Millimeter wave (mmWave) communications has been regarded as a key enabling technology for 5G networks, as it offers orders of magnitude greater spectrum than current cellular bands. In contrast to conventional multiple-input–multiple-output (MIMO) systems, precoding in mmWave MIMO cannot be performed entirely at baseband using digital precoders, as only a limited number of signal mixers and analog-to-digital converters can be supported considering their cost and power consumption. As a cost-effective alternative, a hybrid precoding transceiver architecture, combining a digital precoder and an analog precoder, has recently received considerable attention. However, the optimal design of such hybrid precoders has not been fully understood. In this paper, treating the hybrid precoder design as a matrix factorization problem, effective alternating minimization (AltMin) algorithms will be proposed for two different hybrid precoding structures, i.e., the fully-connected and partially-connected structures. In particular, for the fully-connected structure, an AltMin algorithm based on manifold optimization is proposed to approach the performance of the fully digital precoder, which, however, has a high complexity. Thus, a low-complexity AltMin algorithm is then proposed, by enforcing an orthogonal constraint on the digital precoder. Furthermore, for the partially-connected structure, an AltMin algorithm is also developed with the help of semidefinite relaxation. For practical implementation, the proposed AltMin algorithms are further extended to the broadband setting with orthogonal frequency division multiplexing modulation. Simulation results will demonstrate significant performance gains of the proposed AltMin algorithms over existing hybrid precoding algorithms. Moreover, based on the proposed algorithms, simulation comparisons between the two hybrid precoding structures will provide valuable design insights.
On the other hand, much less attention has been paid on the partially-connected structure @cite_17 @cite_19 @cite_37 @cite_33 @cite_6 @cite_13 . In @cite_17 @cite_19 , codebook-based design of hybrid precoders was presented for narrowband and orthogonal frequency division multiplexing (OFDM) systems, respectively. Although the codebook-based design enjoys a low complexity, there will be certain performance loss, and it is not clear how much performance gain can be further obtained. By utilizing the idea of successive interference cancellation (SIC), an iterative hybrid precoding algorithm for the partially-connected structure was proposed in @cite_37 . The algorithm is established based on the assumption that the digital precoding matrix is diagonal, which means that the digital precoder only allocates power to different data streams, and the number of RF chains should be equal to that of the data streams. However, using only analog precoders to provide beamforming gains is obviously a suboptimal strategy @cite_37 @cite_33 , which also deviates from the motivation of hybrid precoding. So far there is no study directly optimizing the hybrid precoders without extra constraints in the partially-connected structure, which will be pursued in this paper.
@cite_37 @cite_33 @cite_6 @cite_19 @cite_13 @cite_17
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Millimeter wave (mmWave) MIMO will likely use hybrid analog and digital precoding, which uses a small number of RF chains to reduce the energy consumption associated with mixed signal components like analog-to-digital components not to mention baseband processing complexity. However, most hybrid precoding techniques consider a fully connected architecture requiring a large number of phase shifters, which is also energy-intensive. In this paper, we focus on the more energy-efficient hybrid precoding with subconnected architecture, and propose a successive interference cancelation (SIC)-based hybrid precoding with near-optimal performance and low complexity. Inspired by the idea of SIC for multiuser signal detection, we first propose to decompose the total achievable rate optimization problem with nonconvex constraints into a series of simple subrate optimization problems, each of which only considers one subantenna array. Then, we prove that maximizing the achievable subrate of each subantenna array is equivalent to simply seeking a precoding vector sufficiently close (in terms of Euclidean distance) to the unconstrained optimal solution. Finally, we propose a low-complexity algorithm to realize SIC-based hybrid precoding, which can avoid the need for the singular value decomposition (SVD) and matrix inversion. Complexity evaluation shows that the complexity of SIC-based hybrid precoding is only about 10 as complex as that of the recently proposed spatially sparse precoding in typical mmWave MIMO systems. Simulation results verify that SIC-based hybrid precoding is near-optimal and enjoys higher energy efficiency than the spatially sparse precoding and the fully digital precoding. We propose a new hybrid precoding technique for massive multi-input multi-output (MIMO) systems using spatial channel covariance matrices in the analog precoder design. Applying a regularized zero-forcing precoder for the baseband precoding matrix, we find an unconstrained analog precoder that maximizes signal-to-leakage-plus-noise ratio (SLNR) while ignoring analog phase shifter constraints. Subsequently, we develop a technique to design a constrained analog precoder that mimics the obtained unconstrained analog precoder under phase shifter constraints. The main idea is to adopt an additional baseband precoding matrix, which we call a compensation matrix. We analyze the SLNR loss due to the proposed hybrid precoding compared to fully digital precoding, and determine which factors have a significant impact on this loss. In the simulations, we show that if the channel is spatially correlated and the number of users is smaller than the number of RF chains, the SLNR loss becomes negligible compared to fully digital precoding. The main benefit of our method stems from the use of spatial channel matrices in such a way that not only is each user's desired signal considered, but also the inter-user interference is incorporated in the analog precoder design. In this paper, we propose a hybridly connected structure for hybrid beamforming in millimeter-wave (mmWave) massive MIMO systems, where the antenna arrays at the transmitter and receiver consist of multiple sub-arrays, each of which connects to multiple radio frequency (RF) chains, and each RF chain connects to all the antennas corresponding to the sub-array. In this structure, through successive interference cancelation, we decompose the precoding matrix optimization problem into multiple precoding sub-matrix optimization problems. Then, near-optimal hybrid digital and analog precoders are designed through factorizing the precoding sub-matrix for each sub-array. Furthermore, we compare the performance of the proposed hybridly connected structure with the existing fully and partially connected structures in terms of spectral efficiency, the required number of phase shifters, and energy efficiency. Finally, simulation results are presented to demonstrate that the spectral efficiency of the hybridly connected structure is better than that of the partially connected structure and that its spectral efficiency can approach that of the fully connected structure with the increase in the number of RF chains. Moreover, the proposed algorithm for the hybridly connected structure is capable of achieving higher energy efficiency than existing algorithms for the fully and partially connected structures. Hybrid analog digital precoding offers a compromise between hardware complexity and system performance in millimeter wave (mmWave) systems. This type of precoding allows mmWave systems to leverage large antenna array gains that are necessary for sufficient link margin, while permitting low cost and power consumption hardware. Most prior work has focused on hybrid precoding for narrow-band mmWave systems, with perfect or estimated channel knowledge at the transmitter. MmWave systems, however, will likely operate on wideband channels with frequency selectivity. Therefore, this paper considers wideband mmWave systems with a limited feedback channel between the transmitter and receiver. First, the optimal hybrid precoding design for a given RF codebook is derived. This provides a benchmark for any other heuristic algorithm and gives useful insights into codebook designs. Second, efficient hybrid analog digital codebooks are developed for spatial multiplexing in wideband mmWave systems. Finally, a low-complexity yet near-optimal greedy frequency selective hybrid precoding algorithm is proposed based on Gram–Schmidt orthogonalization. Simulation results show that the developed hybrid codebooks and precoder designs achieve very-good performance compared with the unconstrained solutions while requiring much less complexity.