Maximizing the Average Spectral Efficiency of Dual-Branch MIMO Systems With Discrete-Rate Adaptation

Abstract

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> The capacity of multiple-input–multiple-output (MIMO) systems with perfect transmitter and receiver channel state information (CSI) can be attained by decoupling the MIMO channel into a set of independent subchannels and distributing the power among these subchannels in accordance with the <emphasis emphasistype="boldital"> water-filling</emphasis> solution. Implementation of this scheme on a time-varying channel, however, requires continuous-rate adaptation and is not feasible in any such practical system. In this paper, we show how to maximize the average spectral efficiency (ASE) of dual-branch MIMO systems (either two transmit or two receive antennas) with perfect transmitter and receiver CSI when using a fixed number of codes (discrete-rate adaptation). This maximum ASE is compared with the system's ergodic capacity and with the maximum ASE that can be attained if the available power is distributed among the different subchannels in accordance with the water-filling solution although only discrete-rate adaptation is possible. We assume that capacity-achieving codes for additive white Gaussian noise (AWGN) channels are available and that the power available to the transmitter to transmit the <formula formulatype="inline"><tex>$i$</tex></formula>th symbol frame is fixed and independent of the frame index <formula formulatype="inline"><tex>$i$</tex></formula>. </para>