhi, India in 1992. He has over 29 years of teaching experience in leading Indian and Malaysian universities teaching students from various social and cultural backgrounds. He has been conducting frontier research for over 38 years in the area of surface acoustic wave (SAW) devices, signal processing and wireless communication. Starting in 1980 from IIT Delhi soon after his graduation, he worked on government sponsored projects developing SAW Pulse Compression filters, and underwater optical receivers in IIT Madras. He was a Visiting Faculty in Electronics department in Madras Institute of Technology, Anna University for about a year during 1989 to 1990 and joined Delhi Institute of Technology for next 5 years till 1995. He moved to School of Electrical & Electronic Engineering (E. & E. Engg.) in Universiti Sains Malaysia in 1995 and later moved to Dept. of E. & E. Eng. in Universiti Teknologi PETRONAS in 2001. He is presently working in Faculty of Technical Sciences, University of Novi Sad, Serbia as ERA Chair leading research efforts in Stretchable and Textile Electronics. His research interests include, among others, signal processing, SAW sensor-tags, SAW microfluidics and wireless communication for various applications.

Azrina Abd Aziz (Senior Member, IEEE) is currently a senior lecturer at the Department of Electrical and Electronic Engineering of UniversitiTeknologi PETRONAS (UTP), Malaysia. Prior to her academic appointment, she worked briefly in industry handling the final visual inspection process of IC packaging. She received herbachelor’s degree in Electrical and Electronic Engineering (Hons) from The University of Queensland, Australia in 1997 and MSc. in System Level Integration from the Institute for System Level Integration (ISLI), Scotland in 2003. She then completed her Ph.D. degree in Computer Systems Engineering at Monash University, Melbourne, Australia in 2013. Her recent research interests focus on energy-efficient techniques for topology control in wireless sensor networks (WSNs), wireless body area networks (WBANs) for biomedical applications and medical imaging, and machine learning techniques. Azrina is currently leading the SMART assistive and rehabilitation technology research group in UTP. She is a senior member of IEEE, a member of Board of Engineers Malaysia. She is holding the positions of the treasurer of IEEE Robotics and Automation Society and Chair-Elect of IEEE Women in Engineering Malaysia. Azrina is the journal reviewer of Ad Hoc Networks under the ScienceDirect publisher.

Prof. Dr. Goran Stojanović (M’04) is a full professor at Faculty of Technical Sciences (FTS), University of Novi Sad (UNS), Serbia. He received a BSc, MSc and a PhD degree in 1996, 2003 and 2005, respectively, from FTS-UNS, all in electrical engineering.
He has 25 years of experience in R&D. His research interests include sensors, flexible electronics, textile electronics and microfluidics. He is an author/coauthor of 260 articles, including 96 in leading peer-reviewed journals with impact factors, 5 books, 3 patents, 1 chapter in monograph. Keynote speaker for 12 international conferences. Stojanović has been a supervisor of 11 PhD students, 40 MSc students and 60 diploma students at the FTS-UNS. He has more than 14 years’ experience in coordination of EU funded projects (H2020, FP7, EUREKA, ERASMUS, CEI), with total budget exceeding 14.86 MEUR. Currently, he coordinates 4 Horizon2020 projects in the field of green electronics and textile electronics.

Dr. Mitar Simić (S’16, M’18) was born in Ljubovija, Republic of Serbia in 1987. He received the B.Sc. and M.Sc. degrees in electrical engineering from the University of East Sarajevo, Bosnia and Herzegovina, in 2010 and 2012, respectively. He received the Ph.D. degree in electrical engineering from the University of Novi Sad, Serbia in 2017.
He is a Postdoctoral Researcher within the STRENTEX project at the Faculty of Technical Sciences, University of Novi Sad, Serbia.
He is an author/coauthor of one monograph and more than 40 scientific papers. His research interests include sensors, flexible electronics, impedance spectroscopy analysis, equivalent circuit modeling, and development of devices for impedance measurement and data acquisition.

Nazabat Hussain Nazabat Hussain completed his M.Sc. ad Ph.D. in Electrical & Electronics Engineering from UniversitiTeknologi PETRONAS, Malaysia. He is specialized in computational algorithms, image processing, signal processing, AI, embedded system, Wireless Communication, and applied electromagnetics. He has published his research work indexed Journal/Conferences. Currently, he is working as R&D Engineer GE Vingmed Ultrasound AS.

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Asif Iqbal1,*, Micheal Drieberg1, Varun Jeoti2, Azrina Binti Abd Aziz1, Goran M. Stojanović2, Mitar Simić2, and Nazabat Hussain3, A Flexible Multiband Multicarrier Signal Design for Broadband Channel Sounding Applications, Article number: 12:19 (2022) Cite this article 1 Accesses