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A novel capacity scaling law for Multiple-Input Multiple-Output (MIMO) broadcast channels is derived considering a random user distribution. The random locations cause unequal average SNRs amongst the users, whereas prior work typically assumes that all users have the same average SNR. Most centralized wireless networks, e.g. cellular systems, are more accurately captured by the proposed model. For a large number of users, the average sum capacity is shown to scale like M logK instead of M log logK, where M and K denote the number of transmit antennas and the number of users within a cell. This means that the average sum capacity of cellular MIMO broadcast channels grows significantly faster than previous results indicate.
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