Eduard A. Jorswieck

Channel capacity and capacity-range of beamforming in MIMO wireless systems under correlated fading with covariance feedback

We study the optimal transmission strategy of a single-user multiple-input/multiple-output communication system with covariance feedback. We consider the situation with correlated receive and correlated transmit antennas in Rayleigh flat fading. Furthermore, we assume that the receiver has perfect channel state information, while the transmitter knows only the transmit correlation matrix and the receive correlation matrix. We show that transmitting in the direction of the eigenvectors of the transmit correlation matrix is the optimal transmission strategy. In addition to this, the optimal power allocation is studied and a necessary and sufficient condition for optimality of beamforming is derived. All theoretical results are illustrated by numerical simulations.

Performance of MIMO systems with channel inversion

The paper discusses channel inversion which is a spatial equalization technique when channel state information is available at the transmitter. Channel inversion is a straightforward concept without iterations and it might be useful when the data transmission is critical with time e.g. high data rate applications. We discuss performance degradation caused by channel estimation errors, clipping due to the limited range of the transmitted power and the effect of cochannel interference. These results give an insight into the technical constraints of this transmission technique and show how these critical issues can be limited or reduced.

Optimal transmission strategies and impact of correlation in multiantenna systems with different types of channel state information

We study the optimal transmission strategy of a multiple-input single-output (MISO) wireless communication link. The receiver has perfect channel state information (CSI), while the transmitter has different types of CSI, i.e., either perfect CSI, or no CSI, or long-term knowledge of the channel covariance matrix. For the case in which the transmitter knows the channel covariance matrix, it was recently shown that the optimal eigenvectors of the transmit covariance matrix correspond with the eigenvectors of the channel covariance matrix. However, the optimal eigenvalues are difficult to compute. We derive a characterization of the optimum power allocation. Furthermore, we apply this result to provide an efficient algorithm which computes the optimum power allocation. In addition to this, we analyze the impact of correlation on the ergodic capacity of the MISO system with different CSI schemes. At first, we justify the belief that equal power allocation is optimal if the transmitter is uninformed and the transmit antennas are correlated. Next, we show that the ergodic capacity with perfect CSI and without CSI at the transmitter is Schur-concave, i.e., the more correlated the transmit antennas are, the less capacity is achievable. In addition, we show that the ergodic capacity with covariance knowledge at the transmitter is Schur-convex with respect to the correlation properties. These results completely characterize the impact of correlation on the ergodic capacity in MISO systems. Furthermore, the capacity loss or gain due to correlation is quantified. For no CSI and perfect CSI at the transmitter, the capacity loss due to correlation is bounded by some small constant, whereas the capacity gain due to correlation grows unbounded with the number of transmit antennas in the case in which transmitter knows the channel covariance matrix. Finally, we illustrate all theoretical results by numerical simulations.

Transmission strategies for the MIMO MAC with MMSE receiver: average MSE optimization and achievable individual MSE region

In this work, we study the multiuser multiple-input multiple-output (MIMO) multiple access channel (MAC) under the assumption that the base station performs linear multiuser minimum mean-square error (MMSE) detection. We derive the average normalized MSE and the individual MSEs of users. At first, we optimize the average normalized MSE with respect to the transmit covariance matrices of the users. Next, adaptive power allocation is applied to further minimize the average normalized MSE. This leads to the general average normalized MSE optimization under a sum power constraint. We analyze the optimization problems and their connections by their Karush-Kuhn-Tucker conditions. The covariance matrix optimization is solved by iteratively single-user average MSE optimization in which the interference is treated as noise. We develop an iterative algorithm that performs power allocation and covariance matrix optimization. In addition to this, we study the achievable MSE region. We show that the MSE region is convex for the two-user MIMO case. Furthermore, we characterize the optimum power allocation among the users with regard to the single-user range. We show that the user with the maximum singular value of its channel matrix is the first supported user. For low SNR values, the optimal strategy is to have the best user transmitting only. In addition, we derive the individual MSE using single-user MMSE detectors and study the fulfillment of MSE requirements.

Majorization and matrix-monotone functions in wireless communications

This short tutorial presents two mathematical techniques namely Majorization Theory and Matrix-Monotone Functions, reviews their basic definitions and describes their concepts clearly with many illustrative examples. In addition to this tutorial, new results are presented with respect to Schur-convex functions and regarding the properties of matrix-monotone functions. The techniques are applied to solve communication and information theoretic problems in wireless communications. The impact of spatial correlation in multiple antenna systems is characterized for many important performance measures, e.g., average mutual information, outage probability, error performance, minimum Eb/N0 and wide-band slope, zero-outage capacity, and capacity region. The impact of user distribution in cellular systems is characterized for different scenarios including perfectly informed transmitters and receivers, regarding, e.g., the average sum rate, the outage sum rate, maximum throughput. Finally, a unified framework for the performance analysis of multiple antenna systems is developed based on matrix-monotone functions. The optimization of transmit strategies for multiple antennas is carried out by optimization of matrix-monotone functions. The results within this framework resemble and complement the various results on optimal transmit strategies in single-user and multiple-user multiple-antenna systems.

Outage probability in multiple antenna systems

Multiple transmit antennas improve the ergodic and outage capacity of wireless systems. Spatial properties of the channel including the transmit antenna array affect the optimum transmission strategy as well as the achievable capacity and average throughput. First, we study the outage probability of a multiple input single output (MISO) system with perfect channel state information (CSI) at the receiver under different types of CSI at transmitter and with transmit antenna correlation. We prove the conjecture given in Telatars seminal paper and complete the analysis of the optimum transmit strategy without CSI at the transmitter and uncorrelated antennas. Furthermore, we show how the impact of correlation on the outage probability depends on the transmission rate and SNR. We show that the behaviour of the outage probability differs from the behaviour of the ergodic capacity. In terms of ergodic capacity there are clear instructions what is the optimum transmission strategy and what is the impact of correlation. In contrast, the outage probability behaves chameleonic. If the transmitter is aware of the channel correlation matrices, the optimum transmit strategy is to transmit along the eigenvectors of the known correlation matrix. The remaining power allocation problem is difficult since it is a non-convex optimisation problem. However, necessary conditions characterise the optimal allocation. Finally, we analyse the outage probability for the general multiple input multiple output (MIMO) system with spatially correlated transmit and receive antennas in asymptotic high and low SNR regime. The theoretical results are illustrated by numerical simulations. Copyright

Impact of spatial correlation on the performance of orthogonal space-time block codes

We analyze the impact of transmitter and receiver spatial correlation on the performance of a multiple-input multiple-output (MIMO) system which applies an orthogonal space-time block code with no channel state information at the transmitter and perfect channel state information at the receiver. We derive a general formula for the bit error rate of a MIMO system with arbitrary number of transmit and receive antennas as a function of the correlation at the transmitter and the receiver. We prove that the diversity advantage is given by M/spl middot/N if M is the rank of the transmit correlation matrix and N the rank of the receive correlation matrix, respectively.

On the ergodic capacity as a function of the correlation properties in systems with multiple transmit antennas without CSI at the transmitter

In this letter, the impact of correlation of the transmit antennas of a multiple-input single-output (MISO) system, with no channel state information (CSI) at the transmitter and perfect CSI at the receiver is analyzed. We show that the ergodic capacity for the single-user MISO system is Schur-concave with respect to the vector with eigenvalues of the channel covariance matrix, i.e., the more correlation that exists between the transmit antennas, the less is the achievable capacity. Furthermore, the capacity loss for fully correlated transmit antennas in comparison with the uncorrelated case is derived. The results for the ergodic capacity are compared with the impact of correlation on the outage probability. The relationship between correlation properties and outage probability is more complicated than the relationship between the correlation properties and the ergodic capacity. It is shown that the outage probability is Schur-convex in the high signal-to-noise ratio (SNR) regime, and Schur-concave in the low SNR regime.

User selection schemes in multiple antenna broadcast channels with guaranteed performance

Recently, user selection algorithms in combination with linear pre- coding have been proposed that achieve the same scaling as the sum capacity of the MIMO BC. In this work, we study the properties of four user selection algorithms in conjunction with beamforming that guarantee certain SINR requirements under transmit power minimization. It is shown that for a large number of transmit antennas, the norm-based user selection performs close to the optimum. The results are illustrated by various numerical simulations.

Channel aware scheduling for multiple antenna multiple access channels

In this paper, we study the optimum transmission strategy of the multiple access channel in a cellular system in which the base station has multiple antennas. Recently, scheduling algorithms incorporating both the physical and data link layer were proposed e.g. in H. Boche and M. Wiczanowski, (2003), M. J. Neely, et al., (Feb. 2003), E. M. Yeh, (2002), for the multiple antenna case. In this work, we study the scheduling in a SIMO MAC under arbitrary ergodic fading. We assume that the instantaneous channel vector realizations as well as the buffer sizes of all mobiles are known at the base station. The base station performs successive interference cancellation. We propose the optimal scheduling policy. In order to get rid of the time-sharing argument, we define a spatial capacity region in which all rate tupels are achieved by spatial multiplexing only without time-sharing. Finally, we connect the capacity region of the SIMO MAC on the physical layer with the stability region of the corresponding queueing system on the data link layer. It is shown that all bit arrival rate vector lying in the capacity region of the SIMO MAC are achievable, too. All theoretical results are illustrated.