Reconfigurable intelligent surface (RIS) is considered to be an energy-efficient approach to reshape the wireless environment for improved throughput. Its passive feature greatly reduces the energy consumption, which makes RIS a promising technique for enabling the future smart city. Existing beamforming designs for RIS mainly focus on optimizing the spectral efficiency for single carrier systems. Meanwhile, complicated bit/power allocation on different spatial domain subchannels needs to be designed for better bit error rate (BER) performance in conventional singular value decomposition-based beamforming. To avoid this, in this paper, we propose a geometric mean decomposition-based beamforming for RIS-assisted millimeter wave (mmWave) hybrid MIMO systems. In this way, multiple parallel data streams in the spatial domain can be considered to have the same channel gain, so that the better BER can be achieved without sophisticated bit/power allocation. Moreover, by exploiting the common angular-domain sparsity of mmWave massive MIMO channels over different subcarriers, a simultaneous orthogonal matching pursuit algorithm is utilized to obtain the optimal multiple beams from an oversampling 2D-DFT codebook. Besides, by only leveraging the angle of arrival and angle of departure associated with the line of sight (LoS) channels, we further design the phase shifters for RIS by maximizing the array gain for LoS channel. Simulation results show that the proposed scheme can achieve better BER performance than conventional approaches. Our work is an initial attempt to discuss the broadband beamforming for RIS-assisted mmWave massive MIMO with the hybrid architecture.

Vector perturbation (VP) precoding is a promising technique for multiuser communication systems operating in the downlink. In this work, we introduce a hybrid framework to improve the performance of lattice reduction (LR) aided precoding in VP. First, we perform a simple precoding using zero forcing (ZF) or successive interference cancellation (SIC) based on a reduced lattice basis. Since the signal space after LR-ZF or LR-SIC precoding can be shown to be bounded to a small range, then along with sufficient orthogonality of the lattice basis guaranteed by LR, they collectively pave the way for the subsequent application of an approximate message passing (AMP) algorithm, which further boosts the performance of any suboptimal precoder. Our work shows that the AMP algorithm can be beneficial for a lattice decoding problem whose data symbols lie in integers $\mathbb{Z}$ and entries of the lattice basis may bot be i.i.d. Gaussian. Numerical results confirm the low-complexity AMP algorithm can improve the symbol error rate (SER) performance of LR aided precoding significantly. Lastly, the hybrid scheme is also proved effective when solving the data detection problem of massive MIMO systems without using LR.

There exist two issues among popular lattice reduction algorithms that should cause our concern. The first one is Korkine-Zolotarev (KZ) and Lenstra-Lenstra-Lovász (LLL) algorithms may increase the lengths of basis vectors. The other is KZ reduction suffers worse performance than Minkowski reduction in terms of providing short basis vectors, despite its superior theoretical upper bounds. To address these limitations, we improve the size reduction steps in KZ and LLL to set up two new efficient algorithms, referred to as boosted KZ and LLL, for solving the shortest basis problem with exponential and polynomial complexity, respectively. Both of them offer better actual performance than their classic counterparts, and the performance bounds for KZ are also improved. We apply them to designing integer-forcing (IF) linear receivers for multi-input multioutput communications. Our simulations confirm their rate and complexity advantages.

This paper investigates low-dimensional quantizers from the perspective of complex lattices. We adopt Eisenstein integers and Gaussian integers to define checkerboard lattices E_m and G_m . By explicitly linking their lattice bases to various forms of E_m and G_m cosets, we discover the E ⁺ _m,2 lattices, based on which we report the best known lattice quantizers in dimensions 14, 15, 18, 19, 22 and 23. Fast quantization algorithms of the generalized checkerboard lattices are proposed to enable evaluating the normalized second moment (NSM) through Monte Carlo integration.

Conventional hybrid precoding and combining based transceivers require a large number of high-resolution radio frequency (RF) phase shifters (PSs), which impose prohibitive hardware costs and power consumption. To address the above issue, both partially connected RF PSs and low-resolution PSs have been proposed. However, the performance limits of these low-cost designs have not been investigated theoretically. Furthermore, there is room for improvement in their spectral efficiency. To fill this knowledge gap, we derive the mean square error performance discrepancy between an optimal precoder/combiner and the hybrid analog-digital precoder/combiner under the constraint of 1-bit PSs relying on lattice theory. Then, by observing that this performance gap can be reduced by deactivating parts of the PSs whilst improving both the spectral and energy efficiency, we develop an adaptive RF PS connection network. To resolve the associated hybrid precoding and combining problems, we appropriately adapt Babai's algorithm from the lattice decoding literature. Our simulation results demonstrate the superiority of the proposed scheme both in terms of its spectral and energy efficiency.

The Compute-and-Forward protocol in quasi-static channels normally employs lattice codes based on the rational integers Z, Gaussian integers Zi or Eisenstein integers Zω, while its extension to more general channels often assumes channel state information at transmitters (CSIT). In this paper, we propose a novel scheme for Compute-and-Forward in block-fading channels without CSIT, which is referred to as Ring Compute-and-Forward because the fading coefficients are quantized to the canonical embedding of a ring of algebraic integers. Thanks to the multiplicative closure of the algebraic lattices employed, a relay is able to decode an algebraic-integer linear combination of lattice codewords. We analyze its achievable computation rates and show it outperforms conventional Compute-and-Forward based on Z-lattices. By investigating the effect of Diophantine approximation by algebraic conjugates, we prove that the degrees-of-freedom (DoF) of the optimized computation rate is n/L, where n is the number of blocks and L is the number of users.