Hybrid Beamformer Codebook Design and Ordering for Compressive mmWave Channel Estimation

Abstract

In millimeter wave (mmWave) communication systems, beamforming with large antenna arrays is critical to overcome high path losses. Separating all-digital beamforming into analog and digital stages can provide the large reduction in power consumption and small loss in spectral efficiency needed for practical implementations. Developing algorithms with this favorable tradeoff is challenging due to the additional degrees of freedom in the analog stage and its accompanying hardware constraints. In hybrid beamforming systems, for example, channel estimation algorithms do not directly observe the channels, face a high channel count, and operate at low SNR before transmit-receive beam alignment. Since mmWave channels are sparse in time and beam domains, many compressed sensing (CS) channel estimation algorithms have been developed that randomly configure the analog beamformers, digital beamformers, and/or pilot symbols. In this paper, we propose to design deterministic beamformers and pilot symbols for openloop channel estimation. We use CS approaches that rely on low coherence for their recovery guarantees, and hence seek to minimize the mutual coherence of the compressed sensing matrix. We also propose a precoder column ordering to design the pilot symbols. Simulation results show that our beamformer designs reduce channel estimation error over competing methods.

Compressed-Sensing based Beam Detection in 5G NR Initial Access

“…6b). In order for further performance improvement, the deterministic ordering [12] may be considered. The two codebooks achieves similar performance with 64 antennas; however, detection probabilities are degraded with a greater number of antennas in Fig.…”

Channel Estimation Using Multi-stage Compressed Sensing for Millimeter Wave MIMO Systems

“…Due to this, we choose SDR-RBR to detect the unknown data symbols. As mentioned above, considering the N − M unknown data symbols transmitted through the estimated channel, each received signal in (10) can be expressed as:…”

“…Fig. 4 illustrates the NMSE performance comparison of channel estimation for the last stage of our multi-stage CS-based algorithm, codebook based ordering scheme [10], codebook based minimal total coherence scheme (MTC) [8], hierarchical codebook based adaptive CS scheme [7], and oracle scheme. From this figure, we can see that the NMSE performance of our proposed scheme outperforms the other codebook schemes although the use of the same quantized angle grids (G = 160).…”

“…Also, the orthogonality of the deterministic pilots is limited by their number. The work in [10] proposed a precoder column ordering algorithm to achieve a lower mutual coherence where the pilot symbol columns are chosen from the discrete Fourier transform (DFT) matrix. However, the pilot orthogonality is affected, because the pilot columns size equal to RF chain numbers in hybrid mmWave MIMO systems as mentioned above.…”

Joint Hybrid Precoding and Combining Design Based Multi-Stage Compressed Sensing Approach for mmWave MIMO Channel Estimation

“…The CS formulation problem in [23] is solved thanks to the orthogonal matching pursuit (OMP) algorithm by employing a redundant dictionary as a sensing matrix on which the design of optimal beam patterns is based on the minimum total coherence (MTC). In [24], a design of a completely deterministic beamformer codebook and pilot symbols are proposed to minimize mutual coherence by using a precoder column ordering algorithm, where the pilot symbol columns are chosen from the discrete Fourier transform (DFT) matrix. In general, the orthogonality of the deterministic pilots is limited by their number.…”