Achieving the sum-capacity of a multiple-input-multiple- output (MIMO) Gaussian broadcast channel is known to require full channel state information (CSI) at the base station, which implies the need of a large amount of feedback information from the users. Different asymptotics of the sum-capacity, such as its scaling law with respect to the number of users n or the multiplexing gain, are conventionally used to assess the performance of suboptimal schemes with reduced feedback, or equivalently with partial channel state information at the transmitter. In this correspondence, the optimal scaling law of the sum-rate with respect to n, for fixed signal-to-noise ratio (SNR), fixed number of transmit antennas M and any number of receiving antennasN(i.e.,Mlog log nN), is proved to be achievable with a deterministic feedback of only one bit per user. Moreover, the amount of feedback is shown to be further reduced with no asymptotic optimality loss by applying the selective feedback principle, leading to an average feedback rate that scales as log n. Finally, the asymptotic performance with respect to SNR is studied, by assessing how fast the number of users needs to increase with the SNR in order to guarantee a noninterference limited behavior.

The sum-capacity of a multi-antenna broadcast Gaussian channel is known to be achieved by dirty paper coding techniques, or, asymptotically in the number of users n, by beamforming methods, that require full channel state information at the base station. Based on the opportunistic beamforming principle, it has been recently shown that the optimal scaling law of the sum-rate with respect to n, for fixed signal to noise ratio and number of transmitting antennas M, (i.e., M log log n) can be achieved by employing a feedback of only one real and one integer number per user. Moreover, it was proved that a linear scaling with respect of M can be guaranteed only if M scales no faster than log n. In this paper, the optimal scaling law of the sum-rate with respect to n is proved to be achievable with only one bit of feedback per user. The proof builds on opportunistic beamforming and binary quantization of the signal to noise plus interference ratio. Moreover, the linear scaling of the sum-rate with M is demonstrated to hold for M growing no faster than log n even with such a reduced feedback. Finally, the results above are extended to the MIMO case, where each user is equipped with multiple antennas

The sum-capacity of the multi-antenna Gaussian broadcast channel is known to be achieved by Dirty Paper Coding techniques, that require full channel state information at the base station. It has been recently shown that a sum-rate having the same scaling law of the sum-capacity with respect to the number of users n for a fixed signal to noise ratio (i.e., M log log n where M is the number of transmitting antennas) can be achieved by using reduced feedback (or equivalently reduced channel state information at the transmitter). In particular, it has been proved that n real and n integer numbers are enough to guarantee the optimal scaling law. In this paper, the optimal scaling law of the sum-rate is shown to be achievable with an even smaller amount of feedback and, more precisely, with 1) n log2(M + 1) bits, if a deterministic feedback scheme is employed; 2) an average number of feedback bits that scales as M log2M log n with the number of users n, if a selective (random) feedback scheme is employed.

The outage capacity of a Rayleigh flat fading channel completely unknown at the transmitter and partially known at the receiver is considered in this paper. Analytical expressions for the upper and lower bounds of the outage capacity of such channels are obtained as a function of the channel estimation error at the receiver. Those results reveal how the noise level and the channel uncertainty combine in reducing the outage capacity of the fading channel. In addition, by deriving an expression for the estimation error variance of pilot symbol assisted modulation (PSAM), we are able to establish direct relations among estimation parameters, channel characteristics (in terms of SNR and normalized Doppler spread) and its impact on the outage capacity.