Multi-antenna Broadcast Channel Research Articles

How Much Feedback Is Required for TDD Multi-Antenna Broadcast Channels with User Selection?

The enormous gains in a multi-antenna transmitter broadcast channel require the Channel State Information at the Transmitter (CSIT). Although the fundamental question How much feedback is required for a broadcast channel? has been treated in the literature to some extent, a more comprehensive treatment is certainly desirable. We study the time-division duplex broadcast channel with initial assumption of channel state information (CSI) neither at the base station (BS) nor at the users' side. We provide two transmission strategies through which the BS and the users get necessary CSI. We derive novel lower and upper bounds for the sum rate reflecting the rate loss compared to a perfect CSIT system. Corresponding approximate sum rate expressions are also developed for both schemes. These expressions fully capture the benefits of the CSIT feedback, allowing multi-user diversity gain and better inter-user interference cancellation, and the cost of exchange of information required. These expressions can be optimized for any set of system parameters to unveil the trade-off between the cost and the gains associated to feedback. Thus they allow to characterize the optimal amount of feedback which maximizes the sum rate of the broadcast channel, a well-accepted metric of system performance at the physical layer.

Mode Switching for the Multi-Antenna Broadcast Channel Based on Delay and Channel Quantization

Imperfect channel state information degrades the performance of multiple-input multiple-output (MIMO) communications; its effect on single-user (SU) and multi-user (MU) MIMO transmissions are quite different. In particular, MU-MIMO suffers from residual inter-user interference due to imperfect channel state information while SU-MIMO only suffers from a power loss. This paper compares the throughput loss of both SU and MU MIMO on the downlink due to delay and channel quantization. Accurate closed-form approximations are derived for the achievable rates for both SU and MU MIMO. It is shown that SU-MIMO is relatively robust to delayed and quantized channel information, while MU MIMO with zero-forcing precoding loses spatial multiplexing gain with a fixed delay or fixed codebook size. Based on derived achievable rates, a mode switching algorithm is proposed that switches between SU and MU MIMO modes to improve the spectral efficiency, based on the average signal-to-noise ratio (SNR), the normalized Doppler frequency, and the channel quantization codebook size. The operating regions for SU and MU modes with different delays and codebook sizes are determined, which can be used to select the preferred mode. It is shown that the MU mode is active only when the normalized Doppler frequency is very small and the codebook size is large.

Joint Beamforming and Power Control for Multiantenna Relay Broadcast Channel With QoS Constraints

This paper studies the two-hop relay broadcast channel (BC) for a relay-assisted wireless cellular network where the multiuser independent downlink signals from the base station (BS) are first transmitted to a fixed relay station (RS), and then forwarded by the RS to multiple mobile users. Assuming both the BS and RS are equipped with multiantennas, we study the joint optimization of linear beamforming and power control at the BS and RS so as to minimize their weighted sum-power consumption under the user minimum signal-to-interference-noise-ratio (SINR) - quality-of-service (QoS) - constraints. We apply two well-known criteria in the literature, namely, the ldquoSINR balancingrdquo and the ldquochannel-inversion,rdquo for the design of linear precoding in the traditional nonrelay-assisted multiantenna BC to the relay-assisted multiantenna BC. First, a convergence-ensured iterative SINR-balancing algorithm is proposed to successively in turn optimize the transmit parameters at one station (BS or RS) with those at the other station being fixed. Second, a joint BS and RS channel-inversion algorithm is proposed together with a novel technique, termed ldquoeigenmode switching,rdquo at the RS to reduce the power penalty of the channel inversion. Simulation results show that the proposed joint beamforming and power control schemes provide substantial power savings to achieve the assigned user QoS constraints.

Performance of Orthogonal Beamforming for SDMA With Limited Feedback

On the multiantenna broadcast channel, the spatial degrees of freedom support simultaneous transmission to multiple users. The optimal multiuser transmission, which is known as dirty paper coding, is not directly realizable. Moreover, close-to-optimal solutions such as Tomlinson-Harashima precoding are sensitive to channel state information (CSI) inaccuracy. This paper considers a more practical design called per user unitary and rate control (PU2RC), which has been proposed for emerging cellular standards. PU2RC supports multiuser simultaneous transmission, enables limited feedback, and is capable of exploiting multiuser diversity. Its key feature is an orthogonal beamforming (or precoding) constraint, where each user selects a beamformer (or precoder) from a codebook of multiple orthonormal bases. In this paper, the asymptotic throughput scaling laws for PU2RC with a large user pool are derived for different regimes of the signal-to-noise ratio (SNR). In the multiuser interference-limited regime, the throughput of PU2RC is shown to logarithmically scale with the number of users. In the normal SNR and noise-limited regimes, the throughput is found to scale double logarithmically with the number of users and linearly with the number of antennas at the base station. In addition, numerical results show that PU2RC achieves higher throughput and is more robust against CSI quantization errors than the popular alternative of zero-forcing beamforming if the number of users is sufficiently large.

How many users should be turned on in a multi-antenna broadcast channel?

This paper considers broadcast channels with L antennas at the base station and m single-antenna users, where L and m are typically of the same order. We assume that only partial channel state information is available at the base station through a finite rate feedback. Our key observation is that the optimal number of on-users (users turned on), say s, is a function of signal-to-noise ratio (SNR) and feedback rate. In support of this, an asymptotic analysis is employed where L, m and the feedback rate approach infinity linearly. We derive the asymptotic optimal feedback strategy as well as a realistic criterion to decide which users should be turned on. The corresponding asymptotic throughput per antenna, which we define as the spatial efficiency, turns out to be a function of the number of on-users s, and therefore s must be chosen appropriately. Based on the asymptotics, a scheme is developed for systems with finite many antennas and users. Compared with other studies in which s is presumed constant, our scheme achieves a significant gain. Furthermore, our analysis and scheme are valid for heterogeneous systems where different users may have different path loss coefficients and feedback rates.

Differentiated rate scheduling for the down-link of cellular systems

We consider the problem of differentiated rate scheduling for the downlink (i.e., multi-antenna broadcast channel), in the sense that the rates required by different users must satisfy certain constraints on their ratios. When full channel state information (CSI) is available at the transmitter and receivers, the problem can be readily solved using dirty paper coding (DPC) and the application of convex optimization techniques on the dual problem which is the multiple access channel (MAC). Since in many practical application full CSI may not be feasible and computational complexity prohibitive when the number of users is large, we focus on other simple schemes that require very little CSI: time-division opportunistic (TO) beamforming where in different time slots (of different lengths) the transmitter performs opportunistic beamforming to the users requiring the same rate, and weighted opportunistic (WO) beamforming where the random beams are assigned to those users having the largest weighted SINR. For single antenna systems we also look at the capacity-achieving superposition coding (SC) scheme. In all cases, we determine explicit schedules to guarantee the rate constraints and show that, in the limit of large number of users, the throughput loss compared to the unconstrained throughput (sum-rate capacity) tends to zero. We further provide bounds on the rate of convergence of the sum-rates of these schemes to the sum-rate capacity. Finally, we provide simulation results of the performance of different scheduling schemes considered in the paper.

Beam Selection Strategies for Orthogonal Random Beamforming in Sparse Networks

Orthogonal random beamforming (ORB) constitutes a mean to exploit spatial multiplexing and multi-user diversity (MUD) gains in multi-antenna broadcast channels. To do so, as many random beamformers as transmit antennas (M) are generated and on each beam the user experiencing the most favorable channel conditions is scheduled. Whereas for a large number of users the sum-rate of ORB exhibits an identical growth rate as that of dirty paper coding, performance in sparse networks (or in networks with an uneven spatial distribution of users) is known to be severely impaired. To circumvent that, in this paper we modify the scheduling process in ORB in order to select a subset out of the M available beams. We propose several beam selection algorithms and assess their performance in terms of sum-rate and aggregated throughput (i.e., rate achieved with practical modulation and coding schemes), along with an analysis of their computational complexity. Since ORB schemes require partial channel state information (CSI) to be fed back to the transmitter, we finally investigate the impact of CSI quantization on system performance. More specifically, we prove that most of the MUD can be still exploited with very few quantization bits and we derive a beam selection approach trading-off system performance vs. feedback channel requirements.

Scheduling for Multiuser MIMO Downlink Channels with Ranking-Based Feedback

We consider a multi-antenna broadcast channel with more single-antenna receivers than transmit antennas and partial channel state information at the transmitter (CSIT). We propose a novel type of CSIT representation for the purpose of user selection, coined as ranking-based feedback. Each user calculates and feeds back the rank, an integer between 1 and W + 1, of its instantaneous channel quality information (CQI) among a set of W past CQI measurements. Apart from reducing significantly the required feedback load, ranking-based feedback enables the transmitter to select users that are on the highest peak (quantile) with respect to their own channel distribution, independently of the distribution of other users. It can also be shown that this feedback metric can restore temporal fairness in heterogeneous networks, in which users' channels are not identically distributed and mobile terminals experience different average signal-to-noise ratio (SNR). The performance of a system that performs user selection using ranking-based CSIT in the context of random opportunistic beamforming is analyzed, and we provide design guidelines on the number of required past CSIT samples and the impact of finite W on average throughput. Simulation results show that feedback reduction of order of 40‐50% can be achieved with negligible decrease in system throughput.

Convex optimization of error probability of multi-antenna broadcast channel

In this paper, we propose a nonlinear convex optimization problem to minimize the average probability of error of all the users, subject to the peak or the average power constraints in the multi-input–multi-output broadcast channel. The proposed transmitter represents a nonlinear one-to-one mapping between the transmitted data vector and the symbol vector. The transmitted data vector going through the base station antennas is obtained as a solution to the proposed convex error probability optimization problem that can be solved using computationally efficient interior point algorithms. It is proved that the proposed transmitter is always optimal unless the signal-to-noise ratio (SNR) is too low or the channel is nearly singular. Simulation results demonstrate that the proposed transmission scheme significantly improves the probability of error as compared to several earlier approaches to multi-antenna broadcast transmitter design.

Space Division Multiple Access With a Sum Feedback Rate Constraint

On a multi-antenna broadcast channel, simultaneous transmission to multiple users by joint beamforming and scheduling is capable of achieving high throughput, which grows double logarithmically with the number of users. The sum rate for channel state information (CSI) feedback, however, increases linearly with the number of users, reducing the effective uplink capacity. To address this problem, a novel space division multiple access (SDMA) design is proposed, where the sum feedback rate is upper-bounded by a constant. This design consists of algorithms for CSI quantization, threshold based CSI feedback, and joint beamforming and scheduling. The key feature of the proposed approach is the use of feedback thresholds to select feedback users with large channel gains and small CSI quantization errors such that the sum feedback rate constraint is satisfied. Despite this constraint, the proposed SDMA design is shown to achieve a sum capacity growth rate close to the optimal one. Moreover, the feedback overflow probability for this design is found to decrease exponentially with the difference between the allowable and the average sum feedback rates. Numerical results show that the proposed SDMA design is capable of attaining higher sum capacities than existing ones, even though the sum feedback rate is bounded.

Rate maximization in multi-antenna broadcast channels with linear preprocessing

The sum rate capacity of the multi-antenna broadcast channel has recently been computed. However, the search for efficient practical schemes that achieve it is still ongoing. In this paper, we focus on schemes with linear preprocessing of the transmitted data. We propose two criteria for the preceding matrix design: one maximizing the sum rate and the other maximizing the minimum rate among all users. The latter problem is shown to be quasiconvex and is solved exactly via a bisection method. In addition to preceding, we employ a signal scaling scheme that minimizes the average bit-error-rate (BER). The signal scaling scheme is posed as a convex optimization problem, and thus can be solved exactly via efficient interior-point methods. In terms of the achievable sum rate, the proposed technique significantly outperforms traditional channel inversion methods, while having comparable (in fact, often superior) BER performance