Tharmalingam Ratnarajah

On the Performance of Eigenvalue-Based Cooperative Spectrum Sensing for Cognitive Radio

In this paper, the distribution of the ratio of extreme eigenvalues of a complex Wishart matrix is studied in order to calculate the exact decision threshold as a function of the desired probability of false alarm for the maximum-minimum eigenvalue (MME) detector. In contrast to the asymptotic analysis reported in the literature, we consider a finite number of cooperative receivers and a finite number of samples and derive the exact decision threshold for the probability of false alarm. The proposed exact formulation is further reduced to the case of two receiver-based cooperative spectrum sensing. In addition, an approximate closed-form formula of the exact threshold is derived in terms of a desired probability of false alarm for a special case having equal number of receive antennas and signal samples. Finally, the derived analytical exact decision thresholds are verified with Monte-Carlo simulations. We show that the probability of detection performance using the proposed exact decision thresholds achieves significant performance gains compared to the performance of the asymptotic decision threshold.

Power Allocation and Beamforming in Overlay Cognitive Radio Systems

We consider the overlay cognitive radio channel where the cognitive user is admitted to transmit simultaneously with the primary user provided that the instantaneous rate of primary link is not degraded. Assuming causal knowledge of the primary users message at the cognitive transmitter (CT), we analyze the transmission rates of the cognitive user in the single-input multiple-output (SIMO) and the multiple-input single-output (MISO) configurations. In particular, the CT uses a part of its transmit power to assist the primary user in delivering the primary users message and the other part of its power is used to deliver its own message. The transmit power and the beamformers are designed to maximize the rate of the cognitive user while fixing the the rate of the primary user. Our simulation results show that the proposed scheme yields improved system performance compared to the interweave scheme where any interference to the primary user is prohibited.

A Minorization-Maximization Method for Optimizing Sum Rate in the Downlink of Non-Orthogonal Multiple Access Systems

Non-orthogonal multiple access (NOMA) systems have the potential to deliver higher system throughput, compared with contemporary orthogonal multiple access techniques. For a linearly precoded multiple-input single-output (MISO) system, we study the downlink sum rate maximization problem, when the NOMA principle is applied. Being a non-convex and intractable optimization problem, we resort to approximate it with a minorization-maximization algorithm (MMA), which is a widely used tool in statistics. In each step of the MMA, we solve a second-order cone program, such that the feasibility set in each step contains that of the previous one, and is always guaranteed to be a subset of the feasibility set of the original problem. It should be noted that the algorithm takes a few iterations to converge. Furthermore, we study the conditions under which the achievable rates maximization can be further simplified to a low complexity design problem, and we compute the probability of occurrence of this event. Numerical examples are conducted to show a comparison of the proposed approach against conventional multiple access systems.

Eigenvalues and Condition Numbers of Complex Random Matrices

In this paper, the distributions of the largest and smallest eigenvalues of complex Wishart matrices and the condition number of complex Gaussian random matrices are derived. These distributions are represented by complex hypergeometric functions of matrix arguments, which can be expressed in terms of complex zonal polynomials. Several results are derived on complex hypergeometric functions and complex zonal polynomials and are used to evaluate these distributions. Finally, applications of these distributions in numerical analysis and statistical hypothesis testing are mentioned.

Quadratic forms on complex random matrices and multiple-antenna systems

In this correspondence, the densities of quadratic forms on complex random matrices and their joint eigenvalue densities are derived for applications to information theory. These densities are represented by complex hypergeometric functions of matrix arguments, which can be expressed in terms of complex zonal polynomials. The derived densities are used to evaluate the two most important information-theoretic measures, the so-called ergodic channel capacity and capacity versus outage of multiple-input multiple-output (MIMO) spatially correlated Rayleigh-distributed wireless communication channels. We also derive the probability density function of the mutual information between transmitted and received complex signals of MIMO systems with a finite number of transmit and receive antennas. Numerical results show how channel correlation degrades the capacity of MIMO communication systems.

Interference Optimization for Transmit Power Reduction in Tomlinson-Harashima Precoded MIMO Downlinks

A novel strategy for reducing the power loss in Tomlinson-Harashima precoding (THP) is explored in this paper, based on optimizing the interference to be canceled. A multiple input multiple output (MIMO) downlink transmission is considered and the proposed strategy is motivated by the fact that both the desired and interfering signals originate from the base station (BS) of the downlink system itself. The resulting interference can therefore be influenced to reduce the transmission power required to cancel it, without altering the information content of the downlink message. This optimization aims at bringing the interference closer to the replicas of the desired symbols for all users in the THP modulo-extended constellation. By doing so, the quantized distance between the useful signal and interference is reduced and therefore the power required to presubtract interference is decreased. Based on this concept, a new practical THP transmitter for multiple input multiple output systems (MIMO-THP) is designed. The effect of the interference optimization is studied by means of mathematical analysis and simulation and towards this end, the Gaussian-Modulo distribution is derived and used to describe the distribution of the modulo-precoded transmitted symbols. This is proven to provide a closer approximation of the power loss for both conventional and proposed MIMO-THP techniques, compared to the approximation based on the uniform distribution used in the literature. Theoretical and simulation results both confirm that, by optimizing the interference to be canceled, the proposed technique offers a considerable transmit power reduction compared to conventional THP while securing a slightly improved error rate performance.

On the Study of Network Coded AF Transmission Protocol for Wireless Multiple Access Channels

In this paper, the performance of the network coded amplify-forward cooperative protocol is studied. The use of network coding can suppress the bandwidth resource consumed by relay transmission, and hence increase the spectral efficiency of cooperative diversity. A distributed strategy of relay selection is applied to the cooperative scheme, which can reduce system overhead and also facilitate the development of the explicit expressions of information metrics, such as outage probability and ergodic capacity. Both analytical and numerical results demonstrate that the proposed protocol can achieve large ergodic capacity and full diversity gain simultaneously.

On the Performance of Opportunistic Cooperative Wireless Networks

The aim of this paper is to study the impact of channel state information on the design of cooperative transmission protocols. This is motivated by the fact that the performance gain achieved by cooperative diversity comes at the price of the extra bandwidth resource consumption. Several opportunistic relaying strategies are developed to fully utilize the different types of a priori channel information. The analytical and numerical results demonstrate that the use of such a priori information increases the spectral efficiency of cooperative diversity, especially at low signal-to-noise ratio.

A low-complexity soft-MIMO detector based on the fixed-complexity sphere decoder

This paper presents a soft-output version of the fixed-complexity sphere decoder (FSD) previously proposed for uncoded multiple input-multiple output (MIMO) detection. Thus, the soft-FSD (SFSD) can be used in turbo-MIMO systems to exchange extrinsic soft-information with the outer decoder. For that purpose, the SFSD generates a list of candidates that approximates that of the list sphere decoder (LSD) while containing information about all the possible bit values, removing the need for clipping. In addition, it overcomes the two problems of the LSD: its variable complexity and the sequential nature of its tree search. Simulation results show that the SFSD can be used to approximate the performance of the LSD while having a considerably lower and fixed complexity, making the algorithm suitable for hardware implementation.

Joint Transceiver Beamforming in MIMO Cognitive Radio Network Via Second-Order Cone Programming

This paper considers the spectrum sharing multiple- input-multiple-output (MIMO) cognitive radio network, in which multiple primary users (PUs) coexist with multiple secondary users (SUs). Joint transceiver cognitive beam former design is introduced to minimize the transmit power of the SU base station (SBS) while simultaneously targeting lower bounds on the received signal-to-interference-plus-noise ratio (SINR) for the SUs and imposing upper limits on the interference temperature to the PUs. With the perfect knowledge of all links, the optimal secondary transceiver beam former is achieved iteratively. Due to the limited cooperation between SBS and PUs, perfect information of primary links may not be available at SBS which could lead to severe interference to the PUs. Robust designs are developed against the uncertainties in the primary links by keeping the interference to the PU below a prespecifled threshold with high probability. Simulation results are presented to validate the effectiveness of the proposed algorithms that minimizes the total transmit power and simultaneously guarantees quality-of-service (QoS) of both SUs and PUs.