A cellular system in which multi-antenna base stations (BSs) communicate with single-antenna users is considered. BSs are distributed according to a Poisson point process, and each BS uses zero-forcing beamforming (ZFBF) to simultaneously transmit multiple data streams prepared for multiple users. Single-user transmission, which is equivalent to maximum ratio transmission, is also considered as a special case of ZFBF. Net spectral efficiency is the main performance metric used in this paper and is analyzed theoretically to obtain the optimal number of feedback bits required to maximize it. Specifically, tight upper and lower bounds for the derivative of spectral efficiency are newly determined, and the bounds are further used to estimate the optimal number of feedback bits. Consequently, a close estimate of the optimal number is proposed, and the estimate accurately shows the scaling rate of the optimal number. The analytical results of this paper can provide more accurate insights into the required number of feedback bits and achievable system-level performance in interference-limited cellular networks.

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 block diagonalization (BD) based on limited feedback for multiple-antenna broadcast channels. With limited feedback, achievable sum rate is reduced due to multi-user interference. When the chordal distance (ChD) is used as a quantization measure, the number of quantization bits should scale with the signal to noise ratio (SNR) to guarantee full multiplexing gain of MIMO channel. Although the ChD can be used to prove such bit-scaling law, it is not an optimal quantization criterion for limited-feedback-based BD. Moreover, the required number of quantization bits for full multiplexing gain is too large to be realized in practical wireless communications. In this paper, we propose a more-appropriate quantization criterion for channel direction information that can achieve much higher sum capacity with moderate feedback rate than can ChD. We also consider a sufficient condition for quantization bits to maintain achievable multiplexing gain of the proposed quantization criterion.

We consider limited-feedback-based block diagonalization (BD) and user selection for multiple antenna broadcast channels. With limited feedback, the conventional channel norm can not be a good estimate for channel quality of each user, because multiuser interference is not completely eliminated by using BD under limited channel direction information. Therefore, we need an appropriate channel quality indicator (CQI) to increase the diversity gain achieved by multiuser scheduling. To this end, we consider a determinant-based instantaneous channel capacity and propose a new CQI by taking an expectation over precoding matrices that can not be known at the feedback stage. Simulation results show that the sum rate with the proposed CQI is much higher than the sum rate with conventional CQIs.

In this paper, we study low-complexity detection schemes for cooperative multiple-input multiple-output (MIMO) systems with decode-and-forward (DF) relays. In fixed DF protocols, the error propagation effect that limits the diversity gain can be overcome by using joint maximum-likelihood (JML) detection, but its complexity increases exponentially with the number of streams and modulation orders. To develop a low-complexity detection scheme, we first extend the cooperative maximum-ratio combining (C-MRC) scheme to MIMO relay networks, and then investigate the diversity order of the system. We show that C-MRC achieves full diversity gain for orthogonal space-time code, but its diversity gain is limited when the deployed space-time code is non-orthogonal. To address this problem, we propose an effective detection scheme that is applicable to arbitrary space-time codes. On the basis of pairwise error probability approximation, max-log approximation, and the Chernoff bound, we construct an equivalent point-to-point MIMO signal model, and then apply tree-search detection techniques. Compared to JML, the proposed detection scheme significantly reduces the detection complexity while preserving diversity gain. Moreover, it can be readily extended to complex-field network-coding systems whose performance is superior to that of Galois-field network-coding systems. Analysis and simulation results confirm the efficiency of the proposed scheme.

This letter proposes a distributed beamforming scheme based on block diagonalization (BD) for multicell multiuser multiple-input multiple-output (MU-MIMO) downlink systems. Although conventional BD can be directly extended to these systems in a distributed manner, it suffers from sum-rate degradation due to strict zero-forcing (ZF) constraints. To overcome this problem, we introduce a sum-rate maximization problem for BD, to find the optimal selection of ZF constraints. Then we propose a search algorithm to solve the problem in a distributed and heuristic manner. Simulation results show that the proposed scheme effectively finds a near-optimal solution and significantly improves simple extended BD such that it can provide higher sum rate than the conventional schemes.

This paper proposes feedback optimization schemes for multiple-input single-output orthogonal frequency-division multiple access (MISO-OFDMA) systems with heterogeneous users. The proposed scheme adjusts the unit and resolution of the feedback to efficiently exploit the long-term channel statistics, including the path loss, delay spread, and mobility. To develop an analytical optimization framework, we first derive the sum-rate of MISO-OFDMA systems when the channel-state information (CSI) at the transmitter is imperfect because of the quantization error, channel variation, and feedback delay. Based on the derived results, we present effective solutions to the sum-rate maximization problem for distributed and centralized scenarios. When the channel statistics of the users are not available at the base station, each user can improve the sum-rate of the system by minimizing the distortion on CSI feedback under a fixed per-user feedback rate. With the channel statistics of the users, the base station can further control the user set and the feedback rate in addition to the feedback granularity. We evaluate the performance of both distributed and centralized schemes over practical wireless environments, where each user has different long-term channel statistics. Simulation results show that both methods significantly improve the performance of MISO-OFDMA systems.

In this paper, we propose a feedback granularity control scheme for multiuser multiple-input multiple-output orthogonal frequency-division multiple access (MIMO-OFDMA) systems. The proposed scheme resizes the unit and the resolution of the feedback to efficiently exploit channel correlations in both the time and the frequency domains. Two types (centralized and distributed) of granularity search methods are proposed, and their performance characteristics over practical wireless channels are investigated. Simulation results show that the proposed schemes (particularly the distributed method) effectively calculate the optimal granularity, and thus significantly improve the sum-rate of multiuser MIMO-OFDMA systems.

We propose an opportunistic two-stage feedback and scheduling algorithm that is based upon zero-forcing beamforming with semi-orthogonal user selection (ZFBF-SUS) to reduce its feedback load. In an SUS algorithm, a base station schedules semi-orthogonal users using the feedback of all users' channel information. However, such feedback overhead significantly increases with the number of users. To reduce the feedback load of ZFBF-SUS systems, the proposed two-stage feedback scheme opportunistically and separately exploits the signal-to-interference-plus-noise ratio and orthogonality in each stage such that only a fraction of users feed back their channel information. Based on this opportunistic feedback scheme, we decouple the entire process of the SUS into two sub-processes. The proposed two-stage feedback and scheduling scheme effectively exclude the inappropriate users for ZFBF transmission in both feedback and scheduling periods, and thus save the scarce resources consumed for the feedback process. We derive an analytical expression for the average number of feedback bits of the proposed system and optimize it in an averaged sense. Further, the sum-rate of the proposed system is theoretically investigated. Both analytical and simulation results show that the proposed algorithm achieves the performance of conventional ZFBF-SUS systems with a significantly reduced number of feedback bits.