On the Condition Number Distribution of Complex Wishart Matrices

This paper investigates the distribution of the condition number of complex Wishart matrices. Two closely related measures are considered: the standard condition number (SCN) and the Demmel condition number (DCN), both of which have important applications in the context of multiple-input multipleoutput (MIMO) communication systems, as well as in various branches of mathematics. We first present a novel generic framework for the SCN distribution which accounts for both central and non-central Wishart matrices of arbitrary dimension. This result is a simple unified expression which involves only a single scalar integral, and therefore allows for fast and efficient computation. For the case of dual Wishart matrices, we derive new exact polynomial expressions for both the SCN and DCN distributions. We also formulate a new closed-form expression for the tail SCN distribution which applies for correlated central Wishart matrices of arbitrary dimension and demonstrates an interesting connection to the maximum eigenvalue moments of Wishart matrices of smaller dimension. Based on our analytical results, we gain valuable insights into the statistical behavior of the channel conditioning for various MIMO fading scenarios, such as uncorrelated/semi-correlated Rayleigh fading and Ricean fading. © 2010 IEEE.

A new look at dual-hop relaying: Performance limits with hardware impairments

Physical transceivers have hardware impairments that create distortions which degrade the performance of communication systems. The vast majority of technical contributions in the area of relaying neglect hardware impairments and, thus, assume ideal hardware. Such approximations make sense in low-rate systems, but can lead to very misleading results when analyzing future high-rate systems. This paper quantifies the impact of hardware impairments on dual-hop relaying, for both amplify-and-forward and decode-and-forward protocols. The outage probability (OP) in these practical scenarios is a function of the effective end-to-end signal-to-noise-and-distortion ratio (SNDR). This paper derives new closed-form expressions for the exact and asymptotic OPs, accounting for hardware impairments at the source, relay, and destination. A similar analysis for the ergodic capacity is also pursued, resulting in new upper bounds. We assume that both hops are subject to independent but non-identically distributed Nakagami-m fading. This paper validates that the performance loss is small at low rates, but otherwise can be very substantial. In particular, it is proved that for high signal-to-noise ratio (SNR), the end-to-end SNDR converges to a deterministic constant, coined the SNDR ceiling, which is inversely proportional to the level of impairments. This stands in contrast to the ideal hardware case in which the end-to-end SNDR grows without bound in the high-SNR regime. Finally, we provide fundamental design guidelines for selecting hardware that satisfies the requirements of a practical relaying system.

Variance-Constrained Capacity of the Molecular Timing Channel with Synchronization Error

Molecular communication is set to play an important role in the design of complex biological and chemical systems. An important class of molecular communication systems is based on the timing channel, where information is encoded in the delay of the transmitted molecule - a synchronous approach. At present, a widely used modeling assumption is the perfect synchronization between the transmitter and the receiver. Unfortunately, this assumption is unlikely to hold in most practical molecular systems. To remedy this, we introduce a clock into the model - leading to the molecular timing channel with synchronization error. To quantify the behavior of this new system, we derive upper and lower bounds on the variance-constrained capacity, which we view as the step between the mean-delay and the peak-delay constrained capacity. By numerically evaluating our bounds, we obtain a key practical insight: the drift velocity of the clock links does not need to be significantly larger than the drift velocity of the information link, in order to achieve the variance-constrained capacity with perfect synchronization.

Two-Way Relaying under the Presence of Relay Transceiver Hardware Impairments

Hardware impairments in physical transceivers are known to have a deleterious effect on communication systems; however, very few contributions have investigated their impact on relaying. This paper quantifies the impact of transceiver impairments in a two-way amplify-and-forward configuration. More specifically, the effective signal-to-noise-and-distortion ratios at both transmitter nodes are obtained. These are used to deduce exact and asymptotic closed-form expressions for the outage probabilities (OPs), as well as tractable formulations for the symbol error rates (SERs). It is explicitly shown that non-zero lower bounds on the OP and SER exist in the high-power regime---this stands in contrast to the special case of ideal hardware, where the OP and SER go asymptotically to zero.

On the MIMO Capacity with Residual Transceiver Hardware Impairments

Radio-frequency (RF) impairments in the transceiver hardware of communication systems (e.g., phase noise (PN), high power amplifier (HPA) nonlinearities, or in-phase/quadrature-phase (I/Q) imbalance) can severely degrade the performance of traditional multiple-input multiple-output (MIMO) systems. Although calibration algorithms can partially compensate these impairments, the remaining distortion still has substantial impact. Despite this, most prior works have not analyzed this type of distortion. In this paper, we investigate the impact of residual transceiver hardware impairments on the MIMO system performance. In particular, we consider a transceiver impairment model, which has been experimentally validated, and derive analytical ergodic capacity expressions for both exact and high signal-to-noise ratios (SNRs). We demonstrate that the capacity saturates in the high-SNR regime, thereby creating a finite capacity ceiling. We also present a linear approximation for the ergodic capacity in the low-SNR regime, and show that impairments have only a second-order impact on the capacity. Furthermore, we analyze the effect of transceiver impairments on large-scale MIMO systems; interestingly, we prove that if one increases the number of antennas at one side only, the capacity behaves similar to the finite-dimensional case. On the contrary, if the number of antennas on both sides increases with a fixed ratio, the capacity ceiling vanishes; thus, impairments cause only a bounded offset in the capacity compared to the ideal transceiver hardware case.

Shortening design time through multiplatform simulations with a portable OpenCL golden-model: the LDPC decoder case

Hardware designers and engineers typically need to explore a multi-parametric design space in order to find the best configuration for their designs using simulations that can take weeks to months to complete. For example, designers of special purpose chips need to explore parameters such as the optimal bitwidth and data representation. This is the case for the development of complex algorithms such as Low-Density Parity-Check (LDPC) decoders used in modern communication systems. Currently, high-performance computing offers a wide set of acceleration options, that range from multicore CPUs to graphics processing units (GPUs) and FPGAs. Depending on the simulation requirements, the ideal architecture to use can vary. In this paper we propose a new design flow based on OpenCL, a unified multiplatform programming model, which accelerates LDPC decoding simulations, thereby significantly reducing architectural exploration and design time. OpenCL-based parallel kernels are used without modifications or code tuning on multicore CPUs, GPUs and FPGAs. We use SOpenCL (Silicon to OpenCL), a tool that automatically converts OpenCL kernels to RTL for mapping the simulations into FPGAs. To the best of our knowledge, this is the first time that a single, unmodified OpenCL code is used to target those three different platforms. We show that, depending on the design parameters to be explored in the simulation, on the dimension and phase of the design, the GPU or the FPGA may suit different purposes more conveniently, providing different acceleration factors. For example, although simulations can typically execute more than 3x faster on FPGAs than on GPUs, the overhead of circuit synthesis often outweighs the benefits of FPGA-accelerated execution.

Data Mapping for Unreliable Memories

Future digital signal processing (DSP) systems must provide robustness on algorithm and application level to the presence of reliability issues that come along with corresponding implementations in modern semiconductor process technologies. In this paper, we address this issue by investigating the impact of unreliable memories on general DSP systems. In particular, we propose a novel framework to characterize the effects of unreliable memories, which enables us to devise novel methods to mitigate the associated performance loss. We propose to deploy specifically designed data representations, which have the capability of substantially improving the system reliability compared to that realized by conventional data representations used in digital integrated circuits, such as 2's-complement or sign-magnitude number formats. To demonstrate the efficacy of the proposed framework, we analyze the impact of unreliable memories on coded communication systems, and we show that the deployment of optimized data representations substantially improves the error-rate performance of such systems.