This paper examines space division duplexing (SDD) in multiple-input multiple-output (MIMO) systems. The antennas each full-duplex node has are partitioned to form two antenna banks - one for transmission, the other for reception. Self-interference is avoided at each full-duplex node by utilizing the nullspace (or the left nullspace) of corresponding self-interference channel for transmission (or reception). Simulation results are provided on the error performance. Useful insights are obtained on the effects finite precision arithmetic, and quantization errors have on the feasibility of SDD.

A systematic scheme is proposed to facilitate arbitrary virtual channel (VC)-to-user mappings in space dimension, through multiple-input multiple-output physical layer multicasting. It is a divide-and-conquer strategy, which breaks down the VC-to-user mapping to manageable orthogonal sub-mappings, each represented in terms of a multicast antenna group (MAG). A generalized form of block diagonalization is proposed to make transmissions pertaining to distinct MAGs orthogonal. Known non-iterative coordinated beamforming techniques are investigated for intra-MAG beamforming. The approach enables physical layer multicasting with non-iterative beamforming techniques alone.

In this paper we examine the use of generalized singular value decomposition (GSVD) for coordinated beamforming in MIMO systems. GSVD facilitates joint decomposition of a class of matrices arising inherently in source-to-2 destination MIMO broadcast scenarios. GSVD allows two channels of suitable dimensionality to be jointly diagonalized, i.e. to be reduced to non-interfering virtual broadcast channels, through the use of jointly determined transmit precoding and receiver reconstruction matrices. Potential applications for GSVD-based beamforming can be found in MIMO broadcasting, as well as in MIMO relaying under all amplify-and-forward, decode-and-forward, and code-and-forward relay processing schemes. Several of them are highlighted here. We also present simulation-based performance analysis results to justify the use of GSVD for coordinated beamforming.

We examine the distribution of the per virtual-channel received signal-to-noise ratio over a multiple-input multiple-output channel modeled by a rank-2 non-central Wishart matrix. The exact probability density function is derived for all possible non-centrality matrices; and verified through simulation for selected systems. Identities for exact analytic results on the outage probability, the average symbol error rate, and the moment generating function are also derived.

Sums of lognormal random variables (RVs) are of wide interest in wireless communications and other areas of science and engineering. Since the distribution of lognormal sums is not log-normal and does not have a closed-form analytical expression, many approximations and bounds have been developed. This paper develops two computational methods for the moment generating function (MGF) or the characteristic function (CHF) of a single lognormal RV. The first method uses classical complex integration techniques based on steepest-descent integration. The saddle point of the integrand is explicitly expressed by the Lambert function. The steepest-descent (optimal) contour and two closely-related closed-form contours are derived. A simple integration rule (e.g., the midpoint rule) along any of these contours computes the MGF/CHF with high accuracy. The second approach uses a variation on the trapezoidal rule due to Ooura and Mori. Importantly, the cumulative distribution function of lognormal sums is derived as an alternating series and convergence acceleration via the Epsilon algorithm is used to reduce, in some cases, the computational load by a factor of 106! Overall, accuracy levels of 13 to 15 significant digits are readily achievable.

This paper develops highly accurate numerical techniques for evaluating the mgf/ chf of a single lognormal variable and for computing the lognormal sum cdf. Complex integration techniques based on the steepest-descent integration are thus developed for evaluating the lognormal mgf/ chf. The saddlepoint of the integrand is explicitly expressed using the Lambert-W function. The optimal steepest-descent contour passing through the saddlepoint is then derived. Even a simple mid-point-rule-based integration technique can be used along this contour to evaluate the mgf/ chf at extremely high precision. A highly efficient, extremely accurate numerical method is then developed for evaluating the cdf of sum of independent lognormal variables. The cdf is expanded as an alternating series, on which the Epsilon algorithm for convergence acceleration is applied. This reduces the computational load significantly.

The distribution of the received signal power ¿ of a multiple-input multiple-output system, with the associated 2 × 2 complex Wishart matrix having n degrees of freedom, is investigated under the channel inversion power allocation scheme. Exact closed-form expressions are derived for the probability density function and the cumulative distribution function of ¿. The analysis covers systems with transmit-receive antennas {Nt,Nr| min(Nt, Nr) = 2, max(Nt, Nr) ¿ 2}, and independent and identically distributed Rayleigh fading links between each antenna pair. We derive (i) the distribution of Shannon capacity of the multiple-input multiple-output channel (ii) average symbol error rate for a class of modulation schemes that includes Binary Phase Shift Keying.

The outage probability is a fundamental performance metric, which has been widely investigated in the literature. In this paper, we develop a general method to compute the outage given the moment generating function (MGF). When computing the outage using the MGF, integration along the standard Bromwich contour suffers from a loss of accuracy due to oscillatory nature of the integrand. One can address this difficulty by using the Cauchy's theorem to replace the Bromwich contour by an appropriate equivalent contour. For highly-accurate numerical results, the steepest descent contour is the most suitable replacement. Unfortunately, this optimal contour can not be in general expressed in closed-form. The class of Talbot contours characterized by three parameters provides an alternative. However, it is not clear how these parameters need to be tuned for best results. We propose the use of linear regression to set the parameter values so as to minimize the mismatch between corresponding Talbot contour and the steepest-descent contour. The resulting integral has a smooth and rapidly decaying integrand, making it possible for the outage probability to be evaluated with high accuracy by using a simple numerical integration method. This approach is general in a sense that it works for any system where the MGF is known. Thus, it can handle a wide range of fading distributions and a variety of communication systems.