Recursive least square–based fast sparse multipath channel estimation

Abstract

In the next-generation wireless communication systems, the broadband signal transmission over wireless channel often incurs the frequency-selective channel fading behavior and also results in the channel sparse structure, which is supported only by few large coefficients. For the stable wireless propagation to be ensured, linear adaptive channel estimation algorithms, eg, recursive least square and least mean square, have been developed. However, these traditional algorithms are unable to exploit the channel sparsity. Actually, channel estimation performance can be further improved by taking advantage of the sparsity. In this paper, 2 recursive least squarebased fast adaptive sparse channel estimation algorithm is proposed by introducing sparse constraints, L1-norm and L0-norm, respectively. To improve the flexibility of the proposed algorithms, this paper introduces a regularization parameter selection method to adaptively exploit the channel sparsity. Finally, Monte Carlo-based computer simulations are conducted to validate the effectiveness of the proposed algorithms.KEYWORDS adaptive filtering algorithm, recursive least square, sparse channel estimation, sparse constraintBroadband wireless transmission has been considered one of indispensable technologies for the next-generation wireless communications. 1-3 However, wireless signal transmission over the frequency-selective fading channel, accurate channel estimation is necessary to reconstruct finite impulse response (FIR). Currently, adaptive filtering algorithms can be acted as effective channel estimation because of their fast convergence and robust performance. Hence, various adaptive filtering algorithms have been developed during the last few years. On the basis of second-order statistical error criterion, least mean square (LMS) 4,5 and recursive least square (RLS) 5 have been developed.On the basis of fourth-order statistical error criterion, least mean fourth (LMF) 6,7 and (LMS/F) 8,9 have been developed as well. However, these kinds of linear channel estimation algorithms have not been considered to exploit channel sparsity in wireless channels. The channel estimation performance can be improved if we take the advantage of the prior sparsity information.For channel sparsity to be exploited, various sparse LMStype algorithms 10-12 have been proposed. Also, sparse LMF algorithms 7,13-16 and sparse LMS/F algorithms 14,17,18 have been developed in recent years. All of the mentioned sparse channel estimation algorithms based on error criterion function, hence, corresponding sparse channel estimation algorithms can keep the same convergence speed. It is well known that RLS algorithm can achieve faster convergence speed than LMS algorithm, 19 and it does not bring the eigenvalue spread problem. 5 The LMS algorithm aims to reduce the mean square error while the RLS algorithm finds the coefficients recursively to minimize a weighted linear least squares cost function relating to the input training signals. 5 In addition, in the derivation of the LMS and RLS,...

A Modified Recursive Regularization Factor Calculation for Sparse RLS Algorithm with l1-Norm

“…Substituting ( 16) with (17) and P(n) ∼ = σ −2 x (1 − λ)I, the variable regularization factor in (16) becomes the following:…”

“…The authors in [13] also proposed a regularization factor calculation method for the SRLS algorithm. Similar recursive regularization factor selection methods were used in [15][16][17][18][19]. However, the algorithm from [15][16][17][18] is not practical because the regularization factor in [15][16][17] assumed that the true system impulse response is known in advance and set the true system response in part to an arbitrary constant in [18].…”

“…Similar recursive regularization factor selection methods were used in [15][16][17][18][19]. However, the algorithm from [15][16][17][18] is not practical because the regularization factor in [15][16][17] assumed that the true system impulse response is known in advance and set the true system response in part to an arbitrary constant in [18]. The regularization factor selection method in [19] needs no true system impulse response.…”

Regularization Factor Selection Method for l1-Regularized RLS and Its Modification against Uncertainty in the Regularization Factor

“…The sparse RIR model is useful for estimating RIRs in real acoustic environments when the source is given a priori [10]. There has been recent interest in adaptive algorithms for sparsity in various signals and systems [11][12][13][14][15][16][17][18][19][20][21][22]. Many adaptive algorithms based on least mean square (LMS) [11,12] and recursive least squares (RLS) [14][15][16][17] have been reported with different penalty functions.…”

“…The regularization factor calculation method requires information about a true sparse channel response for a good performance. The authors in [18,19] have also proposed recursive regularization factor selection methods; however, these methods still need the true impulse response in advance.…”