Transmit Precoding for MIMO Systems with Partial CSI and Discrete-Constellation Inputs

In this paper, we consider the transmit linear precoding problem for MIMO systems with discrete-constellation inputs. We assume that the receiver has perfect channel state information (CSI) and the transmitter only has partial CSI, namely, the channel covariance information. We first consider MIMO systems over frequency-flat fading channels. We design the optimal linear precoder based on direct maximization of mutual information over the MIMO channels with discrete-constellation inputs. It turns out that the optimal linear precoder is a non-diagonal non-unitary matrix. Then, we consider MIMO systems over frequency selective fading channels via extending our method to MIMO-OFDM systems. To keep reasonable computational complexity of solving the linear precoding matrix, we propose a sub-optimal approach to restrict the precoding matrix as a block-diagonal matrix. This approach has near-optimal performance when we integrate it with a properly chosen interleaver. Numerical examples show that for MIMO systems over frequency flat fading channels, our proposed optimal linear precoder enjoys 6-9 dB gain compared to the same system without linear precoder. For MIMO-OFDM systems, our reduced-complexity sub-optimal linear precoder captures 3-6 dB gain compared to the same system with no precoding. Moreover, for those MIMO systems employing a linear precoder designed based on Gaussian inputs with gap approximation technique for discrete-constellation inputs, significant loss may occur when the signal-to-noise ratio is larger than 0 dB

Linear MIMO Precoding in Jointly-Correlated Fading Multiple Access Channels with Finite Alphabet Signaling

In this paper, we investigate the design of linear precoders for multiple-input multiple-output (MIMO) multiple access channels (MAC). We assume that statistical channel state information (CSI) is available at the transmitters and consider the problem under the practical finite alphabet input assumption. First, we derive an asymptotic (in the large-system limit) weighted sum rate (WSR) expression for the MIMO MAC with finite alphabet inputs and general jointly-correlated fading. Subsequently, we obtain necessary conditions for linear precoders maximizing the asymptotic WSR and propose an iterative algorithm for determining the precoders of all users. In the proposed algorithm, the search space of each user for designing the precoding matrices is its own modulation set. This significantly reduces the dimension of the search space for finding the precoding matrices of all users compared to the conventional precoding design for the MIMO MAC with finite alphabet inputs, where the search space is the combination of the modulation sets of all users. As a result, the proposed algorithm decreases the computational complexity for MIMO MAC precoding design with finite alphabet inputs by several orders of magnitude. Simulation results for finite alphabet signalling indicate that the proposed iterative algorithm achieves significant performance gains over existing precoder designs, including the precoder design based on the Gaussian input assumption, in terms of both the sum rate and the coded bit error rate.Comment: 7 pages, 2 figures, accepted for ICC1

An Overview of Physical Layer Security with Finite-Alphabet Signaling

Providing secure communications over the physical layer with the objective of achieving perfect secrecy without requiring a secret key has been receiving growing attention within the past decade. The vast majority of the existing studies in the area of physical layer security focus exclusively on the scenarios where the channel inputs are Gaussian distributed. However, in practice, the signals employed for transmission are drawn from discrete signal constellations such as phase shift keying and quadrature amplitude modulation. Hence, understanding the impact of the finite-alphabet input constraints and designing secure transmission schemes under this assumption is a mandatory step towards a practical implementation of physical layer security. With this motivation, this article reviews recent developments on physical layer security with finite-alphabet inputs. We explore transmit signal design algorithms for single-antenna as well as multi-antenna wiretap channels under different assumptions on the channel state information at the transmitter. Moreover, we present a review of the recent results on secure transmission with discrete signaling for various scenarios including multi-carrier transmission systems, broadcast channels with confidential messages, cognitive multiple access and relay networks. Throughout the article, we stress the important behavioral differences of discrete versus Gaussian inputs in the context of the physical layer security. We also present an overview of practical code construction over Gaussian and fading wiretap channels, and we discuss some open problems and directions for future research.Comment: Submitted to IEEE Communications Surveys & Tutorials (1st Revision