Limited Feedback in Multiple-Antenna Systems with One-Bit Quantization
Despite the potential gain of precoding and therefore the importance of CSIT, there is — to our knowledge — no work that has considered limited feedback with low-resolution ADCs. The results on limited feedback with infinite-resolution ADCs cannot be directly extended to the low-resolution ADCs — the fundamentals are different. For example, in MISO limited feedback beamforming, the optimum beamformer f is phase invariant, meaning that equivalent performance is also achieved by f e^(j \theta). In our capacity results, we found that the optimum beamformer was the matched filter, and in fact was not phase invariant. The reason is that phase at the receiver is important when the received signal is sliced by 1-bit ADCs; an important function of CSIT is to align the phase of the received signals. One implication is that phase-invariant Grassmannian beamforming codebooks will no longer be appropriate.
We developed an approach for limited feedback in SISO and MISO channels with one-bit ADCs. For the SISO channel, only the phase of the channel is quantized while in the MISO channel, the channel direction and residual phase are both quantized and fed back to the transmitter. We evaluated the power and capacity losses incurred by the use of limited feedback. Based on our analyses and simulation results, we made two important observations. First, feeding back only one bit for the phase (or residual phase in MISO channel) is enough to guarantee good performance in the examples considered. Second, when the capacity of the quantized channel is saturated, the required number of feedback bits guaranteeing a small capacity loss decreases with SNR.
Jianhua Mo and R. W. Heath, Jr., “Limited Feedback in Multiple-Antenna Systems with One-Bit Quantization,” in Proc. of the 2015 Asilomar Conf. on Signals, Systems, and Computers, November 8-11, 2015. Video of presentation.
The work was supported in part by the National Science Foundation under Grant Nos. NSF-CCF-1527079.