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.
Highlights
In the past two decades, a configuration, called multiinput multi-output (MIMO) system, which utilizes multiple antennas at both the transmitter and the receiver, has been extensively studied [1, 2]
For the threshold optimization of the traditional single-threshold scheme, we first derive a closed-form lower bound on the probability of correct rank detection based on the a priori channel rank distribution, the optimal threshold is decided via the maximization of the lower bound
For the observability of the channel rank detection model with respect to all possible rank values, we assume that T ≥ M, which guarantees that the number of independent equations in the training equation is no less than the number of independent unknown coefficients in the channel matrix
Summary
In the past two decades, a configuration, called multiinput multi-output (MIMO) system, which utilizes multiple antennas at both the transmitter and the receiver, has been extensively studied [1, 2]. The covariance matrix estimation needs a very large number of training symbols To overcome this drawback, a reduced-rank multistage Wiener filter design was proposed in [6], which relaxes the requirement on explicit estimate of the signal subspace. Joint transformation and filter designs can be found in [11, 12] Another important issue for MIMO communications is the channel rank detection and channel matrix estimation, since most MIMO transceiver techniques require channel state information (CSI) at the transmitter side and/or the receiver side for smart signal processing. One improved scheme is shrinkage-and-threshold SVD, where the truncated singular values are further shrunk to remove the noise effect In both truncated SVD and shrinkage-and-threshold SVD, the channel estimation accuracy largely depends on the correct truncation of the singular values, which is the rank detection of the MIMO channel matrix. In [18,19,20,21], for asymptotic MIMO channels where both dimensions of the channel matrix approach infinity with a fixed ratio, simple closed-form thresholds were derived for threshold-based rank detection
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