Adam J. Tenenbaum

Linear Processing for the Downlink in Multiuser MIMO Systems with Multiple Data Streams

In this paper we solve the problem of linear precoding for the downlink in multiuser multiple-input multiple-output (MIMO) systems. The transmitter and the receivers may be equipped with multiple antennas and each user may receive multiple data streams. Our objective is to jointly optimize the power allocation and transmit-receive filters for all users. We develop the optimization for two different criteria: (1) minimizing the total transmitted power while satisfying SINR constraints and (2) minimizing the sum mean squared error given a total power budget. We take advantage of the duality between the uplink and downlink to derive the solution.

Joint multiuser transmit-receive optimization using linear processing

In this paper we propose a novel method for joint transmit-receive linear optimization in the downlink of a multiuser MIMO communication system. This new method adapts existing joint linear optimization algorithms from the single user domain for application to the multiuser domain. The optimum transmit matrix is obtained using an iterative procedure based on a minimum mean-squared error (MMSE) criterion and a per-user power constraint; the optimum receive matrices for each user are then derived under an MMSE constraint. The proposed technique improves performance and increases data throughput in multiuser scenarios.

Linear processing and sum throughput in the multiuser MIMO downlink

We consider linear precoding and decoding in the downlink of a multiuser multiple-input, multiple-output (MIMO) system, wherein each user may receive more than one data stream. We propose several mean squared error (MSE) based criteria for joint transmit-receive optimization and establish a series of relationships linking these criteria to the signal-to-interference-plus-noise ratios of individual data streams and the information theoretic channel capacity under linear minimum MSE decoding. In particular, we show that achieving the maximum sum throughput is equivalent to minimizing the product of MSE matrix determinants (PDetMSE). Since the PDetMSE minimization problem does not admit a computationally efficient solution, a simplified scalar version of the problem is considered that minimizes the product of mean squared errors (PMSE). An iterative algorithm is proposed to solve the PMSE problem, and is shown to provide near-optimal performance with greatly reduced computational complexity. Our simulations compare the achievable sum rates under linear precoding strategies to the sum capacity for the broadcast channel.

Linear Precoding for Multiuser MIMO-OFDM Systems

This paper develops linear preceding schemes for the downlink in multiuser multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) systems with multiple data streams per user. We extend an existing multiuser MIMO algorithm, that jointly optimizes the power allocation and the transmit and receive filters, to MIMO- OFDM systems. One extension is to solve the resulting problem of joint power allocation across OFDM subcarriers. This paper also presents efficient methods to reduce the computational load of the algorithm by interpolating the precoding and decoding matrices corresponding to different OFDM subcarriers. The simulations show that the proposed interpolation scheme outperforms previously known schemes, but requires that the precoder for each subcarrier be tailored to the interpolated receiver.

Improved sum-rate optimization in the multiuser MIMO downlink

We consider linear precoding and decoding in the downlink of a multiuser multiple-input, multiple-output (MIMO) system. In this scenario, the transmitter and the receivers may each be equipped with multiple antennas, and each user may receive more than one data stream. We examine the relationship between the sum capacity for the broadcast channel with channel state information at the transmitter under a sum power constraint and the achievable sum rates under linear precoding. We show that achieving the optimum sum throughput under linear precoding is equivalent to minimizing the product of mean squared error (MSE) matrix determinants. The resulting nonconvex optimization problem is solved numerically, guaranteeing local convergence only. The performance of this approach is analyzed via comparison to the sum capacity and to existing approaches for linear precoding.

Minimizing Sum-MSE Implies Identical Downlink and Dual Uplink Power Allocations

In the multiuser downlink, power allocation for linear precoders that minimize the sum of mean squared errors under a sum power constraint is a non-convex problem. Many existing algorithms solve an equivalent convex problem in the virtual uplink and apply a transformation based on uplink-downlink duality to find a downlink solution. In this letter, we analyze the optimality criteria for the power allocation subproblem in the virtual uplink, and demonstrate that the optimal solution leads to identical power allocations in the downlink and virtual uplink. We thus extend the known duality results and, importantly, simplify the existing algorithms used for iterative transceiver design.

Channel prediction and feedback in multiuser broadcast channels

Multiuser linear precoding requires channel state information (CSI) at the transmitter. In the absence of channel reciprocity between the uplink and downlink, a feedback mechanism must be designed to communicate CSI estimates from the mobile receivers to the transmitter. Limiting the total feedback rate is an important design goal for multiuser multiple-input, multiple-output systems, as the feedback overhead can potentially consume a large percentage of system resources, especially when the total number of antennas is large. In this paper, we focus on the challenges of feedback delay and reducing feedback rate; we predict N-frames-ahead, based on the one-step Kalman predictor, and derive a theoretical expression for the prediction mean squared error (MSE). We present simulation results that illustrate a tradeoff between prediction MSE and computational complexity, and also demonstrate situations where adaptive delta modulation (ADM) can be used to exploit temporal redundancy and reduce the required feedback rate.

Energy optimization across training and data for multiuser minimum sum-MSE linear precoding

This paper considers minimum sum mean-squared error (sum-MSE) linear transceiver designs in multiuser downlink systems with imperfect channel state information. Specifically, we derive the optimal energy allocations for training and data phases for such a system. Under MMSE estimation of uncorrelated Rayleigh block fading channels with equal average powers, we prove the separability of the energy allocation and transceiver design optimization problems. A closed-form optimum energy allocation is derived and applied to existing transceiver designs. Analysis and simulation results demonstrate the improvements that can be realized with the proposed design.

Optimizing energy for training vs. data in linearly precoded multiuser sum-rate maximization

We consider the problem of optimizing the allocation of available energy across training and data symbols under linear precoding in multiuser downlink systems with imperfect channel state information (CSI). Our figure of merit is the sum rate across all users. This paper derives a lower bound on achievable rate under linear precoding and extends existing precoder designs to the case of imperfect CSI. Optimality and separability results for the energy allocation and precoder design problems that were found previously for sum-MSE minimization are extended to the problem of sum-rate maximization when channels are modelled using uncorrelated Rayleigh block fading with equal variances of the fading coefficients. Simulation results suggest significant improvements in achievable rate under the proposed algorithm.