Showing papers on "Channel state information published in 2004"

A performance study of dual-hop transmissions with fixed gain relays

Abstract: This letter presents a study on the end-to-end performance of dual-hop wireless communication systems equipped with nonregenerative fixed gain relays and operating over flat Rayleigh-fading channels. More specifically, it first derives generic closed-form expressions for the outage probability and the average probability of error when the relays have arbitrary fixed gains. It then proposes a specific fixed gain relay that benefits from the knowledge of the first hop's average fading power and compares its performance with previously proposed relay gains that in contrast require knowledge of the instantaneous channel state information of the first hop. Finally, the letter investigates the effect of the relay saturation on the performance of the systems under consideration. Numerical results show that nonregenerative systems with fixed gain relays have a comparable performance to nonregenerative systems with variable gain, more complex, relays. These results also show that relay saturation of these systems results in a minimal loss in performance.

Digital Communications Over Fading Channels

Abstract: : In this report, the probabilities of bit error for the most commonly used digital modulation techniques are analyzed. Analytic solutions are developed for the probability of bit error when the signal is affected by the most commonly encountered impairment to system performance for a wireless channel, the transmission of the signal over a fading channel. In this report, the effect of a slow, flat Ricean fading channel on communications systems performance is examined. Since channel fading significantly degrades the performance of a communication system, the performance of digital communication systems that also use forward error correction channel coding is analyzed for hard decision decoding and, where appropriate, for soft decision decoding. Diversity, another technique to mitigate the effect of fading channels on digital communication systems performance, is also discussed. Also included is a discussion of the effect of narrowband noise interference, both continuous and pulsed, on digital communication systems. We then discuss the analysis of the probability of bit error for the combination of error correction coding and diversity. Following this, we briefly discuss spread spectrum systems. Next, we examine the link budget analysis and various models for channel loss. Finally, we examine in detail the second generation digital wireless standard Global System for Mobile (GSM).

Transmitter optimization and optimality of beamforming for multiple antenna systems

Abstract: We solve the transmitter optimization problem and determine a necessary and sufficient condition under which beamforming achieves Shannon capacity in a linear narrowband point-to-point communication system employing multiple transmit and receive antennas with additive Gaussian noise. We assume that the receiver has perfect channel knowledge while the transmitter has only knowledge of either the mean or the covariance of the channel coefficients. The channel is modeled at the transmitter as a matrix of complex jointly Gaussian random variables with either a zero mean and a known covariance matrix (covariance information), or a nonzero mean and a white covariance matrix (mean information). For both cases, we develop a necessary and sufficient condition for when the Shannon capacity is achieved through beamforming; i.e., the channel can be treated like a scalar channel and one-dimensional codes can be used to achieve capacity. We also provide a waterpouring interpretation of our results and find that less channel uncertainty not only increases the system capacity but may also allow this higher capacity to be achieved with scalar codes which involves significantly less complexity in practice than vector coding.

On the design of MIMO block-fading channels with feedback-link capacity constraint

Abstract: In this paper, we propose a combined adaptive power control and beamforming framework for optimizing multiple-input/multiple-output (MIMO) link capacity in the presence of feedback-link capacity constraint. The feedback channel is used to carry channel state information only. It is assumed to be noiseless and causal with a feedback capacity constraint in terms of maximum number of feedback bits per fading block. We show that the hybrid design could achieve the optimal MIMO link capacity, and we derive a computationally efficient algorithm to search for the optimal design under a specific average power constraint. Finally, we shall illustrate that a minimum mean-square error spatial processor with a successive interference canceller at the receiver could be used to realize the optimal capacity. We found that feedback effectively enhances the forward channel capacity for all signal-to-noise ratio (SNR) values when the number of transmit antennas (n/sub T/) is larger than the number of receive antennas (n/sub R/). The SNR gain with feedback is contributed by focusing transmission power on active eigenchannel and temporal power waterfilling . The former factor contributed, at most, 10log/sub 10/(n/sub T//n/sub R/) dB SNR gain when n/sub T/>n/sub R/, while the latter factor's SNR gain is significant only for low SNR values.

Channel capacity and capacity-range of beamforming in MIMO wireless systems under correlated fading with covariance feedback

Abstract: We study the optimal transmission strategy of a single-user multiple-input/multiple-output communication system with covariance feedback. We consider the situation with correlated receive and correlated transmit antennas in Rayleigh flat fading. Furthermore, we assume that the receiver has perfect channel state information, while the transmitter knows only the transmit correlation matrix and the receive correlation matrix. We show that transmitting in the direction of the eigenvectors of the transmit correlation matrix is the optimal transmission strategy. In addition to this, the optimal power allocation is studied and a necessary and sufficient condition for optimality of beamforming is derived. All theoretical results are illustrated by numerical simulations.

Error Rates in Generalized Shadowed Fading Channels

Abstract: Most of the existing models to describe the shadowed fading channels use either the Suzuki or Nakagami-lognormal probability density function (pdf), both based on lognormal shadowing. However, these two density functions do not lead to closed form solutions for the received signal power, making the computations of error rates and outages very cumbersome. A generalized or compound fading model which takes into account both fading and shadowing in wireless systems, is presented here. Starting with the Nakagami model for fading, shadowing is incorporated using a gamma distribution for the average power in the Nakagami fading model. This compound pdf developed here based on a gamma-gamma distribution is analytically simpler than the two pdfs based on lognormal shadowing and is general enough to incorporate most of the fading and shadowing observed in wireless channels. The performance of coherent BPSK is evaluated using this compound fading model.

Adaptive MIMO-OFDM based on partial channel state information

Abstract: Relative to designs assuming no channel knowledge at the transmitter, considerably improved communications become possible when adapting the transmitter to the intended propagation channel. As perfect knowledge is rarely available, transmitter designs based on partial (statistical) channel state information (CSI) are of paramount importance not only because they are more practical but also because they encompass the perfect- and no-knowledge paradigms. In this paper, we first provide a partial CSI model for orthogonal frequency division multiplexed (OFDM) transmissions over multi-input multi-output (MIMO) frequency-selective fading channels. We then develop an adaptive MIMO-OFDM transmitter by applying an adaptive two-dimensional (2-D) coder-beamformer we derived recently on each OFDM subcarrier, along with an adaptive power and bit loading scheme across OFDM subcarriers. Relying on the available partial CSI at the transmitter, our objective is to maximize the transmission rate, while guaranteeing a prescribed error performance, under the constraint of fixed transmit-power. Numerical results confirm that the adaptive 2-D space-time coder-beamformer (with two basis beams as the two "strongest" eigenvectors of the channel's correlation matrix perceived at the transmitter) combined with adaptive OFDM (power and bit loaded with M-ary quadrature amplitude modulated (QAM) constellations) improves the transmission rate considerably.

How accurate channel prediction needs to be for transmit-beamforming with adaptive modulation over Rayleigh MIMO channels?

Abstract: Adaptive modulation improves the system throughput considerably by matching transmitter parameters to time-varying wireless fading channels. Crucial to adaptive modulation is the quality of channel state information at the transmitter. In this paper, we first present a channel predictor based on pilot symbol assisted modulation for multiple-input multiple-output Rayleigh fading channels. We then analyze the impact of the channel prediction error on the bit error rate performance of a transmit-beamformer with adaptive modulation that treats the predicted channels as perfect. Our numerical results reveal the critical value of the normalized prediction error, below which the predicted channels can be treated as perfect by the adaptive modulator; otherwise, explicit consideration of the channel imperfection must be accounted for at the transmitter.

Optimal minimum distance-based precoder for MIMO spatial multiplexing systems

Abstract: We describe a new precoder based on optimization of the minimum Euclidean distance d/sub min/ between signal points at the receiver side and for use in multiple-input multiple-output (MIMO) spatial multiplexing systems. Assuming that channel state information (CSI) can be made available at the transmitter, the three steps ( noise whitening, channel diagonalization and dimension reduction), which are currently used in investigations on MIMO systems, are performed. Thanks to this representation, an optimal d/sub min/ precoder is derived in the case of two different transmitted data streams. For quadrature phase-shift keying (QPSK) modulation, a numerical approach shows that the precoder design depends on the channel characteristics. Comparisons with maximum signal-to-noise ratio (SNR) strategy and other precoders based on criteria, such as water-filling (WF), minimum mean square error (MMSE), and maximization of the minimum singular value of the global channel matrix, are performed to illustrate the significant bit-error-rate (BER) improvement of the proposed precoder.

Adaptive modulation systems for predicted wireless channels

Abstract: When adaptive modulation is used to counter short-term fading in mobile radio channels, signaling delays create problems with outdated channel state information. The use of channel power prediction will improve the performance of the link adaptation. It is then of interest to take the quality of these predictions into account explicitly when designing an adaptive modulation scheme. We study the optimum design of an adaptive modulation scheme based on uncoded M-quadrature amplitude modulation, assisted by channel prediction for the flat Rayleigh fading channel. The data rate, and in some variants the transmit power, are adapted to maximize the spectral efficiency, subject to average power and bit-error rate constraints. The key issues studied here are how a known prediction error variance will affect the optimized transmission properties, such as the signal-to-noise ratio (SNR) boundaries that determine when to apply different modulation rates, and to what extent it affects the spectral efficiency. This investigation is performed by analytical optimization of the link adaptation, using the statistical properties of a particular, but efficient, channel power predictor. Optimum solutions for the rate and transmit power are derived, based on the predicted SNR and the prediction error variance.

Adaptive Modulation for multiantenna transmissions with channel mean feedback

Abstract: Adaptive modulation has the potential to increase the system throughput significantly by matching transmitter parameters to time-varying channel conditions. However, adaptive modulation schemes that rely on perfect channel state information (CSI) are sensitive to CSI imperfections induced by estimation errors and feedback delays. In this paper, we design adaptive modulation schemes for multiantenna transmissions based on partial CSI, that models the spatial fading channels as Gaussian random variables with nonzero mean and white covariance, conditioned on feedback information. Based on a two-dimensional beamformer, our proposed transmitter optimally adapts the basis beams, the power allocation between two beams, and the signal constellation, to maximize the transmission rate, while maintaining a target bit-error rate. Adaptive trellis-coded multiantenna modulation is also investigated. Numerical results demonstrate the rate improvement, and illustrate an interesting tradeoff that emerges between feedback quality and hardware complexity.

Performance of differential chaos-shift-keying digital communication systems over a multipath fading channel with delay spread

Abstract: The performance of the noncoherent differential chaos-shift-keying (DCSK) communication system over a multipath fading channel with delay spread is evaluated. Analytical expressions of the bit error rates are derived under the assumption of an independent Rayleigh fading two-ray channel model. Analytical and simulated results are presented and compared. The multipath performance of the DCSK system is also compared with that of the coherent CSK system as well as conventional generic waveform communication schemes.

Robust noncoherent receiver exploiting UWB channel properties

Abstract: Most UWB radio receivers discussed in the literature are coherent receivers, which can offer high signal sensitivity and support high data rates but require precise timing clock recovery and complex RAKE structures. For UWB radio systems requiring only lower data throughput, noncoherent receiver architectures offer a good performance-complexity tradeoff. In this paper, we describe a noncoherent receiver for 2PPM UWB signals. The key design parameter, the duration of signal integration, can be chosen such that a target BER is achieved for each element of a preselected set of channel realizations. Although the proposed receiver works without channel state information and complex RAKE frontend, its performance compares favorably with that of a coherent 2PAM RAKE receiver of low order. The simple noncoherent receiver exploits most of the multipath diversity offered by the channel and is robust to clock timing errors.

Channel capacity and second-order statistics in Weibull fading

Abstract: The second-order statistics and the channel capacity of the Weibull fading channel are studied. Exact closed-form expressions are derived for the average level crossing rate, the average fade duration, as well as the average Shannon's channel capacity of the Weibull fading process. Numerical results are presented to illustrate the proposed mathematical analysis and to examine the effects of the fading severity on the concerned quantities.

Optimal transmission strategies and impact of correlation in multiantenna systems with different types of channel state information

Abstract: We study the optimal transmission strategy of a multiple-input single-output (MISO) wireless communication link. The receiver has perfect channel state information (CSI), while the transmitter has different types of CSI, i.e., either perfect CSI, or no CSI, or long-term knowledge of the channel covariance matrix. For the case in which the transmitter knows the channel covariance matrix, it was recently shown that the optimal eigenvectors of the transmit covariance matrix correspond with the eigenvectors of the channel covariance matrix. However, the optimal eigenvalues are difficult to compute. We derive a characterization of the optimum power allocation. Furthermore, we apply this result to provide an efficient algorithm which computes the optimum power allocation. In addition to this, we analyze the impact of correlation on the ergodic capacity of the MISO system with different CSI schemes. At first, we justify the belief that equal power allocation is optimal if the transmitter is uninformed and the transmit antennas are correlated. Next, we show that the ergodic capacity with perfect CSI and without CSI at the transmitter is Schur-concave, i.e., the more correlated the transmit antennas are, the less capacity is achievable. In addition, we show that the ergodic capacity with covariance knowledge at the transmitter is Schur-convex with respect to the correlation properties. These results completely characterize the impact of correlation on the ergodic capacity in MISO systems. Furthermore, the capacity loss or gain due to correlation is quantified. For no CSI and perfect CSI at the transmitter, the capacity loss due to correlation is bounded by some small constant, whereas the capacity gain due to correlation grows unbounded with the number of transmit antennas in the case in which transmitter knows the channel covariance matrix. Finally, we illustrate all theoretical results by numerical simulations.

Power allocation for regenerative relay channel with Rayleigh fading

Abstract: Cooperative relaying is considered as an effective way to combat Rayleigh fading, to offer better quality of communication link or channel capacity. From the perspective of information theory, channel capacity depends on the SNR of the received signal, therefore, how to allocate transmit power between transmitter and relay to achieve maximum SNR at the receiver or maximum channel capacity is an important issue. In general, there are two types of relaying system, i.e. non-regenerative and regenerative systems. This paper puts emphasis on the power allocation (PA) of regenerative systems. Based on a 2-hop relaying channel suffering from Rayleigh fading, with and without diversity, an adaptive PA scheme is proposed, under transmit power constraints, to keep the system running at the optimum level. Numerical results indicate that with the proposed PA scheme, the system performance not only outperforms that of the direct transmission system, but also obtains the maximum channel capacity or SNR of the relaying system.

Adaptive optimal transmit power allocation for two-hop non-regenerative wireless relaying system

Abstract: In order to combat fading in wireless networks and increase the capacity of a system, cooperation is allowed among the terminals in a network. The adaptive optimal power allocation (PA) scheme, based on a certain system performance, is an important issue for relaying routing and network operation. The paper analyzes the two-hop non-regenerative (NR) relaying channel with and without diversity, and investigates the optimal PA scheme between the source terminal (Tx) and the relaying terminal (RS) under power constraints. Since, in real relaying environments, the transmitter usually knows the instantaneous channel state information (ICSI) of the 1st hop and the statistical channel state information (SCSI) of the 2nd hop, the proposed PA schemes are based on two-hop ICSI and two-hop mixed channel state information (MCSI) respectively. With the adaptive scheme, the system performance not only outperforms that of the direct transmission system, but also obtains the maximum channel capacity or SNR of the relaying system.

Capacity of fading MIMO channels with channel estimation error

Abstract: In this paper, we investigate the effect of channel estimation error on the capacity of multiple input multiple output (MIMO) systems in i.i.d. Rayleigh flat-fading channels. We study lower and upper bounds of mutual information under channel estimation error, and show that the two bounds are tight for Gaussian inputs. It is seen that the mutual information increases with the. number of antennas, but is limited by channel estimation error at high SNR. We also derive tight lower bounds of ergodic and outage capacities and optimal transmitter power allocation strategies that achieve the bounds. For the ergodic capacity, the optimal strategy is a modified waterfilling over the spatial (subchannel) and temporal (fading) domain. For the outage capacity, it is a spatial waterfilling and temporal truncated channel inversion. Numerical results show that some capacity gain is obtained by spatial power allocation. Temporal power adaptation, on the other hand, gives negligible gain in terms of ergodic capacity, but greatly enhances outage performance.

Finite-state Markov modeling of correlated Rician-fading channels

Abstract: Stochastic properties of the binary channel that describe the successes and failures of the transmission of a modulated signal over a time-correlated flat-fading channel are considered for investigation. This analysis is employed to develop Kth-order Markov models for such a burst channel. The order of the Markov model that generates accurate analytical models is estimated for a broad range of fading environments. The parameterization and accuracy of an important class of hidden Markov models, known as the Gilbert-Elliott channel (GEC), are also investigated. Fading rates are identified in which the Kth-order Markov model and the GEC model approximate the fading channel with similar accuracy. The latter model is useful for approximating slowly fading processes, since it provides a more compact parameterization.

Multiple antenna channels with partial channel state information at the transmitter

Abstract: We investigate transmission strategies for flat-fading multiple antenna channels with t transmit and r receive antennas, and with channel state information (CSI) partially known to the transmitter. We start with an assumption that the first n eigenvectors of H/sup /spl dagger//H, where 0/spl les/n/spl les/min(t,r) and H is the channel matrix in /spl Copf//sup r/spl times/t/, are available at the transmitter as partial spatial information of the channel. A beamforming method is proposed in which a beamforming matrix is determined from the n eigenvectors in some predefined way; as a result, the receiver also knows the beamforming matrix. With this beamforming scheme, we develop a new multiple antenna system concept that provides a mechanism to reduce the amount of channel feedback information. This paper focuses on deriving the channel capacity of the multiple antenna channels employing the proposed beamforming and feedback methods. An important task for achieving capacity is the solution of interesting optimization problems for the optimal power allocation over the transmit symbols. The results show that the proposed methods lead to systems wherein the amount of feedback information can be significantly reduced with a minor sacrifice of achievable transmission rate.

System and method for selecting data rates to provide uniform bit loading of subcarriers of a multicarrier communication channel

Abstract: A data rate is selected for subcarriers of each frequency and spatial channel of a slowly varying frequency selective multicarrier channel to provide uniform bit loading (UBL) for faster link adaptation. Signal to noise ratios (SNRs) for subcarriers of the multicarrier communication channel may be calculated from channel state information and a transmit power level. A throughput may be estimated for the data rates from the SNRs and one of the data rates may be selected based on the estimated throughputs.

High-throughput multicarrier communication systems and methods for exchanging channel state information

Abstract: A frame structure for communicating over a high-throughput communication channel includes a channelization field as part of a current data unit to indicate a frequency and space configuration of subsequent portions of the current data unit.

Impact of relay gain allocation on the performance of cooperative diversity networks

Abstract: We consider a wireless network with one source/destination pair and several linear amplify-and-forward relays. The influence of the gain allocation at the relays on the performance in cooperative relay communication links is analyzed. We present an optimal gain allocation which results in a coherent combining of all signal contributions at the destination and maximizes the instantaneous throughput of the link. If the channel state information (CSI) at the relays is limited, cooperative diversity schemes can be used. We show that the right choice of the amplification gains is crucial to achieve high outage throughput.

An efficient feedback method for MIMO systems with slowly time-varying channels

Abstract: The capacity of a multiple-input multiple-output (MIMO) channel can be improved if the transmitter has a knowledge of the channel. In this paper, we propose an efficient and practical feedback method based on parameterization and quantization of channel parameters. The spatial information of the channel at the transmitter, which is represented as a matrix with orthonormal columns, has a geometrical structure. In parameterization, the geometrical structure is exploited to extract a set of parameters that has a one-to-one mapping to the original matrix. In slowly time-varying channels, the parameters are also found to he smoothly changing in time. We employ adaptive delta modulation to quantize and feed back each parameter. The results show that the proposed feedback scheme has a channel tracking feature and achieves a capacity very close to the perfect feedback case with a reasonable feedback rate.

Cooperative diversity for wireless fading channels without channel state information

Abstract: Relaying and cooperative diversity allow multiple wireless radios to effectively share their antennas and create a virtual antenna array, thereby leveraging the spatial diversity benefits of multiple-input, multiple-output (MIMO) antenna systems. This paper examines the benefits of cooperative diversity for scenarios in which the receivers cannot exploit accurate channel state information (CSI). In particular, noncoherent demodulation is explored for two classes of relay processing, namely, detect-and-forward and amplify-and-forward. A complete maximum likelihood (ML) framework for noncoherent demodulation is developed for detect-and-forward, and is shown to naturally extend the corresponding framework for coherent demodulation. By contrast, the intractability of ML demodulation for noncoherent amplify-and-forward is demonstrated, suggesting a disconnect from the well-developed framework for coherent demodulation. Simulation results exhibit the diversity benefits of the detect-and-forward algorithms.

Sensor networks with mobile access: optimal random access and coding

Abstract: We consider random access and coding schemes for sensor networks with mobile access (SENMA). Using an orthogonal code-division multiple access (CDMA) as the physical layer, an opportunistic ALOHA (O-ALOHA) protocol that utilizes channel state information is proposed. Under the packet capture model and using the asymptotic throughput as the performance metric, we show that O-ALOHA approaches the throughput equal to the spreading gain with an arbitrarily small power at each sensor. This result implies that O-ALOHA is close to the optimal centralized scheduling scheme for the orthogonal CDMA networks. When side information such as location is available, the transmission control is modified to incorporate either the distribution or the actual realization of the side information. Convergence of the throughput with respect to the size of the network is analyzed. For networks allowing sensor collaborations, we combine coding with random access by proposing two coded random access schemes: spreading code dependent and independent transmissions. In the low rate regime, the spreading code independent transmission has a larger random coding exponent (therefore, faster decay of error probability) than that of the spreading code dependent transmission. On the other hand, the spreading code dependent transmission gives higher achievable rate.

Interpolation based unitary precoding for spatial multiplexing MIMO-OFDM with limited feedback

Abstract: Spatial multiplexing with linear precoding is a simple technique to take advantage of the high spectral efficiency provided by multiple-input multiple-output (MIMO) systems, and it can be simply implemented over frequency selective channels by using orthogonal frequency division multiplexing (OFDM). This requires channel state information (CSI) at the transmitter in the form of the precoding matrices for all OFDM subcarriers, which can be achieved using feedback. To reduce the feedback requirements, this paper proposes a new precoding method incorporating quantization of a fraction of precoding matrices followed by a special interpolation at the transmitter. Since the precoding matrices are unitary, a new interpolator is proposed on the space of unitary matrices for which the outputs are also unitary. The parameters of the interpolator are optimized based on a mean square error (MSE) or mutual information criterion. Simulations show that performance near that of complete CSI can be achieved with a reasonable amount of feedback.

Bayesian sequential state estimation for MIMO wireless communications

Abstract: This paper explores the use of particle filters, rooted in Bayesian estimation, as a device for tracking statistical variations in the channel matrix of a narrowband multiple-input, multiple-output (MIMO) wireless channel. The motivation is to permit the receiver to acquire channel state information through a semiblind strategy and thereby improve the receiver performance of the wireless communication system. To that end, the paper compares the particle filter as well as an improved version of the particle filter using gradient information, to the conventional Kalman filter and mixture Kalman filter with two metrics in mind: receiver performance curves and computational complexity. The comparisons, also including differential phase modulation, are carried out using real-life recorded MIMO wireless data.

On power allocation strategies for maximum signal to noise and interference ratio in an OFDM-MIMO system

Abstract: Orthogonal frequency division multiplexing (OFDM) has been recently established for several systems such as HiperLAN/2 and Digital video/audio broadcasting, due the easy implementation of the modulator/demodulator and the equalizer. Moreover, also increasing interest is currently being put on multiple-input multiple-output (MIMO) channels, based on the use of antenna arrays at both the transmitter and the receiver. Here, we propose two joint beamforming strategies of low computational load for systems combining OFDM and MIMO. The ultimate objective is the maximization of the signal-to-noise and interference ratio (SNIR) over the carriers subject to a total transmit power constraint. Specifically, the maximization of the harmonic SNIR mean and the minimum SNIR over the subcarriers are proposed. The asymptotic behavior of the proposed methods is analyzed to provide a complete comparative and general view of the most relevant and already known transmit power allocation strategies. Finally, a theoretical analysis of the performance degradation of these techniques is carried out for the case in which the channel state information (CSI) is not perfect. Monte Carlo simulation results for the system bit-error rate and performance degradation with imperfect CSI are provided.

Training sequence optimization in MIMO systems with colored interference

Abstract: We address the problems of channel estimation and optimal training sequence design for multiple-input multiple-output systems over flat fading channels in the presence of colored interference. In practice, knowledge of the unknown channel is often obtained by sending known training symbols to the receiver. During the training period, we obtain the best linear unbiased estimates of the channel parameters based on the received training block. We determine the optimal training sequence set that minimizes the mean square error of the channel estimator under a total transmit power constraint. In order to obtain the advantage of the optimal training sequence design, long-term statistics of the interference correlation are needed at the transmitter. Hence, this information needs to be estimated at the receiver and fed back to the transmitter. Obviously it is desirable that only a minimal amount of information needs to be fed back from the receiver to gain the advantage in reducing the estimation error of the short-term channel fading parameters. We develop such a feedback strategy in this paper.