Approaching the Zero-Outage Capacity of MIMO-OFDM without Water-Filling

Orthogonal-frequency-division multiplexing (OFDM) transforms a frequency-selective multiple-input multipleoutput (MIMO) fading channel into a MIMO-OFDM channel that has a well-defined outage capacity. According to Shannon theory, a transmitter with channel knowledge can achieve this capacity by a combination of eigenbeamforming and water-filling; the eigenbeamforming transforms the MIMO-OFDM channel into a parallel bank of scalar channels, and the water-filling procedure optimally allocates rate and energy to the scalar channels. Since water-filling adapts the rate to match the channel, it can be viewed as a form of adaptive modulation. Despite its optimality, the practicality of this procedure is limited by its high complexity. This paper shows that the full-blown water-filling procedure is not necessary to approach the zero-outage capacity of the MIMO-OFDM channel; it is sufficient instead to use a combination of eigenbeamforming and a fixed (nonadaptive) rate allocation. The fixed allocation requires no water-filling; instead, it allocates the rates deterministically to match the channel statistics, independent of the particular channel realization. This paper proves that the capacity penalty incurred by the fixed allocation approaches zero as the number of antennas grows large. Furthermore, at high signal-to-noise ratio (SNR), we show that the convergence is fast and that the fixed allocation strategy performs well for even a moderate number of antennas. For example, the fixed allocation suffers a SNR penalty of less than 0.2 dB for a 6×6 Rayleigh-fading MIMO-OFDM channel at 8 bits per signaling interval, when the channel is assumed to be uncorrelated between antennas and between channel taps. A main conclusion is that eigenbeamforming is the most valuable way to exploit knowledge of the channel at the transmitter, and that any subsequent adaptive modulation has minimal relative value.