Matthew R. McKay

Secure Transmission With Artificial Noise Over Fading Channels: Achievable Rate and Optimal Power Allocation

We consider the problem of secure communication with multiantenna transmission in fading channels. The transmitter simultaneously transmits an information-bearing signal to the intended receiver and artificial noise to the eavesdroppers. We obtain an analytical closed-form expression of an achievable secrecy rate and use it as the objective function to optimize the transmit power allocation between the information signal and the artificial noise. Our analytical and numerical results show that equal power allocation is a simple yet near-optimal strategy for the case of noncolluding eavesdroppers. When the number of colluding eavesdroppers increases, more power should be used to generate the artificial noise. We also provide an upper bound on the SNR, above which, the achievable secrecy rate is positive and shows that the bound is tight at low SNR. Furthermore, we consider the impact of imperfect channel state information (CSI) at both the transmitter and the receiver and find that it is wise to create more artificial noise to confuse the eavesdroppers than to increase the signal strength for the intended receiver if the CSI is not accurately obtained.

Performance Analysis of MIMO-MRC in Double-Correlated Rayleigh Environments

We consider multiple-input multiple-output (MIMO) transmit beamforming systems with maximum ratio combining (MRC) receivers. The operating environment is Rayleigh fading with both transmit and receive spatial correlation. We present exact expressions for the probability density function (pdf) of the output signal-to-noise ratio, as well as the system outage probability. The results are based on explicit closed-form expressions which we derive for the pdf and cumulative distribution function of the maximum eigenvalue of double-correlated complex Wishart matrices. For systems with two antennas at either the transmitter or the receiver, we also derive exact closed-form expressions for the symbol-error rate. The new expressions are used to prove that MIMO-MRC achieves the maximum available spatial diversity order, and to demonstrate the effect of spatial correlation. The analysis is validated through comparison with Monte Carlo simulations

Ergodic Capacity Analysis of Amplify-and-Forward MIMO Dual-Hop Systems

This paper presents an analytical characterization of the ergodic capacity of amplify-and-forward (AF) MIMO dual-hop relay channels, assuming that the channel state information is available at the destination terminal only. In contrast to prior results, our expressions apply for arbitrary numbers of antennas and arbitrary relay configurations. We derive an expression for the exact ergodic capacity, simplified closed-form expressions for the high SNR regime, and tight closed-form upper and lower bounds. These results are made possible by employing recent tools from finite-dimensional random matrix theory, which are used to derive new closed-form expressions for various statistical properties of the equivalent AF MIMO dual-hop relay channel, such as the distribution of an unordered eigenvalue and certain random determinant properties. Based on the analytical capacity expressions, we investigate the impact of the system and channel characteristics, such as the antenna configuration and the relay power gain. We also demonstrate a number of interesting relationships between the dual-hop AF MIMO relay channel and conventional point-to-point MIMO channels in various asymptotic regimes.

General capacity bounds for spatially correlated Rician MIMO channels

This paper considers the capacity of spatially correlated Rician multiple-input multiple-output (MIMO) channels. We consider the general case with double-sided correlation and arbitrary rank channel means. We derive tight upper and lower bounds on the ergodic capacity. In the particular cases when the numbers of transmit and receive antennas are equal, or when the correlation is single sided, we derive more specific bounds which are computationally efficient. The bounds are shown to reduce to known results in cases of independent and identically distributed (i.i.d.) and correlated Rayleigh MIMO channels. We also analyze the outage characteristics of the correlated Rician MIMO channels at high signal-to-noise ratio (SNR). We derive the mean and variance of the mutual information and show that it is well approximated by a Gaussian distribution. Finally, we present numerical results which show the effect of the antenna configuration, correlation level (angle spreads), Rician K-factor, and the geometry of the dominant Rician paths.

Adaptive MIMO Transmission for Exploiting the Capacity of Spatially Correlated Channels

We consider a novel low-complexity adaptive multiple-input multiple-output (MIMO) transmission technique. The approach is based on switching between low-complexity transmission schemes, including statistical beamforming, double space-time transmit diversity, and spatial multiplexing, depending on the changing channel statistics, as a practical means of approaching the spatially correlated MIMO channel capacity. We first derive new ergodic capacity expressions for each MIMO transmission scheme in spatially correlated channels. Based on these results, we demonstrate that adaptive switching between MIMO schemes yields significant capacity gains over fixed transmission schemes. We also derive accurate analytical approximations for the optimal signal-to-noise-ratio switching thresholds, which correspond to the crossing-points of the capacity curves. These thresholds are shown to vary, depending on the spatial correlation, and are used to identify key switching parameters. Finally, we propose a practical switching algorithm that is shown to yield significant spectral efficiency improvements over nonadaptive schemes for typical channel scenarios

Rethinking the Secrecy Outage Formulation: A Secure Transmission Design Perspective

This letter studies information-theoretic security without knowing the eavesdroppers channel fading state. We present an alternative secrecy outage formulation to measure the probability that message transmissions fail to achieve perfect secrecy. Using this formulation, we design two transmission schemes that satisfy the given security requirement while achieving good throughput performance.

Error probability and SINR analysis of optimum combining in rician fading

This paper considers the analysis of optimum combining systems in the presence of both co-channel interference and thermal noise. We address the cases where either the desired-user or the interferers undergo Rician fading. Exact expressions are derived for the moment generating function of the SINR which apply for arbitrary numbers of antennas and interferers. Based on these, we obtain expressions for the symbol error probability with M-PSK. For the case where the desired-user undergoes Rician fading, we also derive exact closed-form expressions for the moments of the SINR. We show that these moments are directly related to the corresponding moments of a Rayleigh system via a simple scaling parameter, which is investigated in detail. Numerical results are presented to validate the analysis and to examine the impact of Rician fading on performance.

On the Design of Artificial-Noise-Aided Secure Multi-Antenna Transmission in Slow Fading Channels

In this paper, we investigate the design of artificial-noise-aided secure multi-antenna transmission in slow fading channels. The primary design concerns include the transmit power allocation and the rate parameters of the wiretap code. We consider two scenarios with different complexity levels: 1) the design parameters are chosen to be fixed for all transmissions; and 2) they are adaptively adjusted based on the instantaneous channel feedback from the intended receiver. In both scenarios, we provide explicit design solutions for achieving the maximal throughput subject to a secrecy constraint, given by a maximum allowable secrecy outage probability. We then derive accurate approximations for the maximal throughput in both scenarios in the high signal-to-noise ratio region, and give new insights into the additional power cost for achieving a higher security level while maintaining a specified target throughput. In the end, the throughput gain of adaptive transmission over non-adaptive transmission is also quantified and analyzed.

MIMO multichannel beamforming: SER and outage using new eigenvalue distributions of complex noncentral Wishart matrices

This paper analyzes MIMO systems with multichannel beamforming in Ricean fading. Our results apply to a wide class of multichannel systems which transmit on the eigenmodes of the MIMO channel. We first present new closed-form expressions for the marginal ordered eigenvalue distributions of complex noncentral Wishart matrices. These are used to characterize the statistics of the signal to noise ratio (SNR) on each eigenmode. Based on this, we present exact symbol error rate (SER) expressions. We also derive closed-form expressions for the diversity order, array gain, and outage probability. We show that the global SER performance is dominated by the subchannel corresponding to the minimum channel singular value. We also show that, at low outage levels, the outage probability varies inversely with the Ricean A*-factor for cases where transmission is only on the most dominant subchannel (i.e. a singlechannel beamforming system). Numerical results are presented to validate the theoretical analysis.

Capacity and performance of MIMO-BICM with zero-forcing receivers

This work considers multiple-input multiple-output bit-interleaved coded modulation (MIMO-BICM) with linear zero-forcing (ZF) receivers. We derive the link-level capacity (LLC) under ideal fast-fading conditions, and show that it approaches the maximum-likelihood (ML) LLC as the number of receive antennas approach infinity. We also derive tight analytical bounds on the coded bit-error rate, and prove that with N/sub t/ transmit and N/sub r/ receive antennas, the diversity order is N/sub r/-N/sub t/+1 multiplied by the free Hamming distance of the convolutional code. For the case of a ML receiver, we show that a tight bound is not possible, in general. Our analysis provides insights to explain the relative performance of the ZF and ML receivers. Finally, we validate the analytical results and assess the performance in a practical environment with orthogonal frequency-division multiplexing and channel estimation.