Spectral Efficiency and Energy Efficiency Tradeoff in Massive MIMO Downlink Transmission With Statistical CSIT

This paper investigates the generic signal shaping methods for the multiple-data-stream generalized spatial modulation (GenSM) and the generalized quadrature spatial modulation (GenQSM). Three cases with different channel state information at the transmitter (CSIT) are considered, including no CSIT, statistical CSIT, and perfect CSIT. A unified optimization problem is formulated to find the optimal transmit vector set under size, power, and sparsity constraints. We propose an optimization-based signal shaping (OBSS) approach by solving the formulated problem directly and a codebook-based signal shaping (CBSS) approach by finding the sub-optimal solutions in discrete space. In the OBSS approach, we reformulate the original problem to optimize the signal constellations used for each transmit antenna combination (TAC). Both the size and the entry of all signal constellations are optimized. Specifically, we suggest the use of a recursive design for the size optimization. The entry optimization is formulated as a non-convex large-scale quadratically constrained quadratic programming (QCQP) problem and can be solved by the existing optimization techniques with rather high complexity. To reduce the complexity, we propose the CBSS approach using a codebook generated by the quadrature amplitude modulation (QAM) symbols and a low-complexity selection algorithm to choose the optimal transmit vector set. The simulation results show that the OBSS approach exhibits the optimal performance in comparison with existing benchmarks. However, the OBSS approach is impractical for large-size signal shaping and adaptive signal shaping with instantaneous CSIT due to the demand of high computational complexity. As a low-complexity approach, the CBSS shows comparable performance and can be easily implemented in large-size systems.

In this paper, we investigate energy-efficient multicast precoding for massive multiple-input multiple-output (MIMO) transmission. In contrast with most previous work, where instantaneous channel state information (CSI) is exploited to facilitate energy-efficient wireless transmission design, we assume that the base station can only exploit statistical CSI of the user terminals for downlink multicast precoding. First, in terms of maximizing the system energy efficiency, the eigenvectors of the optimal energy-efficient multicast transmit covariance matrix are identified in closed form, which indicates that optimal energy-efficient multicast precoding should be performed in the beam domain in massive MIMO. Then, the large-dimensional matrix-valued precoding design is simplified into an energy-efficient power allocation problem in the beam domain with significantly reduced optimization variables. Using Dinkelbach’s transform, we further propose a sequential beam domain power allocation algorithm which is guaranteed to converge to the global optimum. In addition, we use the large-dimensional random matrix theory to derive the deterministic equivalent of the objective to reduce the computational complexity involved in sample averaging. We present numerical results to illustrate the near-optimal performance of our proposed energy-efficient multicast precoding for massive MIMO.

Multiple antennas can be used for increasing the packet reliability (spatial diversity) or the spectral efficiency (spatial multiplexing) in wireless communication systems with slow fading. Zheng and Tse showed that both types of gains can be simultaneously obtained for a given multiple antenna channel, but there is a fundamental tradeoff between spatial diversity and spatial multiplexing. They considered the case of no CSIT but perfect CSIR. In this paper, we focus on the role of channel state information at the transmitter (CSIT) on the diversity multiplexing tradeoff. When there is perfect CSIT, there is no packet outage in slow fading channels through proper rate adaptation and hence, the diversity order can be regarded as infinity. However, perfect CSIT is not realistic. Thus, we consider the diversity and multiplexing tradeoff with imperfect CSIT for slow fading MIMO channels. The imperfect CSIT is parameterized by the CSIT estimation error sigma2 DeltaH. Hence, the results obtained are the generalizations of the Zheng-Tse results. We show that when SNRsigma2 DeltaH rarr infin as SNR rarr infin, the availability of the imperfect CSIT does not improve the diversity multiplexing tradeoff

We study a practical version of the broadcast channel (BC) where the channel state information at the transmitter (CSIT) is available only for some of the users, dubbing the system as mixed CSIT. We start with the simplest instance of such a heterogeneous BC where a multi-antenna transmitter base-station (BS) is trying to communicate data to two single-antenna user equipments (UE), having the perfect CSIT about UE1 and no CSIT about UE2. We propose a very simple transmission strategy at the BS for such a system and compare its performance with the interference alignment solution proposed elsewhere which achieves full degrees-of-freedom (DOF) when channel coherence lengths and switching instants abide by certain restrictions. Then with an additional receive antenna granted to UE2 (whose CSIT is not available) and keeping the same CSIT perspective, achievable rates for two users are derived and compared with earlier schemes. Analytical and simulation results show that this additional receive antenna brings significant gains in the system with the same transmission strategy and without any extra requirement of channel training or feedback.

Recently, massive multiple input multiple output (MIMO) is considered as a promising technology to significantly improve the spectral and energy efficiency of fifth generation (5G) networks. Massive MIMO increases the energy efficiency (EE) by three orders of magnitude as compared to single antenna systems. In this paper, we review and analyze energy efficient resource allocation techniques for massive MIMO system. To this end, the energy efficiency of massive massive MIMO with linear processing is formulated. Analytical formulation is provided for the spectral efficiency (SE) and total system power consumption model. The tradeoff on the spectral and energy efficiency is analyzed. The impacts of propagation and system parameters on the SE-EE tradeoff are investigated. Then, large scale fading based analytical approximation for the energy efficiency is formulated. Finally, numerical simulation is done to validate the theoretical analysis.

The degrees of freedom (DoFs) of the two-user multiple-input single-output (MISO) broadcast channel (BC) are studied under the assumption that the form, <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex Notation="TeX">$I_{i},\;i=1, 2$</tex></formula> , of the channel state information at the transmitter (CSIT) for each user's channel can be either perfect <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex Notation="TeX">$(P)$</tex></formula> , delayed <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$(D)$</tex></formula> , or not available <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex Notation="TeX">$(N)$</tex></formula> , i.e., <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$I_{1},I_{2} \in \{P,N,D\}$</tex> </formula> , and therefore, the overall CSIT can alternate between the nine resulting states <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex Notation="TeX">$I_{1}I_{2}$</tex></formula> . The fraction of time associated with CSIT state <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$I_{1}I_{2}$</tex></formula> is denoted by the parameter <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex Notation="TeX">$\lambda_{I_{1}I_{2}}$</tex></formula> and it is assumed throughout that <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex Notation="TeX">$\lambda_{I_{1}I_{2}} = \lambda_{I_{2}I_{1}}$</tex></formula> , i.e., <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\lambda_{PN} = \lambda_{NP}, \lambda_{PD}=\lambda_{DP}, \lambda_{DN}=\lambda_{ND}$</tex> </formula> . Under this assumption of symmetry, the main contribution of this paper is a complete characterization of the DoF region of the two-user MISO BC with alternating CSIT. Surprisingly, the DoF region is found to depend only on the marginal probabilities <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$(\lambda_{P}, \lambda_{D},\lambda_{N})=\left(\sum_{I_{2}}\lambda_{PI_{2}},\sum_{I_{2}}\lambda_{DI_{2}}, \sum_{I_{2}}\lambda_{NI_{2}}\right)$</tex></formula> , <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$I_{2} \in \{P,D,N\}$</tex></formula> , which represent the fraction of time that any given user (e.g., user 1) is associated with perfect, delayed, or no CSIT, respectively. As a consequence, the DoF region with all nine CSIT states, <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">${\cal {D}}(\lambda_{I_{1}I_{2}}:I_{1},I_{2} \in \{P,D,N\})$</tex> </formula> , is the same as the DoF region with only three CSIT states <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">${\cal {D}}(\lambda_{PP}, \lambda_{DD}, \lambda_{NN})$</tex> </formula> , under the same marginal distribution of CSIT states, i.e., <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$(\lambda_{PP}, \lambda_{DD},\lambda_{NN})=(\lambda_{P},\lambda_{D},\lambda_{N})$</tex></formula> . The sum-DoF value can be expressed as <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">${\rm DoF}=\min \left({{4+2\lambda_{P}} \over {3}}, 1+\lambda_{P}+\lambda_{D}\right)$</tex></formula> , from which one can uniquely identify the minimum required marginal CSIT fractions to achieve any target DoF value as <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$(\lambda_{P},\lambda_{D})_{\min}=\left({{3} \over {2}} {\rm DoF}-2,1- {{1} \over {2}} {\rm DoF}\right)$</tex></formula> when <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">${\rm DoF} \in \big [{{4} \over {3}},2\big]$</tex></formula> and <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$(\lambda_{P},\lambda_{D})_{\min}=(0,({\rm DoF}-1)^{+})$</tex></formula> when <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">${\rm DoF} \in \big [0, {{4} \over {3}}\big)$</tex></formula> . The results highlight the synergistic benefits of alternating CSIT and the tradeoffs between various forms of CSIT for any given DoF value. Partial results are also presented for the multiuser MISO BC with <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex Notation="TeX">$M$</tex></formula> transmit antennas and <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$K$</tex> </formula> single antenna users. For this problem, the minimum amount of perfect CSIT required per user to achieve the maximum DoFs of <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\min (M,K)$</tex></formula> is characterized. By the minimum amount of CSIT per user, we refer to the minimum fraction of time that the transmitter has access to perfect and instantaneous CSIT from a user. Through a novel converse proof and an achievable scheme, it is shown that the minimum fraction of time perfect CSIT is required per user in order to achieve the DoF of <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\min (M,K)$</tex></formula> is given by <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\min (M,K)/K$</tex></formula> .

This paper addresses the performance analysis of an adaptive wireless link with one antenna transmitter and a multiple antenna maximum-ratio combining (MRC) receiver. Two main assumptions are used in this paper: (1) Rayleigh fading correlated channels (i.e., MRC branch correlation) and (2) imperfect (outdated) channel state information at the transmitter (CSIT) side. The main contribution of this work lies in the derivation of analytic expressions (in terms of a series expansion) of the statistics of correct packet reception conditional on the decisions made by the transmitter based on outdated CSIT. The novelty of this derivation is the joint modelling of spatially correlated branches, imperfect CSIT, and adaptive modulation based on threshold-trigger decision. Contrary to common belief, the results presented here suggest that spatial correlation not always affects the performance of the MRC receiver: at low signal-to-noise ratio (SNR), correlation can improve performance rather than degrading it. In contrast, at high SNR, correlation is found to always degrade performance. At high SNR, correlation tends to worse the degrading effects of imperfect CSIT, particularly when the number of antennas increases. Imperfect CSIT causes errors in the assignment of MCSs, thus reducing throughput performance. These errors become more evident in the high SNR regime, particularly when the values of branch correlation and the number of antennas increase.

Massive multiple-input multiple-output (MIMO) systems are a main enabler of the excessive throughput requirements in 5G and future generation wireless networks as they can serve many users simultaneously with high spectral and energy efficiency. To achieve this massive MIMO systems require accurate and timely channel state information (CSI), which is acquired by a training process that involves pilot transmission, CSI estimation, and feedback. This training process incurs a training overhead, which scales with the number of antennas, users, and subcarriers. Reducing the training overhead in massive MIMO systems has been a major topic of research since the emergence of the concept. Recently, deep learning (DL)-based approaches have been proposed and shown to provide significant reduction in the CSI acquisition and feedback overhead in massive MIMO systems compared to traditional techniques. In this paper, we present an overview of the state-of-the-art DL architectures and algorithms used for CSI acquisition and feedback, and provide further research directions.

Non-orthogonal multiple access (NOMA) deployment in future wireless networks has been recently considered a promising radio access technology to enhance spectral efficiency (SE). However, gain in SE comes always with the cost of energy efficiency (EE). In this paper, we investigate the SE and EE tradeoff in downlink NOMA with the consideration of quality of service (QoS) requirements based on three population-based multi-objective evolutionary algorithms (MOEAs): multi-objective particle swarm optimization (MOPSO), non-dominated sorting genetic algorithm-II (NSGA-II) and strength Pareto evolutionary algorithm-2 (SPEA2). The tradeoff is optimized and Pareto optimal solutions are obtained through MOEAs. The effectiveness of the algorithms is evaluated based on the hypervolume metric and the capability of solving multi-objective optimization problems. Simulation results reveal that SPEA2 outperforms NSGA-II and MOPSO. Furthermore, NSGA-II is the loser among all algorithms in terms of finding Pareto optimal results.

Research into cutting-edge systems that can satisfy the rising needs for greater data rate and increased reliability is becoming more and more necessary as wireless communication technologies continue to evolve. To enhance the spectral and energy efficiencies, this study examine the performance of massive multiple input multiple output (mMIMO) communication systems using wavelet-order orthogonal frequency division multiplexing (W-OFDM). Also, a communication system was created based on W-OFDM Massive MIMO using MATLAB to model its operation. The simulated system's various stages of operation was examined through detailed analysis and its performance was compare with prior studies and practical networks on OFDM. Key performance metrics, specifically the data throughput, was evaluated to assess the effectiveness and viability of the system. The simulation results indicates that W-OFDM can achieve up to 35% reduction in peak-to-average-power-ratio (PAPR) compared to the traditional OFDM, with a 20% improvement in BER performance under Rayleigh fading conditions. Also, the spectral efficiency of W-OFDM mMIMO outperforms convectional OFDM by 15%, making it a viable technology for future communication networks requiring high data rates and reliability. This implies that, the analytical evaluation confirms that W-OFDM mMIMO provides substantial benefits for improving energy and spectral efficiencies in wireless communication systems, addressing the challenges of increased user demands for high spectrum. This study contributes to the understanding of MIMO systems' performance optimization, highlighting the importance of antenna configuration and cell distance. Comprehensive analysis of spectral efficiency and energy efficiency trade-offs in MIMO systems and identification of optimal antenna configuration for maximum energy efficiency, addressing some of the challenges of future wireless communication systems.

Recently, it has been shown that in a cache-enabled interference channel, the storage at the transmit and receive sides are of equal value in terms of Degrees of Freedom (DoF). This is derived by assuming full Channel State Information at the Transmitter (CSIT). In this paper, we consider a more practical scenario, where a training/feedback phase should exist for obtaining CSIT, during which instantaneous channel state is not known to the transmitters. This results in a combination of delayed and current CSIT availability, called mixed CSIT. In this setup, we derive DoF of a cache-enabled interference channel with mixed CSIT, which depends on the memory available at transmit and receive sides as well as the training/feedback phase duration. In contrast to the case of having full CSIT, we prove that, in our setup, the storage at the receive side is more valuable than the one at the transmit side. This is due to the fact that cooperation opportunities granted by transmitters' caches are strongly based on instantaneous CSIT availability. However, multi-casting opportunities provided by receivers' caches are robust to such imperfection.

Rate Splitting (RS) has emerged as a flexible multiple-access scheme for Multi-User Multiple-Input Multiple-Output (MU-MIMO) systems, generalizing more conventional approaches such as linear precoding or Non-Orthogonal Multiple Access (NOMA), and providing additional robustness against imperfect channel state information at the transmitter. Actual achievable rates cannot be pre-calculated when facing imperfect and/or outdated channel state information at the transmitter (CSIT), so practical real-time mechanisms in the form of link adaptation (LA) are required. The available CSIT is used to design the RS precoders, which can accommodate some degree of robustness, whereas the physical layer feedback reports the outcome of the decoding of the codewords, in the form of acknowledgement (ACK) or negative ACK (NACK), providing the additional meta-robustness needed when the statistical model of CSIT errors is not accurate, and/or the precoders cannot fully track the channel dynamics. We characterize the outage rate region of RS and analyze the convergence of the complete LA-RS system under partial CSIT (non-accurate and non-permanent), providing relevant insights for addressing the adaptation of private and common rates, designing robust precoders with throughput as relevant metric, and handling the time-variant CSIT quality.

This work bridges the gap between sharply contrasting results on the degrees of freedom of the K user broadcast channel where the transmitter is equipped with K transmit antennas and each of the K receivers is equipped with a single antenna. This channel has K DoF when channel state information at the transmitter (CSIT) is perfect, but as shown recently, it has only 1 DoF when the CSIT is limited to finite precision. By considering the full range of partial CSIT assumptions parameterized by β ∈ [0,1], such that the strength of the channel estimation error terms scales as ~ SNR <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-β</sup> relative to the channel strengths which scale as ~ SNR, it is shown that this channel has 1 - β + Kβ DoF. For K = 2 users with arbitrary β <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ij</sub> parameters, the DoF are shown to be 1 + min <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i,j</sub> β <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ij</sub> . To explore diversity of channel strengths, the results are further extended to the symmetric Generalized Degrees of Freedom setting where the direct channel strengths scale as ~ SNR and the cross channel strengths scale as ~ SNR <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">α</sup> , α ∈ [0,1], β ∈ [0,α]. Here, the roles of α and β are shown to counter each other on equal terms, so that the sum GDoF value in the K user setting is (α - β) + K(1 - (α-β )) and for the 2 user setting with arbitrary β <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ij</sub> , is 2 - α + min <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i,j</sub> β <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ij</sub> .

Multiple-input multiple-output (MIMO) systems can be leveraged to increase capacity in fading channels. Especially in multiuser downlink communication systems, it has been shown that knowledge of channel state information at the transmitter (CSIT) is critical to leverage the capacity gain available from multiple antennas. When duplexing is performed using time division, CSIT can often be successfully obtained when channel reciprocity is available. CSIT acquisition, however, is much more difficult in frequency division duplexing. Sending feedback on the uplink has been shown to be a powerful technique to improve downlink performance in single user MIMO systems. The basic idea is to restrict the CSIT to a B bit codebook so that the mobiles can easily transmit these bits on the uplink. In this paper, we consider the multiuser downlink model with unitary precoding when there is a codebook consisting of 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B</sup> unitary matrices that the precoder is restricted to lie in. This codebook is designed offline and known to both the base-station and all users. Each user sends back signal-to-interference plus noise ratio (SINR) information along with binary feedback about the unitary precoder. Based on the CSIT received on the uplink, the base-station selects one of the unitary matrices in the codebook to maximize the sum-rate. For this set-up, we first analyze the sum-rate performance of the unitary precoding scheme. We then show that the codebook of unitary pre-coders represents a collection of points in a special kind of manifold and show how the achievable sum-rate performance relates to the minimum distance of the codebook points in this space. Finally, we present a framework for constructing the codebook to maximize this minimum distance. Monte Carlo simulation results are presented to show the sum-rate performance of the proposed codebook design.

Cell-free (CF) Massive multiple-input multiple-output (MIMO) system is one of the most promising technologies for the fifth generation (5G) wireless communication and beyond, in which the concept of cell boundaries is not respected. This new paradigm aims to cover the users simultaneously through many distributed access points (APs) over the same time/frequency resources based on time-division duplex (TDD) system. In this paper, the uplink spectral efficiency (SE) of a CF Massive MIMO system is investigated based on the stochastic geometry (SG) tool and over Rician fading channels. The distribution of APs is assumed to be random based on the Poisson point process (PPP) to emulate the real AP behavior over the mobile network which has not been considered previously. However, deploying the network's APs irregularly may worsen the phase noise effect and thus the SE of the system. The uplink SE of cell free massive MIMO is derived considering the maximum ratio combining (MRC) at the AP receivers and minimum mean-square error (MMSE) to estimate the channels stats. The simulation results have confirmed that CF Massive MIMO system provides higher SE gain when the APs density is unevenly and largely distributed. However, a considerable cost of the uplink SE is observed when the length of the uplink training period increases for the perfect Channel State Information (CSI) case. Moreover, the performance gap between the perfect and imperfect (CSI) converges when the uplink training increases.