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Abstract-Opportunistic scheduling provides attractive sum-rate capacities in a multiuser network when the base-station has transmit-side channel state information (CSI), which is often estimated at the mobiles and provided to the base station via a feedback channel. This correspondence investigates opportunistic methods in the presence of limited feedback. For flat Rayleigh-fading channels, strategies with only one-bit feedback per user are demonstrated that capture the double-logarithmic capacity growth (with number of users) of full-CSI systems. Furthermore, for a given system configuration, it is shown that if the one-bit feedback is chosen judiciously, there is little to be gained by increasing the feedback rate. Our results provide optimal methods of calculating the one-bit feedback, as well as expressions for the sum-rate capacity in the one-bit feedback regime. It is shown that one may achieve proportional fairness of scheduling in this regime with no loss of throughput. For OFDM multiuser systems, the motivation for limited feedback is even more pronounced. An extension of the one-bit technique is presented for subchannel/user selection under both correlated and uncorrelated subchannel conditions, and optimal growth in capacity is demonstrated.

Abstract-This correspondence studies the capacity of multipleinput-multiple-output (MIMO) channels in the presence of antenna selection. Antenna selection reduces the complexity of the radio devices and requires only a small amount of channel state feedback. For high signal-to-noise ratio (SNR), we define excess rate as the constant term in the expansion of the ergodic capacity in terms of SNR. It is shown that this value is representative of the channel state information (CSI) at the transmitter. The asymptotic behavior of the excess rate is then analyzed for three cases: complete CSI, no CSI, and partial CSI at transmitter (antenna selection). While water-filling provides a excess rate that increases logarithmically in M (the number of transmit antennas), the excess rate of transmit antenna selection behaves only like log(log M).For the low SNR case, we use the concept of channel gain, a measure introduced by Verdú. We show that channel gain for antenna selection increases only logarithmically in M as opposed to water-filling channel gain which increases linearly in M. The same techniques are also applied to the receive selection, and corresponding results are noted in high-and low-SNR regimes. The methodology developed in this correspondence, although motivated by antenna selection, is fairly general and can be used for any system where partial CSI is available at the MIMO transmitter.Index Terms-Antenna selection, capacity scaling, channel state information (CSI), multiple-input-multiple-output (MIMO).

In this paper we study the beamforming vector quantization and feedback transmission problem for a cooperative transmission environment. Feedback is the primary means of providing the transmitter with channel state information (CSI) in a frequency division duplex (FDD) system. The conventional codebook approach uses a common codebook at the transmitter and at the receiver, while the feedback takes the form of the index of the codebook. This approach has a complexity that scales exponentially with the number of transmit antennas , making the approach less favorable when is large. We propose to use trellis-based quantization to reduce the complexity to grow linearly in . A codebook design criteria is derived for the trellisbased quantizer. We also present three enhancements to the base scheme, each giving 0.2-0.8 dB gain. These enhancements address issues relevant to feedback error, trellis termination, and unequal path-loss from different transmission points. Performance results are shown in numerical simulations.Index Terms-Trellis quantization, beamforming vector codebook, cooperative transmission codebook.

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Abstract-The keyhole condition, where the MIMO channel has only one degree of freedom, impairs the performance of MIMO systems. Thus, one may wish to design codes that are robust to this condition. So far, a general analysis of spacetime codes in keyhole conditions has not been available (except in the special case of orthogonal space-time block codes). This work provides pairwise error probabilities for general space-time codes in keyhole condition. We present design criteria in high SNR, providing guidelines for codes that are robust to keyhole conditions. Also included is the proof of the intuitive result that the diversity under keyhole condition is min (M, N), where M and N are the number of transmit and receive antennas, with a slightly unexpected twist in the case of M = N .

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