MIMO Precoding with Limited Rate Feedback: Simple Quantizers Work Well

Abstract

Transmitter precoding is a crucial technique for harnessing the potential of multiple-input multiple-output (MIMO) fading channels. In many practical wireless systems, a limited amount of feedback from the receiver is available at the transmitter, which can be used to direct the choice of the precoder from a codebook to match the channel state. Assuming noiseless, limited-rate feedback, this work studies the design of simple, efficient quantization and feedback schemes which achieve nearoptimal ergodic channel capacity. In the case the precoder takes the form of a beamforming vector for modulating a single symbol stream, it is found that simple scalar quantization of the elements of the vector is nearly optimal over a wide range of feedback rates; it typically costs a fraction of a dB higher SNR to achieve the same capacity as that of far more sophisticated vector quantization schemes. In the case a precoding matrix consisting of multiple beams is used to modulate multiple symbol streams, separate encoding of the beams using scalar quantization also performs well. Roughly speaking, the rate loss due to separate encoding of the beams increases linearly with the number of beams but appears to be constant over a wide range of SNRs. The loss can be reduced substantially by more sophisticated encoding of each beam, e.g., two-state trellis coded quantization. The complexity of such quantization schemes is linear in the number of antennas and the number of feedback bits.

Trellis Coded Line Packing: Large Dimensional Beamforming Vector Quantization and Feedback Transmission

“…Ref. [24] proposes to use a two-state trellis to quantize a vector element-by-element while taking only a slight performance loss from [1]. In this paper, we present techniques to process multiple trellis vector elements per trellis stage to boost performance, in addition to enhancements for our original [1].…”

“…More investigation is needed in this area, and it is outside the scope of this paper. 5) PSK/QAM Codebook [24], [25]: Independently from this work, [24], [25] investigated techniques to simplify the searching of a beamforming codebook. Ref.…”

Noncoherent Trellis Coded Quantization: A Practical Limited Feedback Technique for Massive MIMO Systems

“…Related work: We have already mentioned conventional look-up based quantization approaches and discussed why they do not scale. Trellis-based quantizers for CSI generation have been proposed previously in [31]- [34], but the path metrics used for the trellis search are ad hoc. On the other hand, the mapping to noncoherent sequence detection, similar to NTCQ, has been pointed out in [35].…”

Noncoherent trellis-coded quantization for massive MIMO limited feedback beamforming

“…There has been prior work on trellis quantization schemes for beamformer design [24]- [27]. Euclidean distance trellis quantizers have been used to quantize large-dimensional signals in [24].…”

“…Euclidean distance trellis quantizers have been used to quantize large-dimensional signals in [24]. Further, the connection between beamformer quantization and noncoherent trellis codes was first pointed out in [25] and extended in [26], [27].…”