On the Performance of Turbo Signal Recovery with Partial DFT Sensing Matrices

This letter is on the performance of the turbo signal recovery (TSR) algorithm for partial discrete Fourier transform (DFT) matrices based compressed sensing. Based on state evolution analysis, we prove that TSR with a partial DFT sensing matrix outperforms the well-known approximate message passing (AMP) algorithm with an independent identically distributed (IID) sensing matrix.Comment: to appear in IEEE Signal Processing Letter

Over-the-Air Federated Learning Over MIMO Channels: A Sparse-Coded Multiplexing Approach

The communication bottleneck of over-the-air federated learning (OA-FL) lies in uploading the gradients of local learning models. In this paper, we study the reduction of the communication overhead in the gradients uploading by using the multiple-input multiple-output (MIMO) technique. We propose a novel sparse-coded multiplexing (SCoM) approach that employs sparse-coding compression and MIMO multiplexing to balance the communication overhead and the learning performance of the FL model. We derive an upper bound on the learning performance loss of the SCoM-based MIMO OA-FL scheme by quantitatively characterizing the gradient aggregation error. Based on the analysis results, we show that the optimal number of multiplexed data streams to minimize the upper bound on the FL learning performance loss is given by the minimum of the numbers of transmit and receive antennas. We then formulate an optimization problem for the design of precoding and post-processing matrices to minimize the gradient aggregation error. To solve this problem, we develop a low-complexity algorithm based on alternating optimization (AO) and alternating direction method of multipliers (ADMM), which effectively mitigates the impact of the gradient aggregation error. Numerical results demonstrate the superb performance of the proposed SCoM approach

Sparsity Enhanced Decision Feedback Equalization

For single-carrier systems with frequency domain equalization, decision feedback equalization (DFE) performs better than linear equalization and has much lower computational complexity than sequence maximum likelihood detection. The main challenge in DFE is the feedback symbol selection rule. In this paper, we give a theoretical framework for a simple, sparsity based thresholding algorithm. We feed back multiple symbols in each iteration, so the algorithm converges fast and has a low computational cost. We show how the initial solution can be obtained via convex relaxation instead of linear equalization, and illustrate the impact that the choice of the initial solution has on the bit error rate performance of our algorithm. The algorithm is applicable in several existing wireless communication systems (SC-FDMA, MC-CDMA, MIMO-OFDM). Numerical results illustrate significant performance improvement in terms of bit error rate compared to the MMSE solution