Throughput Scaling of MIMO Channels With Imperfect CSIT in the Low-SNR Regime

We study the effect of channel estimation error on the performance of water-filling in point-to-point multiple-input- multiple-output (MIMO) channels at low signal-to-noise ratios (SNRs). In this regard, we derive the water-filling throughput of a MIMO channel in the presence of imperfect channel state information at the transmitter (CSIT). The asymptotic growth rate for the throughput, i.e., R, is then found and is compared with the asymptotic growth rate for the capacity with perfect CSIT, i.e., CP, as a function of the signal-to-estimation-error ratio (SER). We show that, at low SNR, for moderate values of the SER, water filling based on erroneous channel estimates can still achieve significant throughputs asymptotically.