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We recently proposed a precoder codebook for a transmit-nulling space-division multiple access (TN-SDMA) to share spectrum with existing wireless services. Since a portion of the spatial subspaces of a multiantenna broadcast channel is used to eliminate the interference to coexisting systems, TN-SDMA could benefit the efficiency of spectrum usage from the coexistence of different systems in the same band while it always yields lower throughput per unit bandwidth than the orthogonal SDMA (called per user unitary and rate control (PU2RC)) that utilizes all the spatial subspaces for data transmission. This study aims to theoretically quantify the throughput loss of TN-SDMA relative to PU2RC and to analyze the effect of the main system parameters (signal-to-noise ratio (SNR) and the numbers of transmit antennas, users, and feedback bits) on the throughput loss. We derive the theoretical upper bound of the throughput loss of TN-SDMA relative to PU2RC, with the same feedback bits (codebook size). The throughput loss is lower with more transmit antennas, fewer users, lower SNR, or fewer feedback bits. It is interesting to note that the throughput loss converges to an upper limit with an increase in the SNR, which indicates that the SNR has a comparatively minor effect on the throughput loss in the high-SNR region. We also derive the required additional number of feedback bits for TN-SDMA to achieve the throughput of PU2RC (i.e., zero throughput loss). We find that the throughput achieved is feasible at the cost of a practically small number of additional feedback bits.

Throughput analysis of transmit-nulling SDMA with limited feedback