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 M, making the approach less favorable when M is large. We propose to use trellis-based quantization to reduce the complexity to grow linearly in M. A codebook design criteria is derived for the trellis-based 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.

Trellis-based quantization is a suitable method for reporting channel state information in multi base-station or base-station-relay coordinated transmission schemes. Due to different path loss and shadowing from each transmitting station, the receiver experiences different long-term average signal powers from each transmitter. We first propose to use a tail-biting trellis to improve the performance of the vector quantization proposed in. To reduce decoding complexity, we present a trellis labeling technique where efficient encoding and decoding can be performed by traversing the trellis twice. Lastly, we introduce a mechanism for dynamically allocating quantization bits amongst different parts of the augmented channel state vector. A trellis simplification procedure that keeps the number of trellis states at each stage to four is shown to provide a satisfactory performance.

In this paper we use Renyi representation of order statistics to provide a tight lower bound on the outage probability and a tight upper bound on the average signal-to-noise ratio of orthogonal space-time coded systems with antenna selection. Using these bounds we propose a chi-square approximation to the outage probability. We show through simulations that the bounds and also the chi-square approximation are quite tight for a variety of antenna configurations. The method presented here is quite general and not restricted to the Rayleigh distribution.

This letter presents two results for antenna selection under keyhole condition. First, we analyze the capacity of the antenna-selection keyhole channel. We show that in an MtimesN system a small number of selected antennas can match the capacity of a baseline full-antenna system (baseline system has no feedback). Second, we formally prove the intuitive result, until now unproven, that antenna selection in the keyhole multiple-input multiple-output channel preserves the available diversity of the channel

This correspondence studies the capacity of multiple-input-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 Verdu. 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.

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.

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 space-time 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.

This work investigates the following question: subject to strictly limited (finite-rate) feedback in a multi-user multi-antenna system, what channel state information (CSI) should we send back to the transmitter, and how should it be used? Considering the class of single-beam systems, we suggest a combination of beamforming (array gain) and multi-user diversity. It has been shown that in single antenna systems, one bit of feedback per user can capture almost all gains available due to multi-user diversity, therefore we propose and analyze a compound strategy that uses one bit for multi-user diversity and any further feedback bits for beamforming. We obtain the scaling laws of this compound strategy, showing that it scales as well as any single-beam system with full transmit-CSI.

Cooperative communication is an emerging paradigm where multiple mobiles share their resources (bandwidth and power) to achieve better overall performance. Coded cooperation is a mechanism where cooperation is combined with-and operates through-channel coding, as opposed to the repetition-based methods. This work develops expressions for outage probability of coded cooperation. In this work, each node acts as both a data source as well as a relay, i.e., only active (transmitting) nodes are available to assist other nodes, and each node operates under overall (source + relay) power and bandwidth constraints. Outage expressions confirm that full diversity is achieved by coded cooperation. This shows that despite superficial similarities, coded cooperation is distinct from decode-and-forward, which has been shown to have diversity one. The outage probability expressions developed in this work characterize coded performance at various rates. Furthermore, outage probabilities yield bounds that are arguably more insightful than the bit-error rate (BER) results previously available for coded cooperation. Numerical comparisons shed light on the relative merits of coded cooperation and various repetition-based methods, under various inter-user and uplink channel conditions.

Orthogonal space-time block codes (OSTBC) are among the most practical space-time codes due to their simplicity and optimal decoding. When information about the channel is available at the transmitter, the performance of OSTBC can be significantly improved by exploiting the array gain. However, providing full knowledge of channel state at the transmitter may not he affordable in many practical cases. Thus exploiting partial channel knowledge to improve the performance of OSTBC seems to be attractive. In this work we investigate the design of linear precoders with partial channel knowledge at the transmitter combined with an orthogonal space time code. We derive the condition for optimal precoder subject to a power constraint on the whole transmission block. We also propose a technique for precoder codebook design with limited feedback.

In a system with n users, the sum-rate capacity of the downlink channel grows as log log n, assuming optimal scheduling. However, optimal scheduling requires that the downlink channel state information (CSI) for all users be fully available at the base station. We show that the same capacity growth holds even if the feedback rate from the mobiles to the base station is reduced to one bit. We propose a simple scheduling method to achieve this multiuser capacity and, furthermore, we show that, by a judicious choice of the one-bit quantizer, not only the growth rate, but also most of the capacity of a fully informed system can be preserved.

The keyhole condition, where the MIMO channel has only one degree of freedom, impairs the performance of MIMO systems. In cases that this condition is likely, one may wish to design codes that are robust to this condition. So far, a general analysis of space-time codes in keyhole conditions has not been available (except in the special case of orthogonal space-time block codes). In this work, we provide pairwise error probabilities for general space-time codes in the keyhole condition. We present design criteria in high SNR, providing guidelines for codes that are robust to keyhole conditions. We also prove the intuitive result that the diversity under the keyhole condition is min(M,N), with a slightly unexpected twist in the case of M=N.

Coded cooperation is a new framework recently proposed for cooperative communication. In this work, we present outage probability results for coded cooperation, and demonstrate that full diversity is achieved. In addition, we compare the outage behavior of coded cooperation with other repetition-based cooperative schemes.

In this work we investigate the asymptotic behavior of the capacity of transmit antenna selection, in the limit of large number of transmit antennas, under both low and high SNR regimes. Antenna selection provides a low-cost low complexity solution for MIMO systems.

In this paper we present a simple scheme for subchannel allocation in OFDM multiuser networks in the presence of limited feedback, in particular, when only one bit of information per subchannel is available at the base station. Our objective is to maximize the sum rate capacity of the network in the downlink transmission. We show that even with very limited feedback the sum rate capacity growth is the same as the fully informed transmission. We also extend this result to the case when subchannels are correlated.