On the capacity of multiple-antenna systems and parallel Gaussian channels with amplitude-limited inputs

We propose upper and lower bounds on the capacity of multiple-input multiple-output (MIMO) systems with amplitude-limited inputs. The results are derived by considering an equivalent channel via singular value decomposition, and by enlarging and reducing the corresponding feasible region of the channel input vector, for the upper and lower bounds, respectively. We analytically characterize the asymptotic behavior of the derived bounds for high and low noise levels, and study the gap between them. We also consider parallel Gaussian channels with peak and average power-constrained inputs. For such channels, the capacity-achieving distribution has been reported in the literature to be discrete, which can be computed using numerical optimization techniques. However, there is no closed-form expression and finding the capacity-achieving distribution is computationally tedious. With this motivation, we derive approximate expressions for the capacity at low and high noise variance levels. We illustrate our findings on both MIMO channels and parallel Gaussian channels via several numerical examples. © 1972-2012 IEEE

On source and channel codes for multiple inputs and outputs: does multiple description beat space time?

We compare two strategies for lossy source description across a pair of unreliable channels. In the first strategy, we use a broadcast channel code to achieve a different rate for each possible channel realization, and then use a multiresolution source code to describe the source at the resulting rates. In the second strategy, we use a channel coding strategy for two independent channels coupled with a multiple description source code. In each case, we choose the coding parameters to minimize the expected end-to-end distortion in the source reconstruction. We demonstrate that in point-to-point communication across a pair of non-ergodic channels, multiple description coding can provide substantial gains relative to multiresolution and broadcast coding. We then investigate this comparison in a simple MIMO channel. We demonstrate the inferior performance of space time coding with multiresolution source coding and broadcast channel coding relative to multiple description codes and a time sharing channel coding strategy. These results indicate that for non-ergodic channels, the traditional definition of channel capacity does not necessarily lead to the best channel code from the perspective of end-to-end source distortion

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

Linear Precoding for MIMO Channels with QAM Constellations and Reduced Complexity

In this paper, the problem of designing a linear precoder for Multiple-Input Multiple-Output (MIMO) systems in conjunction with Quadrature Amplitude Modulation (QAM) is addressed. First, a novel and efficient methodology to evaluate the input-output mutual information for a general Multiple-Input Multiple-Output (MIMO) system as well as its corresponding gradients is presented, based on the Gauss-Hermite quadrature rule. Then, the method is exploited in a block coordinate gradient ascent optimization process to determine the globally optimal linear precoder with respect to the MIMO input-output mutual information for QAM systems with relatively moderate MIMO channel sizes. The proposed methodology is next applied in conjunction with the complexity-reducing per-group processing (PGP) technique, which is semi-optimal, to both perfect channel state information at the transmitter (CSIT) as well as statistical channel state information (SCSI) scenarios, with high transmitting and receiving antenna size, and for constellation size up to $M=64$. We show by numerical results that the precoders developed offer significantly better performance than the configuration with no precoder, and the maximum diversity precoder for QAM with constellation sizes $M=16,~32$, and $~64$ and for MIMO channel size $100\times100$

Unified Capacity Limit of Non-coherent Wideband Fading Channels

In non-coherent wideband fading channels where energy rather than spectrum is the limiting resource, peaky and non-peaky signaling schemes have long been considered species apart, as the first approaches asymptotically the capacity of a wideband AWGN channel with the same average SNR, whereas the second reaches a peak rate at some finite critical bandwidth and then falls to zero as bandwidth grows to infinity. In this paper it is shown that this distinction is in fact an artifact of the limited attention paid in the past to the product between the bandwidth and the fraction of time it is in use. This fundamental quantity, called bandwidth occupancy, measures average bandwidth usage over time. For all signaling schemes with the same bandwidth occupancy, achievable rates approach to the wideband AWGN capacity within the same gap as the bandwidth occupancy approaches its critical value, and decrease to zero as the occupancy goes to infinity. This unified analysis produces quantitative closed-form expressions for the ideal bandwidth occupancy, recovers the existing capacity results for (non-)peaky signaling schemes, and unveils a trade-off between the accuracy of approximating capacity with a generalized Taylor polynomial and the accuracy with which the optimal bandwidth occupancy can be bounded.Comment: Accepted for publication in IEEE Transactions on Wireless Communications. Copyright may be transferred without notic