Multi-Scale Multi-Lag Channel Estimation Using Low Rank Approximation for OFDM

Sajjad Beygi, Urbashi Mitra
2015 IEEE Transactions on Signal Processing  
This paper considers the estimation of multi-scale multi-lag (MSML) channels. The MSML channel model is a good representation for wideband communication channels, such as underwater acoustic communication and radar. This model is characterized by a limited number of paths, each parameterized by a delay, Doppler scale, and attenuation factor. Herein, it is shown that an OFDM signal after passing through the MSML channel exhibits a low rank representation. This feature can be exploited to improve
more » ... xploited to improve the channel estimation. By characterizing the received signal, it is shown that the MSML channel estimation problem can be adapted to a structured spectral estimation problem. The challenge is that the unknown frequencies are very close to each other due to the small values of Doppler scales. This feature can be employed to show that the data matrix is approximately low-rank. By exploiting structural features of the received signal, the Prony algorithm is modified to estimate the Doppler scales (close frequencies), delays and channel gains. Two strategies using convex and no-convex regularizers to remove noise from the corrupted signal are proposed. These algorithms are iterative based on the alternating direction method of multipliers. A bound on the reconstruction of the noiseless received signal provides guidance on the selection of the relaxation parameter in the optimizations. The performance of the proposed estimation strategies are investigated via numerical simulations, and it is shown that the proposed non-convex method offers up to 7 dB improvement in low SNR and the convex method offers up to 5 dB improvement in high SNR over prior methods for the MSML channel estimation. DRAFT 2 Underwater acoustic channels, Doppler scaling, Multi-scale multi-lag channel, OFDM, ADMM, nonconvex regularizer, sparse approximation, low rank matrices, wideband channel. the use of OFDM for underwater acoustic communications, e.g., [8], [9], [20] . One of the challenges in OFDM is the sensitivity of carrier orthogonality to time-varying multipath and motion-induced Doppler distortion. Therefore, high quality channel estimation is needed for equalization. For narrowband channels, maximum-likelihood (ML) approaches, which reduce to correlation methods, are effective for estimating the Doppler effect [9], [18] . This follows from the fact that in narrowband communication channels, the Doppler effect can be well modeled as a frequency offset. However, MSML channels estimation via ML requires solving a multi-dimensional non-linear least-squares problem, incurring a high complexity and typically requiring an exhaustive search. Due to the sparse nature of the UWA channel, sparse approximation methods [20] [21] [22] have been employed to estimate the MSML channel. The dictionary is based on discretizing the support of the
doi:10.1109/tsp.2015.2449266 fatcat:byxw5fbnwrfhxln7zvreerfpae