On the Duality of MIMO Transceiver Designs With Bit Allocation

Abstract

Abstract-Bit rate and power are two commonly used optimality criteria for MIMO transceiver design. In the literature, bit rate maximization and power minimization problems are viewed as different problems and solved independently. In this paper, we derive the duality between these two problems for both the cases with and without integer constraint on bit allocation. We will show that if a transceiver is optimal for the power-minimizing problem, it is also optimal for the rate maximizing problem, and the converse is true. Such a duality has not been stated and proved in the literature to the best of our knowledge. The derivation does not involve any existing optimal solution and we can establish duality result even for the rate maximization problem with integer bit constraint, which the optimal solution is not known. The duality also allows us to develop an algorithm for finding the rate-maximizing transceiver with integer bit allocation using the solution of power-minimizing system. We will also consider some possible generalizations of the problem, for example, when there is a constraint on the maximal constellation size and when the subchannel bit error rates (BERs) are constrained. For each of these cases, we will see that the duality between the two problems continued to hold. In the simulations, we will compute the optimal solutions for these two problems and demonstrate the duality between these two.

MIMO Broadcast DFE Transceivers With QoS Constraints: Min-Power and Max-Rate Solutions

“…The optimization problem in (9) reduces to the min-power problem in [14] when there is only one subscriber and the zero-forcing constraint is applied. It shall further reduce to the min-power problem in [8] and [15] if we only consider linear transceivers. Note that per substream SER constraints have been widely used in the min-power and max-rate problems for PTP MIMO channels [8], [10], [12]- [15] to support different types of data streams, even in the cases where the bit allocation variables, , are optimization variables [8], [12]- [19].…”

“…In [8] and [15], linear optimal zero-forcing (ZF) transceivers with bit allocation that minimize the total transmit power for a given target rate and equal per substream symbol error rate (SER) constraints are developed. Linear transceiver designs with bit allocation which maximize total bit rate with power and SER constraints are considered in [12], [13] and [15]. In [14], the authors consider both the min-power and max-rate design problems with possibly unequal SER constraints for DFE transceivers.…”

“…In [15], the authors shows that if the linear transceiver is optimal for the power-minimizing problem, it is also optimal for the rate-maximizing problem. And the converse is true.…”

Bit Allocation and Statistical Precoding for Correlated MIMO Channels With Limited Feedback

“…The noise vector q is assumed to be additive white Gaussian with zero mean and variance N 0 . The channel considered in this paper is of the form 1 The receivers are of the zero-forcing type for convenience of analysis as well as for the reason that zero forcing and minimum mean squared error receivers have similar performance when there is bit allocation [23]. where H w is an M r × M t matrix whose elements are independent Gaussian random variables with unit variance.…”

The Physical Layer Security Beamforming Method based on Large-scale Multi-antenna

“…Thus, large-scale technology is considered the candidate for the fifth-generation radio communication system which has been more and more research. Large-scale system has the following characteristics [6][7][8]:…”