Joint Combiner and Precoding in MU-MIMO Downlink Systems with Limited Feedback

Stochastic geometry provides a powerful analytical framework for evaluating interference-limited cellular networks with randomly deployed base stations (BSs). While prior studies have examined limited channel state information at the transmitter (CSIT) and low-resolution analog-to-digital converters (ADCs) separately, their joint impact in multi-user multiple-input multiple-output (MIMO) systems remains largely unexplored. This paper investigates a downlink cellular network in which BSs are distributed according to a homogeneous Poisson point process (PPP), employing zero-forcing beamforming (ZFBF) with limited feedback, and receivers are equipped with one-bit ADCs. We derive a tractable approximation for the achievable spectral efficiency that explicitly accounts for both the quantization error from limited feedback and the receiver distortion caused by coarse ADCs. Based on this approximation, we determine the optimal feedback rate that maximizes the net spectral efficiency. Our analysis reveals that the optimal number of feedback bits scales logarithmically with the channel coherence time but its absolute value decreases due to coarse quantization. Simulation results validate the accuracy of the proposed approximation and confirm the predicted scaling behavior, demonstrating its effectiveness for interference-limited multi-user MIMO networks.

<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>

ABSTRACTIn this paper, several multi‐user scheduling algorithms with limited channel feedback are proposed for multi‐antenna downland channels. With little channel quality information (CQI) and channel direction information (CDI) at multi‐antenna base station, multi‐user scheduling algorithms are carefully designed to maximise the potential system throughput while reducing the feedback load. We first propose a scheduling algorithm that requires a quantised CDI and a threshold CQI. Then we propose a scheduling that needs limited feedback of a threshold CDI and a perfect CQI. Both scheduling algorithms are studied in terms of the achievable throughput and the feedback load. Analytical results show that the proposed scheduling with limited channel feedback has a small performance degradation compared with the scheduling with unlimited channel feedback when the thresholds for user scheduling are judiciously designed. Moreover, under a per user total bit rate constraint of the feedback channel, we propose a scheduling with the quantisation of both CQI and CDI. It is demonstrated that allocating 1 bit to the CQI with an optimal threshold and the remaining bits to the CDI achieves the near optimal sum‐rate performance. Copyright © 2011 John Wiley & Sons, Ltd.

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.

This paper focuses on the design of user selection algorithm for Unitary Beamforming (UBF) in multi-user multiple-input multiple-output (MIMO) systems. A long step user selection (LSUS) algorithm is proposed, and is verified to be rather robust when combined with the Givens rotation-based iterative optimization UBF. For most of existing user selection algorithms, only the best user is chosen at each selection, we regard the step length as one. However, because members of the optimal user set must both have high channel gains and low inter-user interference, if only one user is considered each step, the user that will be selected at next step can not be guaranteed to have both high channel gain and low inter-user interference with the just selected users. Therefore, an algorithm that two users are considered at each selection is proposed in this paper, the step length is regarded as two. It will in some extent help find the favorable user set and finally lead to a higher capacity. Moreover, Gram-Schmidt orthogonalization is used in our proposed algorithm to select the favorable users and at the same time generate the initial unitary beamforming matrix according to the channel state information (CSI). Two other beamforming schemes are simulated as references to demonstrate the good performance of the proposed algorithm even under low signal-to-noise-ratio (SNR) scenario.

Block diagonalization (BD) is a practically favorable precoding technique that eliminates the interuser interference in downlink multiuser multiple-input multiple-output (MIMO) systems. In this paper, we apply BD to the downlink transmission in a cooperative multi-cell system, where the signals from different base stations (BSs) to all the mobile stations (MSs) are jointly designed with the perfect knowledge of the downlink channels and transmit messages. Specifically, this paper studies the BD precoder design to maximize the weighted sum-rate achievable for all the MSs. The associated optimization problem can be formulated in an auxiliary MIMO broadcast channel (BC) with a set of transmit power constraints equivalent to those for different BSs in the multi-cell system. Based on convex optimization techniques, this paper designs an efficient algorithm to solve this problem, and derives the structure of the corresponding optimal BD precoding matrix. Moreover, for the special case of single-antenna BSs and MSs, it is shown that the proposed solution leads to the optimal zero-forcing beamforming (ZF-BF) precoder design for the multiple-input single-output (MISO) BC with the per-antenna power constraints.

The authors investigate quantisation and feedback of channel state information in a multiuser (MU) multiple-input multiple-output (MIMO) system. Each user may receive multiple data streams. The authors design minimises the sum mean squared error (SMSE) while accounting for the imperfections in channel state information (CSI) at the transmitter. This study makes three contributions: first, the authors provide an end-to-end SMSE transceiver design that incorporates receiver combining, feedback policy and transmit precoder design with channel uncertainty. This enables the proposed transceiver to outperform the previously derived limited feedback MU linear transceivers. Second, the authors remove dimensionality constraints on the MIMO system, for the scenario with multiple data streams per user, using a combination of maximum expected signal combining and minimum MSE receiver. This makes each user's feedback independent of the others and the resulting feedback overhead scales linearly with the number of data streams instead of the number of receiving antennas. Finally, the authors analyse the SMSE of the proposed algorithm at high signal-to-noise ratio (SNR) and large number of transmit antennas. As an aside, the authors show analytically why the bit error rate, in the high SNR regime, increases if quantisation error is ignored.

Multiple input multiple output (MIMO) systems have high potential to achieve maximum channel capacity in wireless communication systems. Multi-user (MU) MIMO network with transmit antennas $$T_x$$ at base station can schedule as many single antenna users in one time slot. This necessitates incorporation of a user scheduling strategy. Maximizing sumrate performance without under utilization of channel resources is a primary objective of such scheduling algorithms. Another key design factor for such techniques is to optimize fairness i.e. allowing equal opportunity to all communicating entities. In this paper, we present a simple approach to solve the scheduling problem in MU-MIMO systems while addressing the conflicting objectives of sumrate and fairness. Two variants of the proposed method are also discussed that provide options for maximizing the cumulative sumrate and improving the fairness. Simulations validate the proposed algorithm as a better choice over other conventional methods as it achieves optimal performance with relatively less computational complexity and without compromising fairness. Fairness results are verified by average sumrate method and Jain’s Fariness Index.

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.

This paper considers weighted sum rate maximization constrained with a per base station (BS) antenna power problem for multiuser multiple-input multiple-output (MIMO) systems. For this problem, we propose new downlink-uplink duality based solution. We solve the problem as follows. First, by introducing additional optimization variables, we reformulate our problem into an equivalent problem that incorporates a weighted sum mean-square-error (MSE) term. Second, we establish novel weighted sum MSE duality. The duality is established by modifying the input covariance matrix of the dual uplink problem, and formulating the noise covariance matrix of the uplink channel as a fixed point function. Third, we optimize the introduced variables and powers in the downlink channel by a Geometric Program (GP) method. Fourth, using the duality result and the solution of GP, we apply alternating optimization technique to solve the original downlink problem. In our simulation results, we have observed that the proposed duality based solution utilizes less power than that of existing algorithms.

Multiuser multiple-input multiple-output (MU-MIMO) wireless systems that employ single-carrier frequency-domain equalization (SC-FDE) for uplink transmissions can provide high data rates with increased spectral efficiency under severe channel conditions. However, the availability of accurate channel estimates at the base station (BS) receiver is crucial for achieving peak performance. In this paper, we investigate the use of subspace decomposition and derive a novel algorithm for the blind estimation of MU-MIMO channels in SC-FDE systems, as specified by the 3GPP LTE. By exploiting the long data blocks available in LTE standards, our proposed blind algorithm can obtain accurate estimates of the MU-MIMO channels over every block of transmitted data. This provides for a bandwidth-efficient solution in SC-FDE systems by eliminating (reducing) the need to allocate an entire block of pilot sequences for each active transmitter. Furthermore, since the channel estimation is deployed at the BS, the computational complexity is not considered to be a significant burden for future systems in exchange for the increased spectral efficiency. The results of simulations over fading channels, using realistic system parameters representative of LTE-Advanced, demonstrate the advantages of our proposed blind subspace-based channel estimation algorithm and support the feasibility of the resulting MU-MIMO SC-FDE scheme with reduced training.

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.

Channel state information (CSI) at the base station (BS) is crucial to achieve beamforming and multiplexing gains in multiple-input multiple-output (MIMO) systems. State-of-the-art limited feedback schemes require feedback overhead that scales linearly with the number of BS antennas, which is prohibitive for 5G massive MIMO. This paper proposes novel limited feedback algorithms that lift this burden by exploiting the inherent sparsity in double-directional MIMO channel representation using overcomplete dictionaries. These dictionaries are associated with angle of arrival and angle of departure that specifically account for antenna directivity patterns at both ends of the link. The proposed algorithms achieve satisfactory channel estimation accuracy using a small number of feedback bits, even when the number of transmit antennas at the BS is large-making them ideal for 5G massive MIMO. Judicious simulations reveal that they outperform a number of popular feedback schemes and underscore the importance of using angle dictionaries matching the given antenna directivity patterns, as opposed to uniform dictionaries. The proposed algorithms are lightweight in terms of computation, especially on the user equipment side, making them ideal for actual deployment in 5G systems.

This paper considers the uplink of a single-cell large-scale multiuser multiple-input multiple-output (MU-MIMO) system. The transmitted data is detected by linear receivers at the base station (BS), that is, maximum ratio combining (MRC), zero-forcing (ZF) and minimum mean square error (MMSE). New non-asymptotic outage expressions that are valid for any number of BS antennas are derived. It is shown that the MMSE scheme always achieves the best outage performance, and the ZF scheme outperforms the MRC scheme in the high signal-to-noise-ratio (SNR) regime, while the opposite holds in the low SNR regime. We also demonstrate that when the number of BS antennas is very large and the number of users is fixed, the asymptotic outage probability tends to zero, providing that the channel state information (CSI) is perfect. However, if both the number of BS antennas and the number of users grow large, it would be a different matter. Extensive numerical results are presented to verify the theoretical analysis.