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

Abstract

In this paper we study the beamforming vector quantization and feedback transmission problem for a cooperative transmission environment. Feedback is the primary means of providing the transmitter with channel state information (CSI) in a frequency division duplex (FDD) system. The conventional codebook approach uses a common codebook at the transmitter and at the receiver, while the feedback takes the form of the index of the codebook. This approach has a complexity that scales exponentially with the number of transmit antennas , making the approach less favorable when is large. We propose to use trellis-based quantization to reduce the complexity to grow linearly in . A codebook design criteria is derived for the trellisbased quantizer. We also present three enhancements to the base scheme, each giving 0.2-0.8 dB gain. These enhancements address issues relevant to feedback error, trellis termination, and unequal path-loss from different transmission points. Performance results are shown in numerical simulations.Index Terms-Trellis quantization, beamforming vector codebook, cooperative transmission codebook.

On the Performance of MIMO Nullforming with Random Vector Quantization Limited Feedback

“…These gaps closely agree with the large-N analysis in (13) and (20) showing the performance gain obtained by feeding back best nullforming vectors rather than best beamforming vectors is 2(M − 1)/M . Fig.…”

“…More often, however, it is necessary to estimate the channels at the receiver and provide some sort of feedback to the transmitter to facilitate multi-antenna transmission with a desired directivity pattern [6]. Since feedback creates overhead, several limited-rate feedback techniques have been developed recently for multi-input multi-output (MIMO) and multi-input single-output (MISO) systems, for example see [7]- [20] and the references therein. These techniques are typically based on vector quantization and usually require carefully designed precoding vector codebooks to achieve good performance with low feedback overhead.…”

MIMO nullforming with RVQ limited feedback and channel estimation errors

“…It is often necessary to estimate the channels at the receiver and provide feedback to the transmitter to facilitate multiantenna transmission with a desired directivity pattern [1]. Since feedback creates overhead, several limited-rate feedback techniques have been developed recently for multi-input multi-output (MIMO) and multi-input single-output (MISO) systems, for example see [2]- [10] and the references therein.…”

Noncoherent trellis-coded quantization for massive MIMO limited feedback beamforming

“…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]. But the path metric for the trellis search in [25]- [27] is ad hoc, resulting in a suboptimal use of the trellis quantizer.…”

“…Further, the connection between beamformer quantization and noncoherent trellis codes was first pointed out in [25] and extended in [26], [27]. But the path metric for the trellis search in [25]- [27] is ad hoc, resulting in a suboptimal use of the trellis quantizer. The duality between noncoherent detection and quantization for transmit precoding was pointed out in [28], but the nontrivial trellis codes used in NTCQ outperform the uncoded constellations used in [28].…”