Abstract-A simple signaling method for broadcast channels with multiple-transmit multiple-receive antennas is proposed. In this method, for each user, the direction in which the user has the maximum gain is determined. The best user in terms of the largest gain is selected. The corresponding direction is used as the modulation vector (MV) for the data stream transmitted to the selected user. The algorithm proceeds in a recursive manner where in each step, the search for the best direction is performed in the null space of the previously selected MVs. It is demonstrated that with the proposed method, each selected MV has no interference on the previously selected MVs. Dirty-paper coding is used to cancel the remaining interference. For the case that each receiver has one antenna, the presented scheme coincides with the known scheme based on Gram-Schmidt orthogonalization (QR decomposition). To analyze the performance of the scheme, an upper bound on the cumulative distribution function (CDF) of each subchannel is derived which is used to establish the diversity order and the asymptotic sum-rate of the scheme. It is shown that using fixed rate codebooks, the diversity order of the jth data stream, 1 j M, is equal to N(M 0 j + 1)(K 0 j + 1), where M, N, and K indicate the number of transmit antennas, the number of receive antennas, and the number of users, respectively. Furthermore, it is proven that the throughput of this scheme scales as M log log(K) and asymptotically (K 0! 1) tends to the sum-capacity of the multiple-input multiple-output (MIMO) broadcast channel. The simulation results indicate that the achieved sum-rate is close to the sum-capacity of the underlying broadcast channel.Index Terms-Dirty-paper coding, multiple-antenna arrays, multiple-input multiple-output (MIMO) broadcast channels, multiuser diversity, multiuser systems, QR decomposition, space-division-multiple access.

In this work we study a Multiple-Input Multiple-Output wireless system where the channel state information is partially available at the transmitter through a feedback link. Based on Singular Value Decomposition, the MIMO channel is split into independent sub-channels which allows separate, and therefore, efficient decoding of the transmitted data signal. Effective feedback of the required spatial channel information entails efficient quantization/encoding of a Haar unitary matrix. The parameter reduction of anparameters is performed through Givens decomposition. We prove that Givens matrices of a Haar unitary matrix are statistically independent. Subsequently, we derive the Probability Distribution Function (PDF) of the corresponding matrix elements. Based on these analyses, an efficient quantization scheme is proposed. 2The performance evaluation is provided for a scenario where the rates allocated to each independent channel are selected according to its corresponding gain. The results indicate a significant performance improvement compared to the performance of MIMO systems without feedback at the cost of a very low-rate feedback link.

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Abstract-In this paper, a MIMO Broadcast Channel (MIMO-BC) with large (K) number of users is considered. It is assumed that all users have a hard delay constraint D. We propose a scheduling algorithm for maximizing the throughput of the system, while satisfying the delay constraint for all users. It is proved that by using the proposed algorithm, it is possible to achieve the maximum throughput and maximum fairness in the network, simultaneously, in the asymptotic case of K → ∞. We introduce a new performance metric in the network, called "Minimum Average Throughput", and prove that the proposed algorithm is capable of maximizing the minimum average throughput in a MIMO-BC, in the asymptotic case of K → ∞. Finally, it is established that the proposed algorithm reaches the boundaries of the capacity region and stability region of the network, simultaneously, in the asymptotic case of K → ∞.

The capacity of time-varying channels with periodic feedback at the transmitter is evaluated. It is assumed that the channel state information is perfectly known at the receiver and is fed back to the transmitter at the regular time-intervals. The system capacity is investigated in two cases: i) finite state Markov channel, and ii) additive white Gaussian noise channel with time-correlated fading. In the first case, it is shown that the capacity is achievable by multiplexing multiple codebooks across the channel. In the second case, the channel capacity and the optimal adaptive coding is obtained. It is shown that the optimal adaptation can be achieved by a single Gaussian codebook, while adaptively allocating the total power based on the side information at the transmitter.

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In this work, we study a multiple-input multiple-output (MIMO) wireless system where the channel state information is partially available at the transmitter through a feedback link. Based on singular value decomposition, the MIMO channel is split into independent sub-channels. Effective feedback of the required spatial channel information entails efficient quantization/encoding of a unitary matrix. We propose two schemes for quantizing unitary matrices via Givens rotations and examine the performance for a scenario where the rates allocated to the sub-channels are selected according to their corresponding gains. Numerical results show that the proposed schemes offer a significant performance improvement as compared to that of MIMO systems without feedback, with a negligible increase in the complexity.

In this paper, a downlink scenario in which a single-antenna base station communicates with K single antenna users, over a time-correlated fading channel, is considered. It is assumed that channel state information is perfectly known at each receiver, while the statistical characteristics of the fading process and the fading gain at the beginning of each frame are known to the transmitter. By evaluating the random coding error exponent of the time-correlated fading channel, it is shown that there is an optimal codeword length which maximizes the throughput. The throughput of the conventional scheduling that transmits to the user with the maximum signal to noise ratio is examined using both fixed length codewords and variable length codewords. Although optimizing the codeword length improves the performance, it is shown that using the conventional scheduling, a gap of Ω( √ log log log K) exists between the achievable throughput and the maximum possible throughput of the system. A simple scheduling that considers both the signal to noise ratio and the channel time variation is proposed. It is shown that by using this scheduling, the gap between the achievable throughput and the maximum throughput of the system approaches zero. Index TermsDownlink scheduling, multiuser diversity, Rayleigh fading, time varying channels. I. INTRODUCTIONIn wireless networks, diversity is a means to combat the time varying nature of the communication link. Conventional diversity techniques over point-to-point links, such as spatial diversity and frequency diversity are widely used and offer performance improvements. In multiuser wireless systems, there exists another form of diversity, called multiuser diversity [1]. In a broadcast channel where users have independent fading and feed back their signal to noise ratio (SNR) to the base station (BS), system throughput is maximized by transmitting to the user with the strongest SNR [1], [2].Multiuser diversity was introduced first by Knopp and Humblet [3]. It is shown that the optimal transmission strategy in the uplink of multiuser systems using power control is to only let the user with the largest SNR transmit. A similar result is shown to be valid for the downlink [4]. Multiuser diversity underlies much of the recent works for downlink scheduling [5]-[8] as in Qualcomm's high data rate (HDR) system [9], [10]. In [8], [11], the opportunistic scheduling is based on the highest data rate which can be reliably transmitted to each user. Distributed scheduling is proposed in an uplink scenario, where full channel state information (CSI) is not required at the transmitter [12], [13]. Multiuser diversity has also been studied in the context of multiple antenna systems [1], [14] and ad-hoc networks [15].In wireless networks, the rate of channel variations is characterized by maximum Doppler frequency which is proportional to the velocity. Utilizing multiuser diversity in such environments needs to be revisited since the throughput depends not only on the received SNR, but also on how fa...