Impact of Line-of-Sight and Unequal Spatial Correlation on Uplink MU-MIMO Systems

Closed-form approximations of the expected per-terminal signal-to-interference-plus-noise-ratio (SINR) and ergodic sum spectral efficiency of a multiuser multiple-input multiple-output system are presented. Our analysis assumes spatially correlated Ricean fading channels with maximum-ratio combining on the uplink. Unlike previous studies, our model accounts for the presence of unequal correlation matrices, unequal Rice factors, as well as unequal link gains to each terminal. The derived approximations lend themselves to useful insights, special cases and demonstrate the aggregate impact of line-of-sight (LoS) and unequal correlation matrices. Numerical results show that while unequal correlation matrices enhance the expected SINR and ergodic sum spectral efficiency, the presence of strong LoS has an opposite effect. Our approximations are general and remain insensitive to changes in the system dimensions, signal-to-noise-ratios, LoS levels and unequal correlation levels.Comment: 4 pages, 2 figures, accepted for publication in the IEEE Wireless Communications Letters, Vol. 6, 201

Uplink Analysis of Large MU-MIMO Systems With Space-Constrained Arrays in Ricean Fading

Closed-form approximations to the expected per-terminal signal-to-interference-plus-noise-ratio (SINR) and ergodic sum spectral efficiency of a large multiuser multiple-input multiple-output system are presented. Our analysis assumes correlated Ricean fading with maximum ratio combining on the uplink, where the base station (BS) is equipped with a uniform linear array (ULA) with physical size restrictions. Unlike previous studies, our model caters for the presence of unequal correlation matrices and unequal Rice factors for each terminal. As the number of BS antennas grows without bound, with a finite number of terminals, we derive the limiting expected per-terminal SINR and ergodic sum spectral efficiency of the system. Our findings suggest that with restrictions on the size of the ULA, the expected SINR saturates with increasing operating signal-to-noise-ratio (SNR) and BS antennas. Whilst unequal correlation matrices result in higher performance, the presence of strong line-of-sight (LoS) has an opposite effect. Our analysis accommodates changes in system dimensions, SNR, LoS levels, spatial correlation levels and variations in fixed physical spacings of the BS array.Comment: 7 pages, 3 figures, accepted for publication in the proceedings of IEEE ICC, to be held in Paris, France, May 201

Information-theoretic analysis of MIMO channel sounding

The large majority of commercially available multiple-input multiple-output (MIMO) radio channel measurement devices (sounders) is based on time-division multiplexed switching (TDMS) of a single transmit/receive radio-frequency chain into the elements of a transmit/receive antenna array. While being cost-effective, such a solution can cause significant measurement errors due to phase noise and frequency offset in the local oscillators. In this paper, we systematically analyze the resulting errors and show that, in practice, overestimation of channel capacity by several hundred percent can occur. Overestimation is caused by phase noise (and to a lesser extent frequency offset) leading to an increase of the MIMO channel rank. Our analysis furthermore reveals that the impact of phase errors is, in general, most pronounced if the physical channel has low rank (typical for line-of-sight or poor scattering scenarios). The extreme case of a rank-1 physical channel is analyzed in detail. Finally, we present measurement results obtained from a commercially employed TDMS-based MIMO channel sounder. In the light of the findings of this paper, the results obtained through MIMO channel measurement campaigns using TDMS-based channel sounders should be interpreted with great care.Comment: 99 pages, 14 figures, submitted to IEEE Transactions on Information Theor

Optimal Transmit Covariance for Ergodic MIMO Channels

In this paper we consider the computation of channel capacity for ergodic multiple-input multiple-output channels with additive white Gaussian noise. Two scenarios are considered. Firstly, a time-varying channel is considered in which both the transmitter and the receiver have knowledge of the channel realization. The optimal transmission strategy is water-filling over space and time. It is shown that this may be achieved in a causal, indeed instantaneous fashion. In the second scenario, only the receiver has perfect knowledge of the channel realization, while the transmitter has knowledge of the channel gain probability law. In this case we determine an optimality condition on the input covariance for ergodic Gaussian vector channels with arbitrary channel distribution under the condition that the channel gains are independent of the transmit signal. Using this optimality condition, we find an iterative algorithm for numerical computation of optimal input covariance matrices. Applications to correlated Rayleigh and Ricean channels are given.Comment: 22 pages, 14 figures, Submitted to IEEE Transactions on Information Theor

Power Scaling of Uplink Massive MIMO Systems with Arbitrary-Rank Channel Means

This paper investigates the uplink achievable rates of massive multiple-input multiple-output (MIMO) antenna systems in Ricean fading channels, using maximal-ratio combining (MRC) and zero-forcing (ZF) receivers, assuming perfect and imperfect channel state information (CSI). In contrast to previous relevant works, the fast fading MIMO channel matrix is assumed to have an arbitrary-rank deterministic component as well as a Rayleigh-distributed random component. We derive tractable expressions for the achievable uplink rate in the large-antenna limit, along with approximating results that hold for any finite number of antennas. Based on these analytical results, we obtain the scaling law that the users' transmit power should satisfy, while maintaining a desirable quality of service. In particular, it is found that regardless of the Ricean $K$-factor, in the case of perfect CSI, the approximations converge to the same constant value as the exact results, as the number of base station antennas, $M$, grows large, while the transmit power of each user can be scaled down proportionally to $1/M$. If CSI is estimated with uncertainty, the same result holds true but only when the Ricean $K$-factor is non-zero. Otherwise, if the channel experiences Rayleigh fading, we can only cut the transmit power of each user proportionally to $1/\sqrt M$. In addition, we show that with an increasing Ricean $K$-factor, the uplink rates will converge to fixed values for both MRC and ZF receivers

Exact ZF Analysis and Computer-Algebra-Aided Evaluation in Rank-1 LoS Rician Fading

We study zero-forcing detection (ZF) for multiple-input/multiple-output (MIMO) spatial multiplexing under transmit-correlated Rician fading for an N_R X N_T channel matrix with rank-1 line-of-sight (LoS) component. By using matrix transformations and multivariate statistics, our exact analysis yields the signal-to-noise ratio moment generating function (m.g.f.) as an infinite series of gamma distribution m.g.f.'s and analogous series for ZF performance measures, e.g., outage probability and ergodic capacity. However, their numerical convergence is inherently problematic with increasing Rician K-factor, N_R , and N_T. We circumvent this limitation as follows. First, we derive differential equations satisfied by the performance measures with a novel automated approach employing a computer-algebra tool which implements Groebner basis computation and creative telescoping. These differential equations are then solved with the holonomic gradient method (HGM) from initial conditions computed with the infinite series. We demonstrate that HGM yields more reliable performance evaluation than by infinite series alone and more expeditious than by simulation, for realistic values of K , and even for N_R and N_T relevant to large MIMO systems. We envision extending the proposed approaches for exact analysis and reliable evaluation to more general Rician fading and other transceiver methods.Comment: Accepted for publication by the IEEE Transactions on Wireless Communications, on April 7th, 2016; this is the final revision before publicatio

Spectral Efficiency Analysis of Multi-Cell Massive MIMO Systems with Ricean Fading

This paper investigates the spectral efficiency of multi-cell massive multiple-input multiple-output systems with Ricean fading that utilize the linear maximal-ratio combining detector. We firstly present closed-form expressions for the effective signal-to-interference-plus-noise ratio (SINR) with the least squares and minimum mean squared error (MMSE) estimation methods, respectively, which apply for any number of base-station antennas $M$ and any Ricean $K$-factor. Also, the obtained results can be particularized in Rayleigh fading conditions when the Ricean $K$-factor is equal to zero. In the following, novel exact asymptotic expressions of the effective SINR are derived in the high $M$ and high Ricean $K$-factor regimes. The corresponding analysis shows that pilot contamination is removed by the MMSE estimator when we consider both infinite $M$ and infinite Ricean $K$-factor, while the pilot contamination phenomenon persists for the rest of cases. All the theoretical results are verified via Monte-Carlo simulations.Comment: 15 pages, 2 figures, the tenth International Conference on Wireless Communications and Signal Processing (WCSP 2018), to appea

Dual-Polarized Ricean MIMO Channels: Modeling and Performance Assessment

In wireless communication systems, dual-polarized (DP) instead of single-polarized (SP) multiple-input multiple-output (MIMO) transmission is used to improve the spectral efficiency under certain conditions on the channel and the signal-to-noise ratio (SNR). In order to identify these conditions, we first propose a novel channel model for DP mobile Ricean MIMO channels for which statistical channel parameters are readily obtained from a moment-based channel decomposition. Second, we derive an approximation of the mutual information (MI), which can be expressed as a function of those statistical channel parameters. Based on this approximation, we characterize the required SNR for a DP MIMO system to outperform an SP MIMO system in terms of the MI. Finally, we apply our results to channel measurements at 2.53 GHz. We find that, using the proposed channel decomposition and the approximation of the MI, we are able to reproduce the (practically relevant) SNR values above which DP MIMO systems outperform SP MIMO systems.Comment: submitted to the IEEE Transactions on Communication