A Systematic Distributed Quantizer Design Method with an Application to MIMO Broadcast Channels

We introduce a systematic distributed quantizer design method, called {\it{localization}}, in which, out of an existing centralized (global) quantizer, one synthesizes the distributed (local) quantizer using high-rate scalar quantization combined with entropy coding. The general localization procedure is presented, along with a practical application to a quantized beamforming problem for multiple-input multiple-output broadcast channels. For our particular application, not only localization provides high performance distributed quantizers with very low feedback rates, but also reveals an interesting property of finite rate feedback schemes that might be of theoretical interest: For single-user multiple-input single-output systems, one can achieve the performance of almost any quantized beamforming scheme with an arbitrarily low feedback rate, when the transmitter power is sufficiently large.