Convex Optimization Theory Applied to Joint Transmitter-Receiver Design in MIMO Channels (original) (raw)
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MIMO Transceiver Optimization With Linear Constraints on Transmitted Signal Covariance Components
This correspondence revisits the joint transceiver optimization problem for MIMO channels. The linear transceiver as well as the transceiver with linear precoding and decision feedback equalization are considered. For both types of transceivers, in addition to the usual total power constraint, an individual power constraint on each antenna element is also imposed. A number of objective functions including the average bit error rate, are considered for both of the above systems under the generalized power constraint. It is shown that for both types of systems the optimization problem can be solved by first solving a class of MMSE problems (AM-MMSE or GM-MMSE depending on the type of transceiver), and then using majorization theory. The first step, under the generalized power constraint, can be formulated as a semidefinite program (SDP) for both types of transceivers, and can be solved efficiently by convex optimization tools. The second step is addressed by using results from majorization theory. The framework developed here is general enough to add any finite number of linear constraints to the covariance matrix of the input.
Correlated MIMO Wireless Channels: Capacity, Optimal Signaling, and Asymptotics
IEEE Transactions on Information Theory, 2005
The capacity of the multiple-input multiple-output (MIMO) wireless channel with uniform linear arrays (ULAs) of antennas at the transmitter and receiver is investigated. It is assumed that the receiver knows the channel perfectly but that the transmitter knows only the channel statistics. The analysis is carried out using an equivalent virtual representation of the channel that is obtained via a spatial discrete Fourier transform. A key property of the virtual representation that is exploited is that the components of virtual channel matrix are approximately independent. With this approximation, the virtual representation allows for a general capacity analysis without the common simplifying assumptions of Gaussian statistics and product-form correlation (Kronecker model) for the channel matrix elements. A deterministic line-of-sight (LOS) component in the channel is also easily incorporated in much of the analysis. It is shown that in the virtual domain, the capacity-achieving input vector consists of independent zero-mean proper-complex Gaussian entries, whose variances can be computed numerically using standard convex programming algorithms based on the channel statistics. Furthermore, in the asymptotic regime of low signal-to-noise ratio (SNR), it is shown that beamforming along one virtual transmit angle is asymptotically optimal. Necessary and sufficient conditions for the optimality of beamforming, and the value of the corresponding optimal virtual angle, are also derived based on only the second moments of the virtual channel coefficients. Numerical results indicate that beamforming may be close to optimum even at moderate values of SNR for sparse scattering environments. Finally, the capacity is investigated in the asymptotic regime where the numbers of receive and transmit antennas go to infinity, with their ratio being kept constant. Using a result of Girko, an expression for the asymptotic capacity scaling with the number of antennas is obtained in terms of the two-dimensional spatial scattering function of the channel. This asymptotic formula for the capacity is shown to be accurate even for small numbers of transmit and receive antennas in numerical examples.
Optimum Linear Joint Transmit-Receive Processing for MIMO Channels with QoS Constraints
IEEE Transactions on Signal Processing, 2004
This paper considers vector communication through a multi-input multi-output (MIMO) channel with a set of Quality of Service (QoS) requirements for the simultaneously established substreams. Linear transmit-receive processing (also termed linear precoder at the transmitter and linear equalizer at the receiver) is designed to satisfy the QoS constraints with minimum transmitted power. Although the original problem is a complicated nonconvex problem with matrix-valued variables, with the aid of majorization theory, we reformulate it as a simple convex optimization problem with scalar variables. We then propose a practical and efficient multi-level water-filling algorithm to optimally solve the problem for the general case of different QoS requirements. The optimal transmit-receive processing is shown to diagonalize the channel matrix only after a very specific pre-rotation of the data symbols. For situations in which the resulting transmit power is too large, we give the precise way to relax the QoS constraints in order to reduce the required power based on a perturbation analysis. We also propose a robust design under channel estimation errors which has a great interest in real implementations. Numerical results from simulations are also given to support the mathematical development of the problem.
Practicable MIMO Capacity in Ideal Channels
2006 IEEE 63rd Vehicular Technology Conference
The impact of communications signal processing such as QAM modulations (instead of gaussian signals), finite block lengths (instead of infinitely long codes), and using simpler algorithms (instead of expensive-to-implement ones), etc., is a lower practicable capacity efficiency than that of the Shannon limit. In this paper, the theoretical and practicable capacity efficiencies for known-channel MIMO are compared for two idealized channels. The motivation is to identify worthwhile trade-offs between capacity reduction and complexity reduction. The channels are the usual complex gaussian random i.i.d., and also the complex gaussian circulant. The comparison reveals new and interesting capacity behaviour, with the circulant channel having a higher capacity efficiency than that of the random i.i.d. channel, for practical SNR values. A circulant channel would also suggest implementation advantages owing to its fixed eigenvectors. Because of the implementation complexity of water filling, the simpler but sub-optimum solution of equal power allocation is investigated and shown to be worthwhile.
Special Issue: Multiple-Input Multiple-Output (MIMO) Communications
Wireless Communications and Mobile Computing, 2004
The idea of using multiple transmit and receive antennas in wireless communication systems is one of the most important breakthroughs in communication theory during the last decade. Popularly referred to as MIMO technology, this concept can greatly improve data throughput and link performance in wireless networks. In principle, a MIMO system can operate in, or anywhere between, one of the two possible modes. If the transmitter knows the channel, then one can use spatial beamforming techniques to steer RF energy in the direction of the receiver. On the other hand, if the transmitter does not know the channel, one can use space-time coding which effectively distributes the transmitted power uniformly in all directions, and in addition augments the data with structure that can be used to combat from fading dips. Sometimes, space-time coding methods are grouped into two categories: those that focus on throughput improvement (e.g. Bell-Labs layered space-time architecture, BLAST), and those that solely aim at improving link performance (including, most notably, orthogonal block coding and transmit diversity schemes); however, this classification is simplistic and many of the currently best known schemes do not fall under any of these two groups.
Ieice Transactions on Fundamentals of Electronics Communications and Computer Sciences, 2006
The average performance of a single-user MIMO system under spatially correlated fading and with different types of CSI at the transmitter and with perfect CSI at the receiver was studied in recent work. In contrast to analyzing a single performance metric, e.g. the average mutual information or the average bit error rate, we study an arbitrary representative of the class of matrix-monotone functions. Since the average mutual information as well as the average normalized MSE belong to that class, this universal class of performance functions brings together the information theoretic and signal processing performance metric. We use Löwner's representation of operator monotone functions in order to derive the optimum transmission strategies as well as to characterize the impact of correlation on the average performance. Many recent results derived for average mutual information generalize to arbitrary matrix-monotone performance functions, e.g. the optimal transmit strategy without CSI at the transmitter is equal power allocation. The average performance without CSI is a Schur-concave function with respect to transmit and receive correlation. In addition to this, we derive the optimal transmission strategy with long-term statistics knowledge at the transmitter and propose an efficient iterative algorithm. The beamforming-range is the SNR range in which only one data stream spatially multiplexed achieves the maximum average performance. This range is important since it has a simple receiver structure and well known channel coding. We entirely characterize the beamforming-range. Finally, we derive the generalized water-filling transmit strategy for perfect CSI and characterize its properties under channel correlation.