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Journal ArticleDOI

Parameter estimation and channel reconstruction based on compressive sensing for ultra-wideband MB-OFDM systems

01 Feb 2020-Signal Processing (Elsevier)-Vol. 167, pp 107318
TL;DR: The proposed CS-based channel parameter estimation method is able to accurately estimate the sparsity and the dictionary size, and can effectively reconstruct the CIR for channels that are either based on a mathematical model or real, measured channels.
About: This article is published in Signal Processing.The article was published on 2020-02-01 and is currently open access. It has received 8 citations till now. The article focuses on the topics: Compressed sensing & Orthogonal frequency-division multiplexing.

Summary (4 min read)

1. Introduction

  • Besides the theoretical channel models considered in the literature, the authors also performed a measurement campaign in a laboratory environment, and show in this paper that the resulting channel is30 sparse.
  • In [8], the applicability of CS for UWB channel estimation is investigated, and the authors employ standard Matching Pursuit (MP) algorithms for CS, such as35 subspace pursuit (SP) [17], orthogonal matching pursuit (OMP) [18] and compressive sampling matching pursuit [19], to accurately reconstruct the CIR.
  • Optimally, the dictionary size and sparsity must be estimated jointly.
  • In Section 5, the authors evaluate the performance of the proposed algorithm and compare its90 performance with that of state-of-the-art algorithms.

2.1. Channel Model

  • This fading coefficient ζlβk,l follows a log-normal distribution: 20 log10(ζlβk,l) ∼ N(µk,l, σ21 + σ22), (5) where σ1 is the standard deviation from the cluster log-normal fading term ζl and σ2 is the standard deviation from the ray log-normal fading term βk,l.
  • Further, the dominant taps are confined in the first part of the CIR, i.e. the tail contains only close-to-zero taps.

2.2. Measured Channel

  • The experiments to measure the sparse channels were carried out in a labora- tory of Ghent University in Belgium.
  • The long side ) approximately has length 16 m and width 5 m, while the small side ) approximately has length 8.5 m and width 5 m.
  • The authors selected one transmitter position and 15 receiver positions ).
  • Taps, i.e. most taps have a near-zero or zero amplitude, implying the channel can indeed be considered as sparse.
  • Similar results were obtained for the other receiver positions.

3. Compressive Sensing Based Channel Reconstruction Scheme

  • The authors discuss the reconstruction of the CIR using CS methods, and analyze the effect of two parameters, i.e. the dictionary size and sparsity of CIR, on the CE.
  • Let us first revisit the principle of CS.
  • To obtain150 accurate estimates of ϕ, the measurement matrix Υ should satisfy the restricted isometry property (RIP), i.e. it should be nearly orthonormal when operating on the sparse vector ϕ.
  • In following subsections, the authors derive the observation model, discuss the RIP of the measurement matrix and the accuracy of the reconstructed sparse channel, and evaluate the effect of the system parameters155 on the performance.

3.1. CS-Based Channel Reconstruction

  • Following [3], the authors consider a frame-based UWB MB-OFDM transmission system, in which several known OFDM symbols are placed in a preamble for channel estimation and synchronization, followed by a payload frame containing160 the OFDM data symbols.
  • The authors assume this preamble is shorter than the total CIR length, i.e. NNp < Ltaps.
  • While it is shown in the literature that, with exponentially high probability, the partial Fourier matrix satisfies the RIP, assuming the number of measurements is nearly linear in the sparsity level, the RIP characteristics of the matrix Φ will not be straightforward to show, as in general, this proof is a strongly NP-hard problem [23, 24].
  • Moreover, the complexity of the CS method is lower than that of the MMSE approach.
  • To obtain170 an accurate reconstruction of the channel, the authors need to select out of the Mtaps channel components, the Ks taps with the largest energy, i.e. determine the positions of the non-zeros components of B, and estimate the values of θ for the selected Mtaps and Ks.

3.2. Effect of the Dictionary Size and Sparsity

  • To solve the l1-norm optimization problem discussed in the previous section, the authors will employ the CoSaMP algorithm [19], as it combines good estimation accuracy with low complexity.
  • Then, some simulations are conducted to verify their analysis.
  • As a result, increasing the dictionary size will have a detrimental effect on both the performance and the complexity.
  • Further, the authors stated that when Ks is too small, some dominant channel taps will not be reconstructed, while when Ks is too large, noise will start to play a larger role.

4. Parameter Estimation

  • The dictionary size Mtaps and the sparsity Ks both affect the precision of235 channel estimation.
  • In realistic scenarios, prior information about these two parameters is often not available, so the authors will estimate these parameters based on the preamble.
  • The authors show that the performance degradation of their method compared to the simplex method is small.
  • This method can accurately estimate Mtaps and Ks, as will be illustrated in Section 5.
  • As this complexity is250 still very high, the simplex algorithm is unsuitable for practical implementation in UWB MB-OFDM systems.

4.2. Adaptive CE Method

  • This optimal value of Mtaps for the260 BER does neither depend on the sparsity Ks nor on the SNR Eb/No.
  • 275 the authors need an initial value for Ks. First, they note that, when Ks > Ks,opt, the optimal value Mtaps,opt becomes (quasi-) independent of Ks. Further, they notice from Figure 5 that selecting Ks >.
  • To find Mtaps,opt, the authors define an initial search interval [Mmin, Mmax].
  • To motivate this lower limit, the authors note that in practice, if the length of the pilot preamble is shorter than the effective CIR length, the channel can not be estimated accurately.

4.2.2. Algorithm 2: Ks estimation

  • The dynamic window search algorithm to find Ks,opt, which is shown in Algorithm 2, is similar to the algorithm to find Mtaps,opt.
  • The initial search310 interval for Ks is set to [Kmin, Kmax] = [1, NNp], i.e. the minimum and maximum Ks that can be estimated with a preamble length NNp.
  • Similarly as in Algorithm 1, the authors select Nb equidistant test values for Ks, with step size Kstep = b(Kmax −Kmin)/Nbc, and reconstruct the CIR with the selected value of Ks and Mtaps,opt from Algorithm 1, and compute the resulting BER of the315 pilot sequence.
  • The authors gradually refine their search interval until the step size Kstep is smaller than or equal to the threshold Kstep,min = 1.
  • The outputs of this algorithm are Ks,opt and the reconstructed CIR.

4.3. Complexity Analysis

  • To show that the proposed algorithm is suitable for practical implementa-320 tion, the authors evaluate the computational complexity of the algorithm.
  • As in this optimization process, the330 dictionary size Mtaps will converge to Mtaps,opt, the authors approximate the complexity of the CoSaMP algorithm by O{Mtaps,opt log2(Mtaps,opt) log2(Ks,initial)}.
  • Within each inner loop, Nb + 1 values of Mtaps are tested, and the inner loop is executed O{logNb(4NNp)} times, leading to the complexity O{(Nb +1)Mtaps,opt log2(Mtaps,opt) log2(Ks,initial) logNb(4NNp)}.
  • To compare the complexity of the proposed algorithm with the complexity of the MMSE estimator and the simplex algorithm, which are O{(NNp)3} and O{Mtaps,opt2Ks,opt log2(Mtaps,opt) log2(Ks,opt)} respectively, the authors consider345 the case where Mtaps,opt = 5NNp, Ks,opt = NNp and Nb = 5.
  • As in most situations, Mtaps,opt and Ks,opt will be smaller than these values, the true complexity will be smaller than the complexity shown in Figure 6.

5. Numerical Results

  • The channel models (CMs) used in their simulations are based on the UWB communication environments and propagation scenarios considered in the360 IEEE 803.15.3a standard [11] (see Table 1 for the parameters of these CMs).
  • The figure demonstrates that when Eb/No increases, the probability of miss detection of both Mtaps and Ks reduces, and drops below 5% when Eb/No is sufficiently large.
  • As can be observed in Figure 8, the proposed algorithm outperforms the other algorithms.
  • Therefore, this pilot preamble will be shortened, implying the proposed method will be an excellent solution to estimate the channel in a practical implementation.
  • Note that the authors can improve the BER for Channel 12 by using the same pilot sequence length as for Channel 14.455 Similar to the results of the simulated channels, the performance difference between the CS-based CE methods and the known channel will be reduced when the length of pilot preamble increases.

6. Conclusion

  • The authors propose an adaptive CS-based parameter estimation algorithm for UWB MB-OFDM systems.
  • Such pilot preamble lengths are often not suitable for practical implementation as they limit the data throughput.
  • Moreover, as the proposed method has low complexity, it is suitable for practical implementation.
  • The authors not only restricted their attention to theoretical channel models, they also evalu-475 ated their algorithm for measured channels obtained with the measurement setup described in this paper.
  • This work is supported by a Belgian EOS grant with project grant number EOS30452698, the Flemish fund for Scientific Research (FWO) and the National Natural Science Foundation of China with grant number 61701531.

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Citations
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Journal ArticleDOI
TL;DR: In this article, chaotic compressive sensing (CS) encryption for OFDM-PON systems is proposed to improve the security of data transmission in orthogonal frequency division multiplexing passive optical networks.
Abstract: In this paper, we propose chaotic compressive sensing (CS) encryption algorithms for orthogonal frequency division multiplexing passive optical network (OFDM-PON), aiming at compressing the transmitted data and enhancing the security of data transmission. Bitstream transmission using CS directly is restricted due to its inability to satisfy the sparsity in neither time nor frequency domain. While the sparsity of the transmitted data can be constructed when transmitting the multimedia. A sensor can be then used to identify whether the data is multimedia. If it is, the CS technique is used, and the sensor’s result is set as side information inserted into the pilot and transmitted to the terminal simultaneously. For encryption processing, a 2-dimensional logistic-sine-coupling map (2D-LSCM) is used to generate pseudo-random numbers to construct the first row of a measurement matrix to encrypt the system. Four transform formats are then applied to generate the sparsity of the transmitted data. Due to the restriction of data transmission in the physical layer, the discrete cosine transform (DCT) is chosen to conduct the CS technique. Four approximation algorithms are also proposed to optimize the performance of compressing the length of bits. We find that ‘Round + Set negative to 0’ shows the best performance. The combination of this chaotic CS encryption technique with the OFDM-PON systems saves the bandwidth and improves the security.

32 citations

Journal ArticleDOI
TL;DR: In this paper, the mechanism of narrowband suppressive jamming on ultra-wideband radio impulse detection radar is mathematically analyzed at first in order to realize adaptive extraction of the impulse signal.

4 citations

Journal ArticleDOI
TL;DR: In this paper , an iterative method that estimates the sparse channel and recovers the original signal, referred to as SCE-DSD, is proposed in order to reduce the overhead of the system due to the large number of pilot subcarriers required.
Abstract: Nonlinear distortions generated by the power amplifier (PA) will affect the performance of channel estimation thus the veracity of signal detection for ultra-wideband (UWB) orthogonal frequency-division multiplexing (OFDM) systems. The existing nonlinear cancellation techniques for tackling this problem reduce the overhead of the system due to the large number of pilot subcarriers required. As the UWB channel can usually be modeled as sparse, an iterative method that estimates the sparse channel and recovers the original signal, referred to as SCE-DSD, is proposed in this letter. Involving the nonlinear distortion in the measurement matrix construction, SCE-DSD estimates the channel and the original signal sequentially. The numerical results show that, compared to the state-of-the-art method, the proposed method has a better performance using a smaller number of pilot subcarriers.

2 citations

Journal ArticleDOI
TL;DR: Two approximate PC robust estimators are derived by tackling two upper bounds of the original optimization problem and converting them to semidefinite programming problems with the safe tractable approximation techniques and demonstrate that there is a tradeoff between the MSE performance and computation complexity in the proposed two PC estimators.

1 citations

Proceedings ArticleDOI
04 Aug 2021
TL;DR: In this paper, a new technique for 5G cellular networks in multiple access (MA) called Power domain sparse code multiple access is proposed, where a hybrid of both code domain and power domain resource elements are used to transmit encoded signals of multiple users over a set of subcarriers or frequencies simultaneously.
Abstract: A new technique for fifth-generation (5G) cellular networks in Multiple Access (MA) called Power domain sparse code multiple access (PSMA) is proposed in this paper. It is then analyzed using resolute decoding and dynamic decoding respectively. In PSMA, a hybrid of both code domain and power domain resource elements are used to transmit encoded signals of multiple users over a set of subcarriers or frequencies simultaneously. Same codebook is used by more than one user whereas, for these users with the same codebook, encoded signals are sent non-orthogonally using Power Domain Non-Orthogonal Multiple Access (PD-NOMA) technique. Inter-cell interference is caused in-between users because of the usage of the same codebook for multiple users at any given point of time. Especially, the receiver part of the PSMA system has been utilized, where the main focus is inclined towards solving the bi-pirate graph/ Factor graph. This graph is formed from the many to many relationships between the Factor nodes and Variable nodes. Our primary analysis showed improved decoding accuracy as well as effective spectral usage if this system is made to work dynamically. So, to tackle these new parameters, this research work has developed a hybrid system that performs user detection by using compressive sensing algorithm and then data detection of these active users is done by using message passing algorithm (MPA). This system considers the multiple users present in a single cell. This paper mainly focuses to maximize the system's resource allocation capacity and error correcting capability when it is subjected to a similar set of network and resource constraints. The proposed system formulates a set of N users, where K users are actively considered. Decoding is done by using Orthogonal Matching Pursuit-Message Passing Algorithm (OMP-MPA). Finally, the effectiveness of the proposed decoder is investigated using numerical results and corresponding graphs.

1 citations

References
More filters
Book
D.L. Donoho1
01 Jan 2004
TL;DR: It is possible to design n=O(Nlog(m)) nonadaptive measurements allowing reconstruction with accuracy comparable to that attainable with direct knowledge of the N most important coefficients, and a good approximation to those N important coefficients is extracted from the n measurements by solving a linear program-Basis Pursuit in signal processing.
Abstract: Suppose x is an unknown vector in Ropfm (a digital image or signal); we plan to measure n general linear functionals of x and then reconstruct. If x is known to be compressible by transform coding with a known transform, and we reconstruct via the nonlinear procedure defined here, the number of measurements n can be dramatically smaller than the size m. Thus, certain natural classes of images with m pixels need only n=O(m1/4log5/2(m)) nonadaptive nonpixel samples for faithful recovery, as opposed to the usual m pixel samples. More specifically, suppose x has a sparse representation in some orthonormal basis (e.g., wavelet, Fourier) or tight frame (e.g., curvelet, Gabor)-so the coefficients belong to an lscrp ball for 0

18,609 citations

Journal ArticleDOI
TL;DR: In this paper, the authors considered the model problem of reconstructing an object from incomplete frequency samples and showed that with probability at least 1-O(N/sup -M/), f can be reconstructed exactly as the solution to the lscr/sub 1/ minimization problem.
Abstract: This paper considers the model problem of reconstructing an object from incomplete frequency samples. Consider a discrete-time signal f/spl isin/C/sup N/ and a randomly chosen set of frequencies /spl Omega/. Is it possible to reconstruct f from the partial knowledge of its Fourier coefficients on the set /spl Omega/? A typical result of this paper is as follows. Suppose that f is a superposition of |T| spikes f(t)=/spl sigma//sub /spl tau//spl isin/T/f(/spl tau/)/spl delta/(t-/spl tau/) obeying |T|/spl les/C/sub M//spl middot/(log N)/sup -1/ /spl middot/ |/spl Omega/| for some constant C/sub M/>0. We do not know the locations of the spikes nor their amplitudes. Then with probability at least 1-O(N/sup -M/), f can be reconstructed exactly as the solution to the /spl lscr//sub 1/ minimization problem. In short, exact recovery may be obtained by solving a convex optimization problem. We give numerical values for C/sub M/ which depend on the desired probability of success. Our result may be interpreted as a novel kind of nonlinear sampling theorem. In effect, it says that any signal made out of |T| spikes may be recovered by convex programming from almost every set of frequencies of size O(|T|/spl middot/logN). Moreover, this is nearly optimal in the sense that any method succeeding with probability 1-O(N/sup -M/) would in general require a number of frequency samples at least proportional to |T|/spl middot/logN. The methodology extends to a variety of other situations and higher dimensions. For example, we show how one can reconstruct a piecewise constant (one- or two-dimensional) object from incomplete frequency samples - provided that the number of jumps (discontinuities) obeys the condition above - by minimizing other convex functionals such as the total variation of f.

14,587 citations

Journal ArticleDOI
TL;DR: It is demonstrated theoretically and empirically that a greedy algorithm called orthogonal matching pursuit (OMP) can reliably recover a signal with m nonzero entries in dimension d given O(m ln d) random linear measurements of that signal.
Abstract: This paper demonstrates theoretically and empirically that a greedy algorithm called orthogonal matching pursuit (OMP) can reliably recover a signal with m nonzero entries in dimension d given O(m ln d) random linear measurements of that signal. This is a massive improvement over previous results, which require O(m2) measurements. The new results for OMP are comparable with recent results for another approach called basis pursuit (BP). In some settings, the OMP algorithm is faster and easier to implement, so it is an attractive alternative to BP for signal recovery problems.

8,604 citations


"Parameter estimation and channel re..." refers background in this paper

  • ...subspace pursuit (SP) [17], orthogonal matching pursuit (OMP) [18] and compressive sampling matching pursuit (CoSaMP) [19], to accurately reconstruct the CIR....

    [...]

  • ...In [8], the applicability of CS for UWB channel estimation is investigated, and the authors employ standard Matching Pursuit (MP) algorithms for CS, such as35 subspace pursuit (SP) [17], orthogonal matching pursuit (OMP) [18] and compressive sampling matching pursuit (CoSaMP) [19], to accurately reconstruct the CIR....

    [...]

  • ...(17) This convex optimization problem can be solved using linear programming techniques like subspace pursuit (SP), orthogonal match pursuit (OMP) and compressive sampling matching pursuit (CoSaMP)....

    [...]

  • ...385 Next, we evaluate the performance of the proposed channel estimator and compare the results with the performance of OMP, SP and CoSaMP....

    [...]

  • ...This can be attributed to the optimized dictionary size and sparsity in our method, resulting in a more accurate reconstruction of the 0 5 10 15 20 25 30 E b /N o (dB) 10-2 10-1 100 101 N M S E OMP SP CoSaMP the proposed algorithm the BER results, we observe that the proposed method outperforms all other CEs, although the gap with the BER of the known channel is still relatively large....

    [...]

01 Aug 2007
TL;DR: In this paper, a greedy algorithm called Orthogonal Matching Pursuit (OMP) was proposed to recover a signal with m nonzero entries in dimension 1 given O(m n d) random linear measurements of that signal.
Abstract: This report demonstrates theoretically and empirically that a greedy algorithm called Orthogonal Matching Pursuit (OMP) can reliably recover a signal with m nonzero entries in dimension d given O(mln d) random linear measurements of that signal. This is a massive improvement over previous results, which require O(m2) measurements. The new results for OMP are comparable with recent results for another approach called Basis Pursuit (BP). In some settings, the OMP algorithm is faster and easier to implement, so it is an attractive alternative to BP for signal recovery problems.

7,124 citations

Journal ArticleDOI
TL;DR: A new iterative recovery algorithm called CoSaMP is described that delivers the same guarantees as the best optimization-based approaches and offers rigorous bounds on computational cost and storage.

3,970 citations


"Parameter estimation and channel re..." refers background or methods in this paper

  • ...In this paper, we extend the CoSaMP algorithm from [19], which combines low complexity and good CE performance, to autonomously estimate the required channel parameters....

    [...]

  • ...From [19], the number of complex multiplications required in the CoSaMP algorithm equals O{Mtaps log2(Mtaps) log2(Ks)}....

    [...]

  • ...subspace pursuit (SP) [17], orthogonal matching pursuit (OMP) [18] and compressive sampling matching pursuit (CoSaMP) [19], to accurately reconstruct the CIR....

    [...]

  • ...Effect of the Dictionary Size and Sparsity To solve the l1-norm optimization problem discussed in the previous section, we will employ the CoSaMP algorithm [19], as it combines good estimation accuracy with low complexity....

    [...]

Frequently Asked Questions (1)
Q1. What have the authors contributed in "Parameter estimation and channel reconstruction based on compressive sensing for ultra-wideband mb-ofdm systems" ?

Therefore, in this paper, the authors propose a CSbased channel parameter estimation method to estimate the dictionary size and the sparsity based on a pilot preamble of which the duration is shorter than the total duration of the CIR. The authors show that the proposed algorithm is able to accurately estimate the sparsity and the dictionary size, and can effectively reconstruct the CIR for channels that are either based on a mathematical model or real, measured channels. Moreover, as the algorithm has acceptable complexity, the proposed ∗Corresponding author Email address: Taoyong.