Reduced Complexity Recursive Grassmannian Quantization

Abstract

We propose a novel recursive multi-stage approach to Grassmannian quantization. Compared to the commonly employed single-stage quantization, our method has the advantage of significantly decreasing the number of codebook searches required for quantization and, thus, reducing the complexity. On the downside, the multi-stage approach causes a slight rate-distortion degradation compared to single-stage quantization. We analyze the rate-distortion performance of the proposed recursive quantization approach, considering random vector quantization within the individual stages. We furthermore propose a bit-allocation optimization amongst the stages of the quantizer, given a constraint on the total number of quantization bits.

Codebook Training for Trellis-Based Hierarchical Grassmannian Classification

“…The considered product classification (2) finds application in two scenarios that are relevant for wireless communications: a) Grassmannian CSI quantization in MIMO communications [21], [22]; b) Non-coherent multi-resolution transmission [10], [11]. We briefly outline this connection below.…”

“…We approximate the joint hierarchical classification problem by a trellis-based classifier, generalizing our approach of [10] from one-dimensional to arbitrary m-dimensional subspaces. Our initial approach to this problem in [21] was a greedy recursive classifier, which has the advantage that it allows for an analytic performance investigation; however, it entails a significant performance loss compared to a joint classification. In [22], we have therefore generalized the recursive classifier to a tree-based structure, which allows to trade-off performance for complexity by performing a pruned tree search.…”

Recursive CSI Quantization of Time-Correlated MIMO Channels by Deep Learning Classification

“…We have proposed recursive multi-stage quantization in [26] as a means to reduce the quantization complexity in case a large quantization codebook is employed. In this approach, the CSI is recursively quantized in R stages according tô…”

“…, and find the codebook entry that maximizes the chordal distance. The details of this equivalent, yet less complex quantization problem formulation are explained in [26].…”

“…Contribution: In [26], we have proposed a recursive multistage quantization approach that can reduce the complexity of high resolution Grassmannian quantization in moderate to large-scale MIMO systems by orders of magnitude. In this paper, we show that this approach can effectively be enhanced by DNN classification to further reduce the implementation complexity and, thus, support high resolution Grassmannian quantization with low complexity.…”