Feedback Reduction for Multiuser MIMO Broadcast Channel with Zero-Forcing Beamforming

In the multiuser multiple-input multiple-output (MU-MIMO) system, to reduce the influence of channel correlation on system performance, the base station (BS) should select the appropriate subset of user equipments (UEs) according to their channel state information (CSI). Due to a lack of channel reciprocity, the downlink CSI needs to be fed back to the BS in frequency division duplexing (FDD) mode. Some scholars have exploited kinds of deep neural networks (DNNs) for sensing and recovering CSI. However, user selection after all the CSI is reconstructed by DNNs will bring a great time delay. In this paper, we propose a deep learning-based CSI feedback scheme called US-CsiNet. Based on adversarial autoencoder (AAE), US-CsiNet can explicitly cover user schedule information while representing CSI. At the UE side, the encoder of US-CsiNet maps the CSI into codewords of which part are feature information for user schedule. Then the BS applies these partial codewords to separate the UEs into different groups and select active UEs. Finally, the decoder of AAE reconstructs the CSI of these active UEs. US-CsiNet can not only simplify the user selection process but also guarantee the accuracy of CSI reconstruction. The simulation results show that the proposed approach outperforms maximum channel gain (MCG) user selection algorithms and achieves the nearly same performance with semiorthogonal user selection (SUS) which needs full CSI of all users at the BS.

In downlink multiuser multiple-input multiple-output (MIMO) systems, system performance highly depends on the reliability of downlink channel state information (CSI) at the base station (BS). In frequency division duplexing, the most practical solution is to have downlink CSI from the users fed back to the BS. Most work on this feedback design has assumed independent block fading channels. However, this paper proposes a new differential feedback scheme using the observation that the channel realizations are usually temporally correlated. The sum-rate loss assuming differential feedback is analyzed for a system with the number of users K equal to the number of transmit antennas M. When K >; M, a user selection algorithm based on an approximated signal-to-interference plus noise ratio (SINR) estimation is proposed. In simulation results, the proposed differential feedback scheme increases the sum-rate compared to previous differential feedback schemes. Moreover, the proposed user selection algorithm outperforms semi-orthogonal user selection in the moderate signal-to-noise ratio (SNR) region, despite requiring less feedback information. In low mobility channels, utilizing the channels' time correlation during quantization is shown to play a bigger role in determining sum-rate performance than multiuser diversity for most SNR regimes when a practical number of users is considered.

In this paper, we discuss the influence of feedback channel delay on throughput of linear multi-user multiple-input multiple-output (MIMO) systems employing vector quantization (VQ) algorithms for encoding channel state information (CSI). We consider an approach where the mobile receiver estimates the downlink channel and chooses one of the predefined channel characterization codewords whose indices are transmitted back to the base station transmitter. In practice, the feedback channel introduces delay in transmission of the indices and we evaluate the resulting channel throughput loss for different system setups. Moreover, we define two new parameters of VQ MIMO systems: the channel eigenmode coherence time and singular value coherence time, and discuss their influence on system design. We demonstrate the performance of two types of systems, one using time division multiplexing of individual mobile users and another transmitting to multiple users at the same time. The simulation results show that feedback delay sensitivity of the multiple-user system throughput is much higher than in the TDM approach. Based on those results we propose a simple method allowing a selection of the VQ resolution for the given channel characteristics and system setup.

<p>This thesis considers the analysis of current and future cellular communication systems. The main focus is on multiuser multiple-input multiple-output (MU-MIMO) antenna systems. The goal of this work is to characterize the achievable spectral efficiency of MU-MIMO systems, as well as to analyze the performance of practical, linear MU-MIMO transceiver structures in heterogeneous propagation environments. The analytical derivations in this thesis are based on the mathematical theory of finite and large dimensional random matrices. A collection of new general random matrix theory results, which permit efficient numerical evaluation are derived. With downlink regularized zero-forcing (RZF) processing at a cellular base station (BS), a general framework for the analysis of the expected (average) signal-to-interference-plus-noise-ratio (SINR) and ergodic sum spectral efficiency is developed for uncorrelated and semi-correlated Rayleigh fading, as well as uncorrelated Ricean fading propagation channels. In contrast to existing results, the presented analyses are extremely general, applicable to single-cellular, multi-cellular, as well as distributed antenna systems. These systems could consist of arbitrary numbers of transmit and receive antennas, link signal-to-noise-ratios (SNRs), equal and unequal transmit correlation structures, and line-of-sight (LoS) levels, respectively. Numerical results are presented for single-cellular, as well as for two-tier multi-cellular systems demonstrating the impact of novel BS coordination strategies to suppress dominant inter-cellular interference. With dominant LoS directions in the propagation channel, the instantaneous downlink zero-forcing (ZF) SNR of a given terminal is analyzed. The ZF SNR is shown to be approximated by a gamma distribution for any number of transmit and receive antennas, link SNRs, and LoS levels. Furthermore, for moderately sized MU-MIMO systems, simplified instantaneous and ergodic sum spectral efficiency analyses are presented with RZF, ZF and matched-filter (MF) transmission on the downlink, and minimum-mean-squared-error, ZF and maximum-ratio combining (MRC) on the uplink, respectively. The simple nature of the derived expressions lead to the discovery of several valuable system level insights as a function of the contributing network parameters. Numerical results are presented for conventional and moderate MU-MIMO systems. Considering downlink semi-correlated Rayleigh fading channels with spatial correlation at the BS, it is mathematically proven that common correlation patterns for each terminal predicts lower ergodic sum spectral efficiencies in comparison to terminal specific correlation patterns. Closed-form approximations for the expected SINR and ergodic sum spectral efficiency are derived for both MF and ZF precoding, demonstrating the sensitivity of unequal correlation structures on the expected signal, interference and noise powers, respectively. The presented numerical results provide a cautionary tale of the impact of unequal correlation patterns on MU-MIMO performance and the importance of modeling this phenomenon. Finally, an approximate uplink performance analysis of large MU-MIMO systems with MRC and space-constrained uniform linear antenna arrays (ULA) is presented for semi-correlated Ricean fading channels. A space-constrained channel model is proposed, encapsulating the effects of unequal receive spatial correlation, unequal LoS levels, and unequal link gains for each terminal. The per-terminal and cell-wide ergodic sum spectral efficiencies are characterized and numerous practical special cases are presented. A limiting analysis of the ergodic per-terminal and cell-wide spectral efficiencies is also carried out, as the number of BS antennas grow without bound with a finite number of terminals and fixed physical dimensions of the ULA. Numerical results demonstrate the impact of space-constrained ULAs on the MU-MIMO system performance with variation in the LoS levels, correlation structures, physical array dimensions, and system size, respectively.</p>

In this paper, an expression for the user's achievable data rate in the multi-user multiple-input multiple-output (MU-MIMO) system with limited feedback (LF) of channel state information (CSI) is derived. The energy efficiency (EE) is optimized through power allocation under quality of service (QoS) constraints. Based on mathematical equivalence and Lagrange multiplier approach, an energy-efficient unequal power allocation (EEUPA) with LF of CSI scheme is proposed. The simulation results show that as the number of transmitting antennas increases, the EE also increases which is promising for the next generation wireless communication networks. Moreover, it can be seen that the QoS requirement has an effect on the EE of the system. Ultimately, the proposed EEUPA with LF of CSI algorithm performs better than the existing energy-efficient equal power allocation (EEEPA) with LF of CSI schemes.

This paper investigates the zero-forcing (ZF) beamforming transmit strategy in the multiple-antenna multiuser downlink systems. We consider the case of mobile users equipped with multiple antennas. Although the capacity of such systems can be achieved by dirty paper coding (DPC), DPC is extremely difficult and challenging to implement. Thus, simple but suboptimal linear beamforming techniques like ZF beamforming can be deployed. However, the number of users that can be served using this strategy is limited by the number of transmit antennas at the base station. The solution for this limitation is user selection (scheduling), which also exploits multiuser diversity. Therefore, user selection can be used to enhance the throughput of the system. Recently, it has been shown that ZF beamforming strategy with user selection is asymptotically optimal for a large number of users. In this paper, a semi-orthogonal user selection (SUS) algorithm is extended to the system with multiple-antenna mobile users. This algorithm aims to select users, which are semi-orthogonal. The optimal ZF beamforming matrices are obtained and it is shown that the optimal ZF beamforming throughput is related to the eigenvalues of the user channels. Therefore, SUS is aimed to select the proper group of users based on maximizing the channel eigenvalues and therefore improving the optimal ZF beamforming throughput of the system.

Expressions are derived for the coverage probability and average rate of both multi-user multiple input multiple output (MU-MIMO) and single input multiple output (SIMO) systems in the context of a fractional frequency reuse (FFR) scheme. In particular, given a reuse region of $\frac{1}{3}$ (FR3) and a reuse region of 1 (FR1) as well as a signal-to-interference-plus-noise-ratio (SINR) threshold $S_{th}$ , which decides the user assignment to either the FR1 or FR3 regions, we theoretically show that: $1)$ the optimal choice of $S_{th}$ which maximizes the coverage probability is $S_{th} = T$ , where $T$ is the target SINR required for ensuring adequate coverage, and $2)$ the optimal choice of $S_{th}$ which maximizes the average rate is given by $S_{th}= T^{\prime}$ , where $T^{\prime}$ is a function of the path loss exponent, the number of antennas and of the fading parameters. The impact of frequency domain correlation amongst the OFDM sub-bands allocated to the FR1 and FR3 cell-regions is analysed and it is shown that the presence of correlation reduces both the coverage probability and the average throughput of the FFR network. Furthermore, the performance of our FFR-aided MU-MIMO and SIMO systems is compared. Our analysis shows that the (2 $\times$ 2) MU-MIMO system achieves 22.5% higher rate than the (1 $\times$ 3) SIMO system and for lower target SINRs, the coverage probability of a (2 $\times$ 2) MU-MIMO system is comparable to a (1 $\times$ 3) SIMO system. Hence the former one may be preferred over the latter. Our simulation results closely match the analytical results.

A major hindrance to the adoption of orthogonalized space-division multiplexing (SDM) via block diagonalization (BD) in multi-user MIMO downlinks is the need for channel state information (CSI) feedback from user terminals. Another drawback is lower than optimal sum rates, theoretically achievable with dirty paper coding (DPC). While multi-user diversity could be leveraged via user selection to narrow the sum- rate performance gap, it requires the presence of very large user pools. To help raise the practical feasibility of BD-SDM, we propose a scheme that jointly reduces CSI feedback while approaching optimal DPC sum rates with smaller user-pool sizes. Additionally, BD-SDM offers the flexibility for spatial mode allocation to cater for individual transmission rate requirements. This presents a challenging resource allocation problem because mode selection at one terminal affects the rates achieved at all other terminals and in turn, the overall sum rate. The proposed scheme offers a systematic means for resource allocation, while minimizing rate loss at the overall- and individual levels. It represents a streamlined process that simultaneously reduces CSI feedback while achieving sum rate maximization, user selection and systematic rate-loss minimizing resource allocation.

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.

Multiple input multiple output (MIMO) processing techniques are of interest for the next generation wireless communication systems due to their potential ability to dramatically improve the system capacity. There have been existed several multi-user MIMO (MU-MIMO) transmit schemes such as zero-forcing dirty paper coding (ZF-DPC), and zero-forcing beamforming (ZFBF). In this paper, we analysis and compare the dynamic transmission schemes based on TDMA and SDMA under perfect and imperfect channel state information (CSI). The system throughput (sum data rate), the optimal user number that can be supported are evaluated under perfect CSI by computer simulations. The effect of imperfect CSI on the throughput of TDMA and SDMA is also investigated. The results show that under perfect channel state information at both transmitter and receiver, the SDMA schemes can achieve a larger throughput than the TDMA scheme because SDMA can fully explore the multiuser diversity by transmitting to the optimal set of users. In contrast, the results show that the system performance of SDMA scheme is sensitive to the channel error.

This work presents a first comprehensive analysis of the impact of vector coded caching (VCC) in multi-user multiple-input multiple-output (MU-MIMO) systems with multiple receive antennas and variable pathloss — two key factors that critically influence systems with inherent MU unicasting behavior. We investigate two widely adopted precoding strategies: (i) block-diagonalization (BD) at the transmitter combined with maximal ratio combining (MRC) at the receivers, and (ii) zero-forcing (ZF) precoding. Our analysis explicitly accounts for practical considerations such as channel fading, channel state information (CSI) acquisition overhead, and fairness-oriented power allocation. Our contributions span both analytical and simulation-based fronts. On the analytical side, we derive analytical expressions for the achievable throughput under BD-MRC and ZF, highlighting the performance benefits of equipping multi-antenna users with cache-aided interference management. Specifically, we develop a low-complexity BD-MRC optimization method that leverages matrix structure to significantly reduce the dimensionality involved in precoding computation, followed by solving the associated max-min fairness problem through an efficient one-dimensional search. In the massive MIMO regime, an asymptotic expression for the achievable throughput over Rayleigh fading channels is also derived. Simulations validate our theoretical results, confirming that VCC delivers substantial performance gains over optimized cacheless MU-MIMO systems. For example, with 32 transmit antennas and 2 receive antennas per user, VCC yields throughput improvements exceeding 300%. These gains are further amplified under imperfect CSI at the transmitter, where VCC’s ability to offload interference mitigation to the receivers ensures robust performance even in the face of degraded CSI quality and elevated acquisition costs.

Deep learning (DL)-based channel state information (CSI) feedback improves the capacity and energy efficiency of massive multiple-input multiple-output (MIMO) systems in frequency division duplexing mode. However, multiple neural networks with different lengths of feedback overhead are required by time-varying bandwidth resources. The storage space required at the user equipment (UE) and the base station (BS) for these models increases linearly with the number of models. In this paper, we propose a DL-based changeable-rate framework with novel quantization scheme to improve the efficiency and feasibility of CSI feedback systems. This framework can reutilize all the network layers to achieve overhead-changeable CSI feedback to optimize the storage efficiency at the UE and the BS sides. Designed quantizer in this framework can avoid the normalization and gradient problems faced by traditional quantization schemes. Specifically, we propose two DL-based changeable-rate CSI feedback networks CH- CsiNetPro and CH- DualNetSph by introducing a feedback overhead control unit. Then, a pluggable quantization block (PQB) is developed to further improve the encoding efficiency of CSI feedback in an end-to-end way. Compared with existing CSI feedback methods, the proposed framework saves the storage space by about 50% with changeable-rate scheme and improves the encoding efficiency with the quantization module.

This paper investigates a precoding method in downlink multiuser multiple-input multiple-output (MIMO) transmission with multiple base station (BS) cooperation, where each user device basically feeds back the instantaneous channel state information (CSI) to only the nearest BS, but the users near the cell edge additionally feedback the instantaneous CSI to the second nearest BS among the cooperating BSs. Our precoding method is categorized as a form of multi-cell processing (MCP) [5], in which the transmission information to a user is shared by the cooperating BSs in order to utilize fully the degrees of freedom of the spatial channel, and is based on block diagonalization of the channel matrix. However, since some elements of the channel matrix are unknown, we allow partially non-orthogonal transmission. More specifically, we allow inter-user interference to users with limited instantaneous CSI feedback from the channel where the instantaneous CSIs of those users are not obtained at the BSs. The other sources of inter-user interference are set to zero based on the block diagonalization of the channel matrix. The proposed method more efficiently utilizes the degrees of freedom of the spatial channel compared to the case with full orthogonal transmission at the cost of increased inter-user interference. Simulation results show the effectiveness of the proposed method compared to the conventional approaches, which can accommodate the partial CSI feedback scenario, from the viewpoints of the required transmission power and achievable throughput.

In this work we investigate the degrees of freedom (DoF) performance of the multiple-input multiple-output (MIMO) interference channel (IC) with limited channel state information (CSI) feedback. We generalise two space-time interference alignment (STIA) algorithms to the K user MIMO IC with a transmit power constraint and show how these schemes exploit both current and outdated CSI to achieve an improved DoF performance. We show that by combining the STIA schemes with traditional methods major DoF gain can be achieved for a variety of limited CSI feedback scenarios in comparison to what would be obtained via the use of the traditional techniques on their own. In particular we prove that optimal DoF can still be achieved in situations where current CSI is unavailable for a derived fraction of the time. Finally we validate the promised DoF results via system simulation and show how these DoF gains reflect in terms of sum rate achievable.

In a multiuser multiple-input multiple-output (MU-MIMO) downlink system, users are susceptible to interuser interference (IUI) because of data being simultaneously transmitted over the same time-frequency resources. Conventionally, precoding algorithms aim to eliminate the IUI. However, constructive interference (CI) precoding can achieve better error performance by exploiting the IUI. This article presents a high-throughput CI precoder. Design optimization across the algorithm and the architecture layers is conducted, reducing the complexity for multiplications by 81.6%. As the number of iterations for convergence varies, dynamic resource allocation is utilized to support each modulation mode with maximized utilization: time-multiplexing for the 4-QAM mode and parallel-processing for the 16-QAM mode. The proposed symbol updater also allows more efficient scheduling. As a proof of concept, a CI precoder chip that supports up to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$16 \times $ </tex-math></inline-formula> MU-MIMO systems is designed based in a 40-nm CMOS technology. The performance gains at a bit error rate (BER) <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$= 10^{-4}$ </tex-math></inline-formula> are 10.7 and 12.5 dB for 4-QAM and 16-QAM, respectively, compared with conventional regularized zero-forcing (RZF) schemes. The precoder delivers a maximum throughput of 3.2 Gb/s at a clock frequency of 200 MHz for the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$16 \times $ </tex-math></inline-formula> MU-MIMO configuration.