A Design Framework for Scalar Feedback in MIMO Broadcast Channels

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 schemes for feedback reduction in MIMO broadcast channels are considered for a multi-user system. We consider a case where the number of single antenna users K >> M where M is the size of antenna array at the base station (BS). We consider zero-forcing beamforming system with semi-orthogonal user selection algorithm in which channel state information is splitted into channel quality information (CQI) and channel direction information (CDI). In such a user-dense multi-user system feedback channel is inundated if all the users are feedbacking even in the case where only a limited feedback is employed. In order to reduce the feedback load we propose threshold based schemes in which threshold is applied on CQI or CDI. We show that by employing proposed feedback reduction schemes feedback load can be significantly reduced without sacrificing much of the sum-capacity of the system.

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.

In this paper we analyze and design a Heterogenous cellular networks (HetNets) where base stations (BSs) are equipped with multi-antennas, serving a number of singleantenna user equipments (UEs) in downlink. We focus of space division multiple access (SDMA) whereby (i) zero-forcing beamforming vectors at the BSs are chosen based on the quantized channel direction information (CDI) and (ii) scheduled data rates are specified adaptively based on the quantized channel quality information (CQI). Adopting tools of stochastic geometry, we firstly, provide a tight approximation of the coverage performance of quantized SDMA beamforming in a closed-form that encompasses impacts of feedback capacity, density of BSs, and SIR thresholds under max-SIR cell association rule. Assuming CQI of each UE is its experienced SIR, we then exploit our analysis to devise a proper optimization problem to adaptively share feedback capacity between tiers, and also between CDI and CQI feedback. We do so by introducing net spatial throughput (NST) as the main performance metric, which is defined as the spatial throughput minus uplink penalty of feedback capacity per area per frame. Our numerical results show that serving more UEs calls for higher capacity of feedback channel without delivering strong NST. We further observe that one way to coup with such a weak performance is to densify the network in tier 2 wherever path-loss exponent is adequately large, e.g., installing many femto-cells in indoor.

We consider two-user MIMO broadcast and interference channels in which confidential messages intended for each receiver are kept secret from the other receiver. The confidential secrecy rates are nonconvex functions of transmit covariance matrices, which makes it intractable to find optimal transmit covariance matrices analytically. In the MIMO broadcast channels, we prove the weighted secrecy sum rate maximization has zero duality gap and KKT conditions are necessary conditions for the optimal solution. We apply the block successive lower-bound maximization technique to nonconvex weighted secrecy sum rate maximization problems. We also derive numerical algorithms for MIMO interference channels and Gaussian wiretap channels with a cooperative jammer. Every limit point achieved by the proposed algorithms is a local optimal solution that satisfies the KKT conditions. Numerical results show that the proposed algorithms outperform existing suboptimal algorithms in terms of secrecy rates.

This letter proposes a robust joint linear precoding scheme based on the minimum mean squared error (MMSE) criterion for amplify-and-forward (AF) multiple-input multiple-output (MIMO) relay broadcast systems with limited feedback, where only the quantized channel direction information (CDI) of the forward channel is available for the base station (BS) and the relay station (RS). The proposed scheme employs an iterative algorithm which alternately optimizes the BS and RS precoders to jointly minimize the expected MSE conditioned on the quantized CDI.

A two-hop multiple-input multiple-output (MIMO) relay network which comprises a multiple antenna source, an amplify-and-forward MIMO relay and many potential users are studied in this paper. Consider the achievable sum rate as the performance metric, a joint design method for the processing units of the BS and relay node is proposed. The optimal structures are given, which decompose the multiuser MIMO relay channel into several parallel single-input single-output relay channels. With these structures, the signal-to-noise ratio at the destination users is derived; and the power allocation is proved to be a convex problem. We also show that high sum rate can be achieved by pairing each link according to its magnitude. The sum rate of three broadcast strategies, time division multiple access (TDMA) to the strongest user, dirty paper coding (DPC), and beamforming (BF) are investigated. The sum rate bounds of these strategies and the sum capacity (achieved by DPC) gain over TDMA and BF are given. With these results, it can be easily obtained that how far away TDMA and BF are from being optimal in terms of the achievable sum rate.

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.

To maintain a specific degree of multiplexing gain with limited feedback in multiple-input/multiple-output broadcast channels, the number of feedback bits has been increased linearly with the signal-to-noise ratio (SNR) measured in decibel, and conditions for the slope of this increase have been derived in previous studies. However, previous studies mostly focused on the chordal distance (ChD) for channel quantization, although it is not an optimally designed distance measure. Thus, the possibility exists that the same degree of multiplexing gain can be obtained by using fewer feedback bits than the existing method requires. In this paper, we propose an optimal distance measure that can maximize the multiplexing gain achieved by limited-feedback-based block diagonalization over broadcast channels. Then, we provide a sufficient condition for the number of feedback bits to achieve a specific degree of multiplexing gain with the proposed method. The sufficient number of feedback bits is given by a linear function of the SNR (decibel) as in previous studies, but the slope of the linear increase can be much less than that obtained in previous studies. As a consequence, the proposed method achieves higher multiplexing gain and corresponding throughput than the existing methods with the same number of feedback bits.

We consider a MIMO broadcast channel where both the transmitter and receivers are equipped with multiple antennas. A novel joint scheduling and precoding scheme based on the limited feedback is proposed. In the proposed scheme, each receiver feeds back the index which indicates the preferable precoding vector in a predefined codebook and one scalar denoting the quantization error. By using the feedback information from each receiver, the transmitter generates a unitary precoding matrix and schedules users whose channels can match the precoding matrix well according to the scheduling function. This paper explores the scheduling function based on the minimal chordal distance between the generated precoding vector and the quantized preferable precoding vector. Simulation results are exhibited to indicate that the proposed scheme can provide further system performance improvement than other MU-MIMO schemes without increasing the feedback load and avoid the scheduling failure at the transmitter.

Random unitary beamforming (RUB) is an attractive transmission scheme for MIMO broadcast channels because of its ability to achieve high sum-rate capacity with limited feedback. In this letter, we derive the exact analytical expressions for the ergodic sum rate of MIMO broadcast channels with RUB. The analysis is facilitated by the development of the complete statistical characterization of ordered beam SINRs for a user, which can find their application in many related problems.

Multiple antennas at the base station can be employed to serve multiple single-antenna users in the downlink of a system. When the number of active users K is larger than the number of transmit antennas M, the base station can exploit multiuser diversity by cleverly scheduling a set of M users. For this purpose, the base station needs to know the downlink channel state information of all the users in the system. In a frequency division duplex (FDD) system, this is attained with limited feedback from the users. Albeit most of the literature assumes a per-user limited feedback, a system limited feedback is actually more appropriate. Given a constraint on the total amount of airtime available for feedback, in this work we are interested in determining the optimum number of users that should feed back. We observe a tradeoff between the attainable degree of multiuser diversity and the feedback quality. The users are scheduled based on minimizing the sum of the mean square error (MSE) for the selected set of users.

In this paper, we consider two different models of partial channel state information at the base station transmitter (CSIT) for multiple antenna broadcast channels: 1) the shape feedback model where the normalized channel vector of each user is available at the base station and 2) the limited feedback model where each user quantizes its channel vector according to a rotated codebook that is optimal in the sense of mean squared error and feeds back the codeword index. This paper is focused on characterizing the sum rate performance of both zero-forcing dirty paper coding (ZFDPC) systems and channel inversion (CI) systems under the given two partial CSIT models. Intuitively speaking, a system with shape feedback loses the sum rate gain of adaptive power allocation. However, shape feedback still provides enough channel knowledge for ZFDPC and CI to approach their own optimal throughput in the high signal-to-noise ratio (SNR) regime. As for limited feedback, we derive sum rate bounds for both signaling schemes and link their throughput performance to some basic properties of the quantization codebook. Interestingly, we find that limited feedback employing a fixed codebook leads to a sum rate ceiling for both schemes for asymptotically high SNR.

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.

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.