Spatial Intercell Interference Cancellation with CSI Training and Feedback

We investigate intercell interference cancellation (ICIC) with a practical downlink training and uplink channel state information (CSI) feedback model. The average downlink throughput for such a 2-cell network is derived. The user location has a strong effect on the signal-to-interference ratio (SIR) and the channel estimation error. This motivates adaptively switching between traditional (single-cell) beamforming and ICIC at low signal-to-noise ratio (SNR) where ICIC is preferred only with low SIR and accurate channel estimation, and the use of ICIC with optimized training and feedback at high SNR. For a given channel coherence time and fixed training and feedback overheads, we develop optimal data vs. pilot power allocation for CSI training as well as optimal feedback resource allocation to feed back CSI of different channels. Both analog and finite-rate digital feedback are considered. With analog feedback, the training power optimization provides a more significant performance gain than feedback optimization; while conversely for digital feedback, performance is more sensitive to the feedback bit allocation than the training power optimization. We show that even with low-rate feedback and standard training, ICIC can transform an interference-limited cellular network into a noise-limited one.Comment: 24 pages, 10 figures, submitted to IEEE Trans. Wireless Commun., May, 201

Tranceiver Design using Linear Precoding in a Multiuser MIMO System with Limited Feedback

We investigate quantization and feedback of channel state information in a multiuser (MU) multiple input multiple output (MIMO) system. Each user may receive multiple data streams. Our design minimizes the sum mean squared error (SMSE) while accounting for the imperfections in channel state information (CSI) at the transmitter. This paper makes three contributions: first, we 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, we remove dimensionality constraints on the MIMO system, for the scenario with multiple data streams per user, using a combination of maximum expected signal combining (MESC) and minimum MSE receiver. This makes the feedback of each user 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, we analyze SMSE of the proposed algorithm at high signal-to-noise ratio (SNR) and large number of transmit antennas. As an aside, we show analytically why the bit error rate, in the high SNR regime, increases if quantization error is ignored.Comment: Submitted to IET Journals in Communication

Joint Bi-Directional Training of Nonlinear Precoders and Receivers in Cellular Networks

Joint optimization of nonlinear precoders and receive filters is studied for both the uplink and downlink in a cellular system. For the uplink, the base transceiver station (BTS) receiver implements successive interference cancellation, and for the downlink, the BTS station pre-compensates for the interference with Tomlinson-Harashima precoding (THP). Convergence of alternating optimization of receivers and transmitters in a single cell is established when filters are updated according to a minimum mean squared error (MMSE) criterion, subject to appropriate power constraints. Adaptive algorithms are then introduced for updating the precoders and receivers in the absence of channel state information, assuming time-division duplex transmissions with channel reciprocity. Instead of estimating the channels, the filters are directly estimated according to a least squares criterion via bi-directional training: Uplink pilots are used to update the feedforward and feedback filters, which are then used as interference pre-compensation filters for downlink training of the mobile receivers. Numerical results show that nonlinear filters can provide substantial gains relative to linear filters with limited forward-backward iterations.Comment: 12 pages, 9 figures, submitted to IEEE Trans. Signal Process., Aug. 201

Multiuser MIMO Sequential Beamforming with Full-duplex Training

Multiple transmitting antennas can considerably increase the downlink spectral efficiency by beamforming to multiple users at the same time. However, multiuser beamforming requires channel state information (CSI) at the transmitter, which leads to training overhead and reduces overall achievable spectral efficiency. In this paper, we propose and analyze a sequential beamforming strategy that utilizes full-duplex base station to implement downlink data transmission concurrently with CSI acquisition via in-band closed or open loop training. Our results demonstrate that full-duplex capability can improve the spectral efficiency of uni-directional traffic, by leveraging it to reduce the control overhead of CSI estimation. In moderate SNR regimes, we analytically derive tight approximations for the optimal training duration and characterize the associated respective spectral efficiency. We further characterize the enhanced multiplexing gain performance in the high SNR regime. In both regimes, the performance of the proposed full-duplex strategy is compared to the half-duplex counterpart to quantify spectral efficiency improvement. With experimental data [1] and 3D channel model [2] from 3GPP, in a 1.4 MHz 8X8 system LTE system with the block length of 500 symbols, the proposed strategy attains a spectral efficiency improvement of 130% and 8% with closed and open loop training, respectively.Comment: Accepted on Sep-28-2016 for publications at IEEE Transactions on Wireless Communications. Please check the IEEE website for the final published versio

Symbol-level and Multicast Precoding for Multiuser Multiantenna Downlink: A Survey, Classification and Challenges

Precoding has been conventionally considered as an effective means of mitigating the interference and efficiently exploiting the available in the multiantenna downlink channel, where multiple users are simultaneously served with independent information over the same channel resources. The early works in this area were focused on transmitting an individual information stream to each user by constructing weighted linear combinations of symbol blocks (codewords). However, more recent works have moved beyond this traditional view by: i) transmitting distinct data streams to groups of users and ii) applying precoding on a symbol-per-symbol basis. In this context, the current survey presents a unified view and classification of precoding techniques with respect to two main axes: i) the switching rate of the precoding weights, leading to the classes of block- and symbol-level precoding, ii) the number of users that each stream is addressed to, hence unicast-/multicast-/broadcast- precoding. Furthermore, the classified techniques are compared through representative numerical results to demonstrate their relative performance and uncover fundamental insights. Finally, a list of open theoretical problems and practical challenges are presented to inspire further research in this area.Comment: Submitted to IEEE Communications Surveys & Tutorial

Achievable Rates of FDD Massive MIMO Systems with Spatial Channel Correlation

It is well known that the performance of frequency-division-duplex (FDD) massive MIMO systems with i.i.d. channels is disappointing compared with that of time-division-duplex (TDD) systems, due to the prohibitively large overhead for acquiring channel state information at the transmitter (CSIT). In this paper, we investigate the achievable rates of FDD massive MIMO systems with spatially correlated channels, considering the CSIT acquisition dimensionality loss, the imperfection of CSIT and the regularized-zero-forcing linear precoder. The achievable rates are optimized by judiciously designing the downlink channel training sequences and user CSIT feedback codebooks, exploiting the multiuser spatial channel correlation. We compare our achievable rates with TDD massive MIMO systems, i.i.d. FDD systems, and the joint spatial division and multiplexing (JSDM) scheme, by deriving the deterministic equivalents of the achievable rates, based on popular channel models. It is shown that, based on the proposed eigenspace channel estimation schemes, the rate-gap between FDD systems and TDD systems is significantly narrowed, even approached under moderate number of base station antennas. Compared to the JSDM scheme, our proposal achieves dimensionality-reduction channel estimation without channel pre-projection, and higher throughput for moderate number of antennas and moderate to large channel coherence time, though at higher computational complexity

Joint Spatial Division and Multiplexing

We propose Joint Spatial Division and Multiplexing (JSDM), an approach to multiuser MIMO downlink that exploits the structure of the correlation of the channel vectors in order to allow for a large number of antennas at the base station while requiring reduced-dimensional Channel State Information at the Transmitter (CSIT). This allows for significant savings both in the downlink training and in the CSIT feedback from the user terminals to the base station, thus making the use of a large number of base station antennas potentially suitable also for Frequency Division Duplexing (FDD) systems, for which uplink/downlink channel reciprocity cannot be exploited. JSDM forms the multiuser MIMO downlink precoder by concatenating a pre-beamforming matrix, which depends only on the channel second-order statistics, with a classical multiuser precoder, based on the instantaneous knowledge of the resulting reduced dimensional effective channels. We prove a simple condition under which JSDM incurs no loss of optimality with respect to the full CSIT case. For linear uniformly spaced arrays, we show that such condition is closely approached when the number of antennas is large. For this case, we use Szego asymptotic theory of large Toeplitz matrices to design a DFT-based pre-beamforming scheme requiring only coarse information about the users angles of arrival and angular spread. Finally, we extend these ideas to the case of a two-dimensional base station antenna array, with 3-dimensional beamforming, including multiple beams in the elevation angle direction. We provide guidelines for the pre-beamforming optimization and calculate the system spectral efficiency under proportional fairness and maxmin fairness criteria, showing extremely attractive performance. Our numerical results are obtained via an asymptotic random matrix theory tool known as deterministic equivalent approximation.Comment: 10 figure

Base Station Cooperation with Feedback Optimization: A Large System Analysis

In this paper, we study feedback optimization problems that maximize the users' signal to interference plus noise ratio (SINR) in a two-cell MIMO broadcast channel. Assuming the users learn their direct and interfering channels perfectly, they can feed back this information to the base stations (BSs) over the uplink channels. The BSs then use the channel information to design their transmission scheme. Two types of feedback are considered: analog and digital. In the analog feedback case, the users send their unquantized and uncoded CSI over the uplink channels. In this context, given a user's fixed transmit power, we investigate how he/she should optimally allocate it to feed back the direct and interfering (or cross) CSI for two types of base station cooperation schemes, namely, Multi-Cell Processing (MCP) and Coordinated Beamforming (CBf). In the digital feedback case, the direct and cross link channel vectors of each user are quantized separately, each using RVQ, with different size codebooks. The users then send the index of the quantization vector in the corresponding codebook to the BSs. Similar to the feedback optimization problem in the analog feedback, we investigate the optimal bit partitioning for the direct and interfering link for both types of cooperation. We focus on regularized channel inversion precoding structures and perform our analysis in the large system limit in which the number of users per cell ($K$) and the number of antennas per BS ($N$) tend to infinity with their ratio $\beta=\frac{K}{N}$ held fixed

QoS Constrained Power Minimization in the MISO Broadcast Channel with Imperfect CSI

We consider the design of linear precoders and receivers in a Multiple-Input Single-Output (MISO) Broadcast Channel (BC). We aim at minimizing the transmit power while fullfiling a set of per-user Quality-of-Service (QoS) constraints expressed in terms of per-user average rate requirements. The Channel State Information (CSI) is assumed to be perfectly known at the receivers but only partially at the transmitter. To solve the problem we transform the QoS constraints into Minimum Mean Square Error (MMSE) constraints. We then leverage the MSE duality between the BC and the Multiple Access Channel (MAC), as well as standard interference functions in the dual MAC, to perform power minimization by means of an Alternating Optimization (AO) algorithm. Problem feasibility is also studied to determine whether the QoS constraints can be fulfilled or not. Finally, we present an algorithm to balance the average rates and manage situations that may be unfeasible or lead to an unacceptably high transmit power

Robust Transmission for Massive MIMO Downlink with Imperfect CSI

In this paper, the design of robust linear precoders for the massive multi-input multi-output (MIMO) downlink with imperfect channel state information (CSI) is investigated. The imperfect CSI for each UE obtained at the BS is modeled as statistical CSI under a jointly correlated channel model with both channel mean and channel variance information, which includes the effects of channel estimation error, channel aging and spatial correlation. The design objective is to maximize the expected weighted sum-rate. By combining the minorize-maximize (MM) algorithm with the deterministic equivalent method, an algorithm for robust linear precoder design is derived. The proposed algorithm achieves a stationary point of the expected weighted sum-rate maximization problem. To reduce the computational complexity, two low-complexity algorithms are then derived. One for the general case, and the other for the case when all the channel means are zeros. For the later case, it is proved that the beam domain transmission is optimal, and thus the precoder design reduces to the power allocation optimization in the beam domain. Simulation results show that the proposed robust linear precoder designs apply to various mobile scenarios and achieve high spectral efficiency.Comment: 14 pages, 9 figures, Accepted by IEEE Transactions on Communication