A Weighted K-SVD-Based Double Sparse Representations Approach for Wireless Channels Using the Modified Takenaka-Malmquist Basis

In this paper, a new double-sparse representation scheme for wireless channel is proposed based on the modified Takenaka-Malmquist basis (MTMB) functions. Given a series of wireless channel samples with different Doppler shifts, the MTMB functions are first generated from these samples, and then an initial dictionary is constructed by these functions. What is more, the completeness and orthogonality of this dictionary have been proved, which is the theoretical support that the dictionary can be used for the above sparsity model. Second, in order to make the MTMB functions fit into the sparsity model better, a training method is developed to obtain the adaptive public weighted MTMB (PWMTMB) functions based on the proposed weighted K-SVD algorithm. In this method, the unnecessary extra storage and computational complexity can be reduced by only storing the basis functions strongly associated with the wireless channels in the initial dictionary. Besides, different weights are given to the basis functions according to the prior information of these channels, so each has the proper level of influence in the weighted sparse coding stage of the weighted K-SVD algorithm. As a result, sparser representations of wireless channels can be achieved through these PWMTMB functions. In addition, the proposed method can also be implemented in parallel via updating multiple basis functions each time, forming the parallel PWMTMB (PPWMTMB) functions which can also be used as the sparse basis functions for these channels. Our results show that the PWMTMB and the PPWMTMB are able to suit these types of wireless channels, giving a sparse representation per each.