Theoretical Linear Convergence of Deep Unfolding Network for Block-Sparse Signal Recovery

In this paper, we consider the recovery of the high-dimensional block-sparse signal from a compressed set of measurements, where the non-zero coefficients of the recovered signal occur in a small number of blocks. Adopting the idea of deep unfolding, we explore the block-sparse structure and put forward a block-sparse reconstruction network named Ada-BlockLISTA, which performs gradient descent on every single block followed by a block-wise shrinkage. Furthermore, we prove the linear convergence rate of our proposed network, which also theoretically guarantees exact recovery for a potentially higher sparsity level based on underlyingblock structure. Numerical results indicate that Ada-BlockLISTA yields better signal recovery performance compared with existing algorithms, which ignore the additional block structure in the signal model.

Block-Sparse Recovery Network for Two-Dimensional Harmonic Retrieval

As a typical signal processing problem, multidimensional harmonic retrieval (MHR) has been adapted to a wide range of applications in signal processing. Block-sparse signals, whose nonzero entries appearing in clusters, have received much attention recently. An unfolded network, named Ada-BlockLISTA, was proposed to recover a block-sparse signal at a small computational cost, which learns an individual weight matrix for each block. However, as the number of network parameters is increasingly associated with the number of blocks, the demand for parameter reduction becomes very significant, especially for large-scale MHR. Based on the dictionary characteristics in two-dimensional (2D) harmonic retrieve problems, we introduce a weight coupling structure to shrink Ada-BlockLISTA, which significantly reduces the number of weights without performance degradation. In simulations, our proposed block-sparse reconstruction network, named AdaBLISTA-CP, shows excellent recovery performance and convergence speed in 2D harmonic retrieval problems.

Structured LISTA for Multidimensional Harmonic Retrieval

Learned iterative shrinkage thresholding algorithm (LISTA), which adopts deep learning techniques to learn optimal algorithm parameters from labeled training data, can be successfully applied to small-scale multidimensional harmonic retrieval (MHR) problems. However, LISTA computationally demanding for large-scale MHR problems because the matrix size of the learned mutual inhibition matrix exhibits quadratic growth with the signal length. These large matrices consume costly memory/computation resources and require a huge amount of labeled data for training, restricting the applicability of the LISTA method. In this paper, we show that the mutual inhibition matrix of a MHR problem naturally has a Toeplitz structure, which means that the degrees of freedom (DoF) of the matrix can be reduced from a quadratic order to a linear order. By exploiting this characteristic, we propose a structured LISTA-Toeplitz network, which imposes a Toeplitz structure restriction on the mutual inhibition matrices and applies linear convolution instead of the matrix-vector multiplication involved in the traditional LISTA network. Both simulation and field test for air target detection with radar are carried out to validate the performance of the proposed network. For small-scale MHR problems, LISTAToeplitz exhibits close or even better recovery accuracy than traditional LISTA, while the former significantly reduces the network complexity and requires much less training data. For large-scale MHR problems, where LISTA is difficult to implement due to the huge size of the mutual inhibition matrices, our proposed LISTA-Toeplitz still enjoys desirable recovery performance.

DeepSIC: Deep Soft Interference Cancellation for Multiuser MIMO Detection

Digital receivers are required to recover the transmitted symbols from their observed channel output. In multiuser multiple-input multiple-output (MIMO) setups, where multiple symbols are simultaneously transmitted, accurate symbol detection is challenging. A family of algorithms capable of reliably recovering multiple symbols is based on interference cancellation. However, these methods assume that the channel is linear, a model which does not reflect many relevant channels, as well as require accurate channel state information (CSI), which may not be available. In this work we propose a multiuser MIMO receiver which learns to jointly detect in a data-driven fashion, without assuming a specific channel model or requiring CSI. In particular, we propose a data-driven implementation of the iterative soft interference cancellation (SIC) algorithm which we refer to as DeepSIC. The resulting symbol detector is based on integrating dedicated machine-learning (ML) methods into the iterative SIC algorithm. DeepSIC learns to carry out joint detection from a limited set of training samples without requiring the channel to be linear and its parameters to be known. Our numerical evaluations demonstrate that for linear channels with full CSI, DeepSIC approaches the performance of iterative SIC, which is comparable to the optimal performance, and outperforms previously proposed ML-based MIMO receivers. Furthermore, in the presence of CSI uncertainty, DeepSIC significantly outperforms model-based approaches. Finally, we show that DeepSIC accurately detects symbols in non-linear channels, where conventional iterative SIC fails even when accurate CSI is available.