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In this paper, we study joint antenna activity detection, channel estimation, and multiuser detection for massive multiple-input multiple-output (MIMO) systems with general spatial modulation (GSM). We first establish a double-sparsity massive MIMO model by considering the channel sparsity of the massive MIMO channel and the signal sparsity of GSM. Based on the double-sparsity model, we formulate a blind detection problem. To solve the blind detection problem, we develop message-passing based blind channel-and-signal estimation (BCSE) algorithm. The BCSE algorithm basically follows the affine sparse matrix factorization technique, but with critical modifications to handle the double-sparsity property of the model. We show that the BCSE algorithm significantly outperforms the existing blind and training-based algorithms, and is able to closely approach the genie bounds (with either known channel or known signal). In the BCSE algorithm, short pilots are employed to remove the phase and permutation ambiguities after sparse matrix factorization. To utilize the short pilots more efficiently, we further develop the semi-blind channel-and-signal estimation (SBCSE) algorithm to incorporate the estimation of the phase and permutation ambiguities into the iterative message-passing process. We show that the SBCSE algorithm substantially outperforms the counterpart algorithms including the BCSE algorithm in the short-pilot regime.

Multicarrier modulation in the form of orthogonal frequency-division-multiplexing (OFDM) has been actively pursued in underwater acoustic communications. However, carrier frequency offset (CFO) can cause significant performance degradation in OFDM systems. Although underwater acoustic communication was recently the focus of research, literatures about joint interference mitigation with channel estimation using compressed sensing (CS) has been very limited in underwater acoustic OFDM. In the Cyclic prefix orthogonal frequency division multiplexing (CP-OFDM) system, a novel method was proposed which combined interference mitigation with channel estimation based on compressed sensing (CS).The novel joint optimization model combined CFO estimation with CS-based channel estimation based on the sparse in the delay-Doppler domain by using the null sub-carriers. Simulations and tank experiments have verified the performance of the receiver based on the joint interference mitigation and CS channel estimation. This method enables the OFDM system is effective against the CFO, and has better robustness.