Precoder design for MIMO systems over spatially correlated Ricean fading channels

Abstract

In response to the considerable increase in mobile data tra±c driven by multimedia and cloud-based services, multiple input multiple output (MIMO) is one of the most powerful communication technologies to deal with this continuously growing demand. By using a precoder, to be designed with the knowledge of channel state information (CSI) at the transmitter (CSIT) to transform the input signal prior to MIMO transmission, the bit error rate (BER) and data rate can be improved. A precoder designed with perfect instantaneous CSI can achieve either best BER performance or best data rate performance. However, perfect CSI is practically unavailable because of estimation errors, feedback delay, and quantization errors. Imperfect CSI can substantially degrade the system performance. Furthermore, the frequent feedback of instantaneous CSI costs expensive bandwidth overhead. Statistical CSIT, including channel mean and spatial correlation, is an e±cient measure to CSI. Its slowly varying nature does not need frequent CSI feedback to the transmitter, so that it can save much bandwidth overhead. So, the design of an optimal precoder based on statistical CSIT is of vital importance. The objective of this thesis is to investigate precoder design methods over spatially correlated Ricean fading channels for MIMO systems with statistical CSI. Regarding the statistical CSI feedback, the spatial correlation requires more feedback overhead than the mean. Also, the estimation of the spatial correlation using training data will consume bandwidth and will incur delay, apart from computations. Therefore, analytical spatial correlation analysis to derive a correlation expression for given spatial antenna configurations can reduce feedback and bandwidth in training data. Clustered channels with a hierarchical angle structure to describe azimuth angle in terms of the direction of departures (DOD) at the transmitter antenna array and the direction of arrival (DOA) at the receiver antenna array have been used to model communication channels in standards such as the 3GPP spatial channel model (SCM). The cluster is a resolvable channel path composed of a number of unresolvable subpaths. In the hierarchical angle structure, the DOAs and DODs of the sub-paths are expressed as the sum of the cluster's centered angle and the sub-paths' angle offsets. In this thesis, two different hierarchical angle models are investigated to derive analytical spatial correlation formulas for clustered channels. The first model assumes that the centered angles of the clusters are independent Gaussian random variables while the sub-paths' angle offsets are deterministic as defined by 3GPP SCM. For the above angle model, existing methods either require many expansion terms or limit clustered angle spread within a small range to achieve the desired accuracy. This thesis derives a simplified spatial correlation analysis by using the Gauss-Hermite quadrature, to avoid numerical integration for uniform linear array (ULA) and uniform circular array (UCA). Compared with the existing expansion solutions, the number of terms, e.g., less than 10, required to generate accurate spatial correlations is much reduced. The second hierarchical angle model treats the cluster's centered angle and subpaths' angle offsets as random variables. Hence the hierarchical angle is a bivariate, which is different from the single random variable approach of the first model and existing methods. It is assumed that the centered angle is Gaussian distributed while the angle offset is Laplacian distributed. An analytical correlation formula is derived for the above angle model for ULA and UCA . Computer evaluation shows that the derived formula matches well with the simulated correlations with channel parameters defined in the 3GPP SCM. The analytical spatial correlation expressions are useful for system performance evaluation and precoder design. In the literature, several precoder design methods using statistical CSIT over correlated Ricean fading channels were proposed. However, these methods can only provide either asymptotic solutions with degraded performance or non-eigen-structured iterative solutions with slow convergence and high computational complexity. In this thesis, the eigen-structure of the precoder is exploited to improve the convergence and computations. This eigen-structure approach is to convert the precoder design into a joint power allocation and unitary beamforming design problem. Kronecker correlation model is commonly used for modeling the spatial covariance matrix. Two transmit precoding schemes are proposed for MIMO systems over correlated Ricean channels with Kronecker covariance matrix. The first scheme deals with the case of correlated receive antennas' received data and uncorrelated transmit antennas' transmitted waveform. It is known that the optimal BER based precoder is the one-dimensional scheme using the largest eigen-mode (rank one) and equal power control scheme for low and high signal-to-noise ratios (SNRs), respectively. Based on these asymptotic solutions at low and high SNRs, a simple scheme is proposed that assumes only two values for power allocation. A bigger value is assigned to the largest eigen-beam and a smaller value to the rest of eigen-beams. The two power control values are optimized to minimize a pair error probability (PEP) bound. Simulations show that the simplified solution can achieve a performance close to the existing optimal solution with fast convergence speed. The second scheme handles the general case of correlated transmit and receive antennas. For this general correlation problem, the PEP bound is used as design criterion with an average power constraint. Expressing the constrained optimization problem in terms of power control matrix and unitary matrix of the precoder, the objective function and power constraint become nonlinear functions of the power control parameters and unitary matrix. This optimization problem suffers from local solution and convergence. By defining a new set of power constraint variables, the power constraint is now a linear function of the new power control variables. For given unitary matrix, the constrained optimization is a convex problem and the new power parameters can be solved by numerical methods namely interior point method. For given the power control parameters, we propose to employ the Riemannian optimization method to solve for the unitary beamforming matrix from the Lie group of unitary space. The above iterative optimization procedure is shown to achieve local optimal solution and guarantee convergence by computer simulation. A generalized precoding scheme is proposed to handle the channel covariance matrix of no specified spatial correlation structure. This general correlation structure can cover any double correlated channel including those of distributed antenna systems. The existing iterative method that needs to search a full-rank precoding matrix of large dimension has high computational complexity and slow convergence. Unfortunately, the convergence cannot be guaranteed. Our precoding scheme is also an eigen-structure based solution composed of power allocation and unitary beamforming. Using a formulation similar to the Kronecker case, power allocation can be solved as a sequential quadratic programming (SQP) problem and the unitary matrix obtained from the optimization method on Riemannian manifold. In comparing with the existing method, the proposed method has a much lower matrix dimension and thus has significant less computation. Simulation results show that the proposed method can give a local optimal solution with guaranteed convergence.

Date of Award	3 Oct 2014
Original language	English
Awarding Institution	City University of Hong Kong
Supervisor	Shu Hung LEUNG (Supervisor)