New rank detection methods for reduced-rank MIMO systems

Abstract

In practical multi-input multi-output (MIMO) systems, the channel matrices often have reduced rank. Reliable detection of the channel rank is essential in achieving the significant gain provided by MIMO configuration. Existing work on MIMO channel rank detection assume a static channel model, so the proposed methods only consider the noise distributions while the distributions of the MIMO channels are not considered. In this paper, we employ a random channel model and propose three threshold-based rank detection methods which take into account the distributions of both the channels and the noises. In our first algorithm, following existing single-threshold rank detection scheme, we rigorously derive an analytical lower bound on the correct rank detection probability and propose a systematic threshold selection method by maximizing the lower bound. Then we propose two new rank detection methods which use multiple thresholds, where each threshold corresponds to one possible rank value. The thresholds are optimized based on the derived lower bounds on the rank detection probability for different channel rank values. The convergence and complexity of the proposed algorithms are analyzed. Simulation results on the correct rank detection probability of the proposed schemes are provided to show their advantage over existing schemes. The mean-squared-error (MSE) and outage probability are also simulated to show the importance of reliable rank detection in MIMO communications.

Optimal modeling of nonlinear systems Method of variable injections

“…Nevertheless, it is possible to represent these sets in terms of their numerical characteristics, such as the expectation and covariance matrices. Typical examples are engineering [66,44,23,8], statistics [15,38,16,74], stochastic signal processing [61,36,92,88,9], and image processing [17,60]; in the latter case, a digitized image, presented by a matrix, is often interpreted as the sample of a stochastic signal.…”

“…While the theory of a system representation with any given accuracy is well elaborated (see, e.g., [31,19,67,69,68,34,24]), the theory of optimal constrained and constructive system representation is still not so well developed, although this is an area of intensive research (see, e.g., [22,21]). Despite increasing demands from applications [72,6,20,63,92,88,9,38,16,74,66,44,23,8,60,22,21,28,79,51,3,32,29,5,62,65] this subject is hardly tractable because of intrinsic difficulties in optimal approximation techniques, especially when the approximating model should have a specific structure implied by the underlying problem.…”

Best approximations of non-linear mappings: Method of optimal injections

“…Nevertheless, it is possible to represent these sets in terms of their numerical characteristics, such as the expectation and covariance matrices. Typical examples are stochastic signal processing [15][16][17][18][19], statistics [20][21][22][23][24], engineering [25][26][27][28] and image processing [29,30]; in the latter case, a digitized image, presented by a matrix, is often interpreted as the sample of a stochastic signal.…”

“…While the theory of operator approximation with any given accuracy is well elaborated (see, e.g., [11], [5], [6], [14]), [2], [10], [3], [1], [4], [13], [8], [7], [9], [12]), the theory of best constrained constructive operator approximation is still not so well developed, although this is an area of intensive recent research (see, e.g., [31][32][33][34][35][36]). Despite increasing demands from applications [17][18][19][21][22][23][25][26][27][28][30][31][32][33][34][36][37][38][39][40][41][42][43][44][45][46] this subject is hardly tractable because of intrinsic difficulties in best approximation techniques, especially when the approximating operator should have a specific structure implied by the underlying problem.…”

“…Let us denote by R m×n rj the set of all m × n matrices of rank at most r j . In the RHS of (18), only the last term depends on S j . Therefore, on the basis of [24,[58][59][60][61][62], the minimal Frobenius norm solution to the problem min…”