Multiple Antenna Broadcast Channels With Shape Feedback and Limited Feedback

We consider the block diagonalization (BD) and user selection based on limited feedback in multiple antenna broadcast channels. With limited feedback, due to the imperfect channel state information at the transmitter (CSIT), BD cannot completely eliminate multiuser interference, and the throughput is correspondingly lower than that achieved with perfect CSIT. Nevertheless, the achievable multiuser diversity gain can be the same, such that limited-feedback-based BD can achieve an optimal throughput growth as the number of users increases. To show this, we first propose a channel quality indicator (CQI) for user selection. The CQI is designed to accurately estimate an achievable rate of each user and is given by an expected rate, where the expectation is solely taken over precoding matrices which cannot be known at the feedback stage. With the proper CQI, user selection can benefit from a large number of users in the system. As a result, we show that the BD can achieve an asymptotically optimal growth in throughput with the proposed CQI, based solely on a finite-rate feedback of channel information.

The traditional limited feedback scheme can use imperfect channel state information to achieve interference alignment (IA) in a fully connected situation. But these solutions could no longer be used directly in heterogeneous networks where partial connectivity is considered. To solve this problem, this article proposes an IA scheme based on limited feedback with differentiation for the two‐tiered heterogeneous network. First, users who are affected by different types and numbers of interference and corresponding base stations are divided into different units according to the partial connectivity of heterogeneous networks. Then, we design interference alignment algorithm for each unit separately. Next, considering the imperfect channel state information, we derive the leakage of interference caused by the limited feedback, and give expressions for the upper bound of sum rate loss in various units. Finally, dynamic feedback bit allocation is carried out to each unit with the goal of minimizing the throughput loss in the limited feedback system. The simulation results show that the proposed IA scheme can eliminate interference well and efficiency of limited feedback can be improved through dynamic feedback bit allocation, so that system can obtain higher sum rate than other schemes.

This paper presents an empirical study of the achievable data rates of network multiple-input multiple-output (MIMO) techniques including zero-forcing (ZF), zero-forcing dirty paper coding (ZF-DPC) and dirty paper coding (DPC) using actual 4-by-4 indoor wireless channel measurements at 3.5 GHz. Their performances are contrasted with those of conventional techniques, in which either the base stations are not coordinated (NC), or their interference is avoided using frequency division (FD) multiplexing. The measurements were taken in aisle-to-office and large unobstructed hall scenarios. The study of these results reveals that, at high signal-to-noise ratios (SNRs), DPC and ZF-DPC can yield more than a three-fold increase in attainable data rates when compared to NC and FD. The gains obtained using ZF are smaller, but still significant. At low SNRs the system is noise-(rather than interference-) limited, and only DPC exhibits gains. The evaluations in this paper also show that collaborative systems such as DPC can benefit from interference-prone environments to yield increased transmission capacity. With regard to the propagation channel, the classical log-normal plus Rayleigh/Ricean fading model, with parameters fitted to the scenario type, was found to be good at predicting the statistics of the achievable data rates of all the strategies considered.

A resource allocation algorithm for orthogonal frequency division multiple access-based and infrastructure-based relay networks is introduced in this paper. The algorithm is applied in the downlink of a single cell. Channel state information is exploited at the transmitting base station (BS) and at the transmitting relay stations (RSs). The algorithm coordinates the allocation of subcarriers, bits, and power distributed over the BS and RSs. The goal of the resource allocation algorithm is that the sum rate in a cell is maximized. Simultaneously, each subscriber station (SS) achieves a requested data rate called minimum data rate, and a tolerated bit error probability is ensured on each link. Simulation results show that a sum rate in a cell is achieved which is near to an upper bound introduced in the paper. Even if the sum of the minimum data rates of all SSs is large, the proposed algorithm offers the minimum data rate nearly as reliable as the upper bound. Additionally, simulation results show that the proposed algorithm achieves a superior sum rate compared to the sum rate of other resource allocation algorithms.

Joint linear beamforming and scheduling are performed in a system where limited feedback is present at the transmitter side. The feedback conveyed by each user to the base station consists of channel direction information (CDI) based on a predetermined codebook and a scalar metric with channel quality information (CQI) used to perform user scheduling. In this paper, we present a design framework for scalar feedback in MIMO broadcast channels with limited feedback. An approximation on the sum rate is provided for the proposed family of metrics, which is validated through simulations. For a given number of active users and average SNR conditions, the base station is able to update certain transmission parameters in order to maximize the sum-rate function. On the other hand, the proposed sum-rate function provides a means of simple comparison between transmission schemes and scalar feedback techniques. Particularly, the sum rate of SDMA and time division multiple access (TDMA) is compared in the following extreme regimes: large number of users, high SNR, and low SNR. Simulations are provided to illustrate the performance of various scalar feedback techniques based on the proposed design framework.

We consider the uplink three-cell single-user cellular systems with limited feedback interference alignment (IA). Considering the exchange of channel state information (CSI) between base stations (BSs), IA solution can be done at BSs. Then the indices of the quantized precoding vectors are fed back to users. A joint quantization strategy, which quantizes the precoding vectors for different users jointly, is proposed. The proposed quantization scheme enlarges the codebooks and quantizes precoding vectors jointly through the exchange of codebook information between BSs. The quantized precoding vectors for different users are set to have a same index. Only one of the three BSs is appointed to broadcast the same index so that the total feedback cost would not be increased. With the proposed quantization scheme, the quantization errors are mitigated and the system sum rate is increased. A quantization criterion, which we refer to as the maximum sum rate criterion, is also proposed. Compared with the general minimum chordal distance criterion, the proposed quantization criterion can achieve a higher sum rate. Performance improvement of the proposed scheme is analyzed. Simulations also confirm its effectiveness.

Near-orthogonal transmission over MIMO broadcast channels with limited feedback is addressed, identifying the intrinsic tradeoffs that govern the system performance in terms of sum rate. A low-complexity scheme is proposed for joint scheduling and beamforming, which employs feedback in the form of quantized channel directions and lower bounds on each user's received SINR, given a maximum orthogonality factor epsi between transmit beamforming vectors (epsi = 0 if orthogonal beamforming). The authors assume a simple power allocation, which consists of distributing the available power equally over the active beams. In a system with K active users and a given average SNR, the authors show that the sum rate is a function of the number of antennas, the number of active beams (considered less than or equal to the number of antennas), the orthogonality factor epsi and the quantization codebook size. A practical rate function is derived for the described system which approximates the average sum rate accurately as validated through computer simulations. Based on the proposed rate function, optimality of SDMA vs. TDMA systems with asymptotically large number of users is shown. In addition, the authors provide a performance comparison between the proposed algorithm with limited feedback and other approaches with different level of channel state information at the transmitter.

Orthogonal frequency division multiplexing (OFDM) is a practical technique for communicating over broadband channels in multi-path fading environments. It is well known that varying the power allocation from frequency tone-to-frequency tone, commonly called power loading, can improve capacity or error rate performance. Unfortunately, the implementation of power loading is complicated by the fact that the transmitter must have knowledge of the forwardlink channel. This assumption is often unrealistic, particularly in systems using frequency division duplexing (FDD). In this paper we present a limited feedback approach for power loading OFDM symbols. In this approach, the receiver, which is assumed to have full forwardlink channel knowledge, designs a power loading vector and conveys it to the transmitter over a limited rate feedback channel. The technique uses a codebook of power loading vectors known to both the transmitter and receiver. We design limited feedback schemes for error rate optimized and capacity optimized power loading. We show how to design quantizers using iterative optimization techniques from the theory of vector quantization for the case of error rate selection. In the capacity case, we characterize optimal feedback schemes for asymptotic signal-to-noise ratio (SNR) scenarios and present a simple method called multi-mode power loading that uses a codebook that switches subcarriers off and on. Simulation results show that the limited feedback techniques provide performance close to perfect channel knowledge power loading.

We study a two-user multiple-input single-output Gaussian interference channel with limited rate feedback and transmitter cooperation. Each receiver quantizes the channel state information of the direct and cross channels, and sends the codebook indices back to the transmitters through two sum-rate-limited feedback channels. The quantization errors reduce the beamforming gain from the direct transmitter, and cause interference leakage from the cross transmitter. Under an assumption of high signal-to-noise ratio, we first approximate the average transmission rate of each link, and use the sum rate to find the optimal transmit power and corresponding feedback bit allocation. We show that the maximum sum throughput is achieved using full transmit power, and the achievable sum rate under limited feedback is bounded above by a constant. We then extend the results to the case where secrecy is desired. In contrast to the first problem, increasing the transmit power beyond a certain point decreases the secrecy performance. Additionally, we analyze the asymptotic behavior of the solutions when the total feedback bandwidth and the number of transmit antennas grow large. We derive all results in closed form. Simulations validate the theoretical analysis and demonstrate the significant performance gains that result from the use of optimal transmit power control and intelligent feedback bit allocation.

We consider the downlink of a multiuser communication system with multiple antennas at the transmitter and at each receiver. A new transmission scheme that employs dirty-paper coding (DPC) with partial interference cancellation is proposed. It is shown that given any user ordering the achievable throughput is asymptotically optimal in the high signal-to-noise ratio (SNR) regime and for all values of the SNR it improves over the throughput of the zero-forcing dirty-paper coding (ZFDPC) scheme [1]. Due to its implementation complexity issues, we also consider a low complexity linear transmission scheme. A precoding technique where interference is canceled successively at the base station is proposed. In this case, users treat the partial interference at the receiver as an independent noise, and it is shown that compared to other linear transmission schemes such as the block-diagonalization (BD) and the zero-forcing schemes, the achievable throughput of the proposed precoding scheme is improved for all SNR values.

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 this paper, we consider practical multiuser multiple-input multiple-output (MU-MIMO) systems where each user has multiple receive antennas and limited channel feedback is available at the base station (BS). The joint combiner and precoding scheme for downlink transmission is proposed, in which we consider the joint use of the receive antenna combiner at each user and precoding at the BS. In the proposed scheme, each user independently chooses the codeword as its preferred-beam vector from the predefined codebook, which maximizes the effective channel gain after the receive antenna combiner. Utilizing the received feedback from users, the BS can easily construct the precoding matrix by zero-forcing beamforming (ZFBF) criterion. In addition, a user selection algorithm is provided to select served users, when the number of users exceeds the number of transmit antennas. Numerical results show that the proposed scheme improves the sum-rate performance of MU-MIMO downlink systems.

We consider the beamformer design for zero-forcing dirty paper coding (ZF-DPC), a suboptimal transmission technique for MISO broadcast channels (MISO BCs). For the sum rate maximization problem under a total power constraint, the existing beamformer designs in the literature are based on the QR decomposition (QRD), which is used to satisfy the ZF constraints. However, the optimality of the QRD-based design has been unknown previously. In this paper, we prove that the QRD-based design is optimal for ZF-DPC for any performance measure under a sum power constraint. For the per-antenna power constraints, the QRD-based designs become suboptimal, and we propose an optimal design, using a convex optimization framework. Low-complexity suboptimal designs are also presented, and numerically shown to achieve a significant fraction of the sum rate provided by the optimal design.

The objective of this paper is to study the performance of a multicell vector perturbation (MVP) precoding technique under practical situations in a network multiple-input multiple-output (MIMO) scheme employing joint transmission. The conventional perturbation strategy that minimizes the total power is considered, and the power at each base station (BS) is properly scaled to enforce per-BS power constraints. In our scenario, we consider multiple-antenna users and use block diagonalization (BD) as the linear front-end precoder for VP. The sum rate for the MVP in the case of uniformly distributed input and an asymptotic upper bound on the sum rate at high signal-to-noise ratios (SNRs) are derived. In addition, using the asymptotic upper bound on the individual user rates, we propose a proportionally fair (PF) user scheduling algorithm of lower complexity and better performance compared with the benchmark fair semiorthogonal user selection (SUS) algorithm. As opposed to the PF-SUS, the proposed PF scheduling algorithm requires no predefined correlation threshold. Furthermore, we study the impact of backhaul delay on the performance of both VP and BD by deriving bounds on the sum rate. The numerical results show that MVP in the case of perfect channel state information (CSI) outperforms multicell BD. In the presence of a backhaul delay, the performance of MVP significantly degrades, but the upper bound on the sum rate for MVP is still higher than for multicell BD.

A two-user cooperative diversity system based on Alamouti signaling was proposed, which utilizes the orthogonal structure of Alamouti signaling to make cooperative users relay on the shared channel resources so that the spectral efficiency of the traditional cooperative system can be improved. When M-ary phase shift keying (M-PSK) modulation and an improved selection decode-and-forward (SDF) relaying protocol with limited feedback are used at the users and m(m ⩾1) receive antennas are configured at the base station, the average bit-error-rate (BER) system performance for statistically similar uplink channels was derived and it was verified by simulations. Under various channel scenarios of interest, numerical and simulation results show that the diversity gain achieved and the BER performance of the proposed system increase with the interuser channel quality, and the full transmit diversity order of two can be obtained for sufficiently high interuser signal-to-noise ratios (SNRs).