X 1 channel vector, where matrix H = [h1,h2,.. ,hnul is the Nr X Nu complex-valued uplink channel matrix. As mentioned earlier, perfect knowledge of the channel state information is necessary at the transmitter in order to achieve the capacity of a multi-user MIMO channel. However, in practical systems, the receiver only provides partial channel state information through uplink feedback channels to the transmitter, i.e., the multi-user MIMO precoding with limited feedback. The received signal in the downlink of an MU-MIMO system with limited feedback precoding is mathematically expressed as yk + Nk, k = 1,2, Nu. Since the transmit vector for limited feedback precoding is where E is the error vector generated as a result of the limited feedback and vector quantization, the received signal can be rewritten as: kkk1,u (10-45) where is the residual interference due to the limited feedback precoding. To reduce the residual interference term, one should use more accurate channel state information feedback which results in the use of more uplink resources for the feedback. It is shown in reference [55] that the number of feedback bits per mobile B must be increased linearly with the SNR PdB (in decibels) at the rate of B = (N t - 1)log2 p = PdB(Nt - 1)/3 in order to achieve the full multiplexing gain of Nt. In addition, the scaling of B guarantees that the throughput loss relative to zero-forcing precoding with perfect channel state information knowledge at the transmitter is upper-bounded by N bps/Hz, which corresponds to a 3 dB power offset. The throughput of a feedback-based zero-forcing system is bounded, if the SNR approaches infinity and the number of feedback bits per mobile is fixed. Reducing the number of feedback bits according to B = alog2 p for any a < N - 1 results in a strictly inferior multiplexing gain of N[a/(N - 1)] where N is the number of transmit antennas and p is the SNR of the downlink channel. In order to calculate the amount of the feedback required to maintain certain throughput, the difference