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In narrowband Multiple-Input Multiple-Output (MIMO) communication systems, when the Channel State Information (CSI) is known perfectly at the transmitter and the receiver, techniques such as water-filling may use the singular value decomposition to separate the MIMO channel into independent single-input single-output sub-channels. The signal-to-noise ratios of these sub-channels are easily found, and, therefore, so are the sub-channel bit allocations. In practice, perfect CSI is difficult to obtain. Imperfect CSI results in sub-channel coupling and co-channel interference. In this paper, simple first-order expressions are presented for the signal and interference/noise powers for each sub-channel for the imperfect CSI case.
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