This survey provides a brief introduction to compressed sensing as well as several major algorithms to solve it and its various applications to communications systems. We firstly review linear simultaneous equations as ill-posed inverse problems, since the idea of compressed sensing could be best understood in the context of the linear equations. Then, we consider the problem of compressed sensing as an underdetermined linear system with a prior information that the true solution is sparse, and explain the sparse signal recovery based on l1 optimization, which plays the central role in compressed sensing, with some intuitive explanations on the optimization problem. Moreover, we introduce some important properties of the sensing matrix in order to establish the guarantee of the exact recovery of sparse signals from the underdetermined system. After summarizing several major algorithms to obtain a sparse solution focusing on the l1 optimization and the greedy approaches, we introduce applications of compressed sensing to communications systems, such as wireless channel estimation, wireless sensor network, network tomography, cognitive radio, array signal processing, multiple access scheme, and networked control

This paper presents a deep learning-aided iterative detection algorithm for massive overloaded multiple-input multiple-output (MIMO) systems where the number of transmit antennas $n$ is larger than that of receive antennas $m$ . Since the proposed algorithm is based on the projected gradient descent method with trainable parameters, it is named the trainable projected gradient-detector (TPG-detector). The trainable internal parameters, such as the step-size parameter, can be optimized with standard deep learning techniques, i.e., the back propagation and stochastic gradient descent algorithms. This approach is referred to as data-driven tuning and ensures fast convergence during parameter estimation in the proposed scheme. The TPG-detector mainly consists of matrix-vector product operations whose computational cost is proportional to $m n$ for each iteration. In addition, the number of trainable parameters in the TPG-detector is independent of the number of antennas. These features of the TPG-detector result in a fast and stable training process and reasonable scalability for large systems. The numerical simulations show that the proposed detector achieves a comparable detection performance to those of the existing algorithms for the massively overloaded MIMO channels, e.g., the state-of-the-art IW-SOAV detector, with a lower computation cost.

This paper proposes signal detection schemes for massive multiple-input multiple-output (MIMO) systems, where the number of receive antennas is less than that of transmitted streams. Assuming practical baseband digital modulation and taking advantage of the discreteness of transmitted symbols, we formulate the signal detection problem as a convex optimization problem, called sum-of-absolute-value (SOAV) optimization. Moreover, we extend the SOAV optimization into the weightedSOAV (W-SOAV) optimization and propose an iterative approach to solve the W-SOAV optimization with updating the weights in the objective function. Furthermore, for coded MIMO systems, we also propose a joint detection and decoding scheme, where log likelihood ratios of transmitted symbols are iteratively updated between the MIMO detector and the channel decoder. In addition, a theoretical performance analysis is provided in terms of the upper bound of the size of the estimation error obtained with the W-SOAV optimization. Simulation results show that the bit error rate performance of the proposed scheme is better than that of conventional schemes, especially in large-scale overloaded MIMO systems.

One limiting issue in implementing high-speed wireless systems is the impairment associated with analog processing due to component imperfections. In uplink transmission of multiuser systems, a major source of such impairment is in-phase/quadrature-phase imbalance (IQI) introduced at multiple transmitters. In this paper, we deal with orthogonal-frequency-division multiple access (OFDMA) and single-carrier frequency-division multiple access (SC-FDMA) which have received attention in recent years as physical layer protocol in WiMAX and 3GPP Long Term Evolution (LTE) and analyze the effect of the transmitter (Tx) IQIs on OFDMA and SC-FDMA receivers. To cope with the interuser interference problem due to Tx IQIs, we propose a widely linear receiver for OFDMA and SC-FDMA systems and also propose a novel subcarrier allocation scheme, which has high tolerance to such Tx IQ distortion.

We propose generic relay and subcarrier allocation schemes for multicarrier (MC) system with amplify-and-forward (AF) relays. The outage probability bounds are derived analytically for each scheme. Simulation results show that these bounds are very tight and better than the bounds obtained straightforwardly from the analysis in the Single-Carrier (SC) case. This is because in our analysis we reckon with the increased degree of freedom brought by the parallel channels. One of the proposed schemes, the Average Best Relay Selection scheme, is best suited for practical implementation since it approaches the best performance while minimizing the required amount of signaling.

Radio resource allocation for downlink transmissions in a cellular system based on orthogonal frequency-division multiple access (OFDMA) has been the subject of many research studies over the past few years. Nowadays, increasing attention has turned to cellular systems with relays, but only a few algorithms have been designed for OFDMA-based relay systems. In this paper, resource-allocation schemes are proposed for the cases of one relay station (RS) and multiple RSs in the cell. Due to the specific design of these algorithms, which operate in an RS-aided base station centralized manner, the amount of required channel-state information and algorithm complexity are minimized, making them suited for practical use. The idea of adaptive RS activation is introduced, where the frame structure is adapted depending on the active RS. Different numbers of relays are considered, and the corresponding algorithms are accordingly adapted. Simulation results show that our algorithms achieve a very good throughput/outage tradeoff.