Optimization and tradeoff analysis of two-way limited feedback beamforming systems

Sch. of Electr. & Comput. Eng., Purdue Univ., West Lafayette, IN, USA
IEEE Transactions on Wireless Communications (Impact Factor: 2.5). 06/2009; DOI: 10.1109/TWC.2009.080366
Source: IEEE Xplore


In a two-way system where two users transmit data to each other, limited feedback beamforming is a simple method to supply channel state information to the transmitter (CSIT) for a multiple-input-multiple-output (MIMO) system when channel reciprocity is unavailable. For analytical tractability, most existing papers assume the existence of an ideal fixed-rate feedback channel to assist the transmitter to adapt to instantaneous channel conditions. The relationship between the feedback rate and data rate is typically analyzed in a unidirectional manner. In reality, judicious resource allocation to transmitting feedback and data leads to a tradeoff between the effective forward and reverse data rates. In this paper, we represent the achievable rate by effective SNRs, and we present a framework to analyze the tradeoff. We find that the forward and reverse rate tradeoff can be decomposed into two local tradeoffs, resulting from the resource allocation policy of each user. The local tradeoff region for each user is found in closed-form, whereas the overall tradeoff region is approximated for the special case when the two users have equal hardware configurations.

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    • "It is worthwhile to note that the results are the same for the Grassmannian and random codebooks. In the previous works on limited feedback systems, the performance analysis was focused on the average SNR or the average rate loss [30]. In an average sense, the Grassmannian codebook is in general outperforms the random codebook. "
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    ABSTRACT: In this paper, we propose an opportunistic downlink interference alignment (ODIA) for interference-limited cellular downlink, which intelligently combines user scheduling and downlink IA techniques. The proposed ODIA not only efficiently reduces the effect of inter-cell interference from other-cell base stations (BSs) but also eliminates intra-cell interference among spatial streams in the same cell. We show that the minimum number of users required to achieve a target degrees-of-freedom (DoF) can be fundamentally reduced, i.e., the fundamental user scaling law can be improved, by using the ODIA, compared to the existing downlink IA schemes. In addition, we introduce a limited feedback strategy in the ODIA framework, and then analyze the required number of feedback bits leading to the same performance as that of the ODIA assuming perfect feedback. To further improve the sum-rate performance, we also modify the ODIA, which achieves optimal multiuser diversity gain, i.e., $\log \log N$, per spatial stream even in the presence of downlink inter-cell interference, where $N$ denotes the number of users in a cell. Simulation results show that the ODIA significantly outperforms existing interference management and user scheduling techniques in terms of sum-rate in realistic cellular environments. The ODIA operates in a distributed and decoupled manner while requiring no information exchange among BSs and no iterative optimization between BSs and users, thus leading to an easier implementation.
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    • "One is to minimize the total transmit power whereas the other is to maximize the minimum of the two transceiver signal to noise ratios (SNRs). The twoway beamforming system with limited feedback is analyzed in [8]. In [9], two relay processing schemes in two-way relaying based on zero forcing (ZF) and minimum mean square error (MMSE) criteria are studied, and two power control strategies are proposed for ZF system. "
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    ABSTRACT: In this paper, we consider a two-way relay network, where multiple pairs of users exchange their information with the help of a multi-antenna relay station by means of two-way relaying. A relay processing scheme based on minimum mean square error (MMSE) criterion is employed at the relay station to suppress inter- and intra-pair interference. We formulate the optimization problem of minimizing the total transmit power of all users under the relay transmit power constraint and the given sum rate constraint. To solve the optimization problem and get the joint relay processing and power control policy, we propose an iteration algorithm. Simulation results show the performance of the proposed schemes and are coherent with what we expected.
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    • "For this system, bounds on the feedback rate for maximizing net throughput are derived. For a similar system, net throughput is maximized in [26] by optimizing power allocation to training, feedback and data transmission. Net throughput optimization for the beamforming system is also investigated in [27] in terms of optimal bandwidth allocation to feedback and data transmission. "
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    ABSTRACT: Transmit beamforming is a simple multi-antenna technique for increasing throughput and the transmission range of a wireless communication system. The required feedback of channel state information (CSI) can potentially result in excessive overhead especially for high mobility or many antennas. This work concerns efficient feedback for transmit beamforming and establishes a new approach of controlling feedback for maximizing net throughput, defined as throughput minus average feedback cost. The feedback controller using a stationary policy turns CSI feedback on/off according to the system state that comprises the channel state and transmit beamformer. Assuming channel isotropy and Markovity, the controller's state reduces to two scalars. This allows the optimal control policy to be efficiently computed using dynamic programming. Consider the perfect feedback channel free of error, where each feedback instant pays a fixed price. The corresponding optimal feedback control policy is proved to be of the threshold type. This result holds regardless of whether the controller's state space is discretized or continuous. Under the threshold-type policy, feedback is performed whenever a state variable indicating the accuracy of transmit CSI is below a threshold, which varies with channel power. The practical finite-rate feedback channel is also considered. The optimal policy for quantized feedback is proved to be also of the threshold type. The effect of CSI quantization is shown to be equivalent to an increment on the feedback price. Moreover, the increment is upper bounded by the expected logarithm of one minus the quantization error. Finally, simulation shows that feedback control increases net throughput of the conventional periodic feedback by up to 0.5 bit/s/Hz without requiring additional bandwidth or antennas. Comment: 29 pages; submitted for publication
    IEEE Transactions on Signal Processing 09/2009; 58(6). DOI:10.1109/TSP.2010.2045426 · 2.79 Impact Factor
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