Performance limitation of closed-loop transmit antenna diversityover fast Rayleigh fading channels

Previously, transmit antenna diversity (TAD) has been considered as a key technique to improve the capacity of wireless systems over a fading channel. A type of TAD is closed-loop TAD, which utilizes channel conditions. Closed-loop TAD has a drawback caused by the feedback delay under a fast fading channel environment. If the channel information is outdated due to the feedback delay, the performance can be severely degraded. In this correspondence, we find the bit error rate (BER) of the closed-loop TAD with the feedback delay for a time-variant Rayleigh fading channel. For example, it is observed that there is about 2-dB degradation at the BER of 10-2 when four transmit antennas are used, and the feedback delay is 5 ms with the updating rate 400 Hz     

Performance analysis of the closed-loop transmit antenna diversitysystem over Rayleigh fading channels

As a diversity technique, transmit antenna diversity (TAD) recently has been considered for third-generation (3G) code-division multiple-access systems. There are two different types of TAD techniques: closed loop and open loop. In this correspondence, the performance of the closed-loop TAD system equipped with multiple transmit and receive antennas is analyzed using bounds of the pairwise error probability (PEP) under a flat fading channel environment. In addition, the cutoff rate from the Chernoff bound has been considered to understand the overall performance, which may include channel coding     

Performance Analysis of Multiuser Diversity on OSTBC MIMO Systems with Antenna Selection in the Presence of Feedback Delay CSI

In this paper, we studied a comprehensive analytical symbol error probability (SEP) performance analysis of downlink multiuser diversity (MUD) on orthogonal space–time block code (OSTBC) system with transmit antenna selection (TAS) in the presence of imperfect channel state information (CSI) due to feedback delay over Rayleigh fading channels. The novel analytical approach is suitable for MUD with TAS/OSTBC systems in which effective receiver signal-to-noise ratio (SNR) is described as highest order statistic of Chi square distribution. Based on this framework, the closed-form SEP expressions are evaluated for the MUD exploiting TAS/OSTBC with normalized SNR based scheduling in heterogeneous wireless networks. Further, we derive approximate SEP; upper bound and lower bound SEP at high SNR under delayed feedback CSI. Thereafter the impact of feedback delay and antenna structures with significance on the consideration of MUD on the performance of the system has been analyzed.

     

An adaptive technique for transmit antenna diversity with feedback

Transmit antenna diversity (TAD) has been employed for third-generation wireless systems. We propose an adaptive technique for TAD with feedback. It is shown that the proposed adaptive technique can efficiently increase the number of transmit antennas without significantly increasing the feedback bit rate under ideal conditions. As a result, we can increase the number of transmit antennas and expect a performance improvement. Unfortunately, the proposed adaptive technique suffers from channel variation and error propagation due to feedback error. From this, the use of the adaptive technique shall be limited: it can be effective for indoor communications and for pedestrians with a reliable feedback channel     

Capacity of Generalized UTRA FDD Closed-Loop Transmit Diversity Modes

Transmit diversity techniques have received a lot of attention recently, and open-loop and closed-loop downlink transmit diversity modes for two transmit antennae have been included into universal terrestrial radio access (UTRA) frequency division duplex (FDD) specification. Closed-loop modes provide larger system capacity than open-loop modes, but they need additional side information of the downlink channel in the transmitter. In FDD systems this requires a separate feedback channel. Quantization of channel state information (CSI) in closed-loop transmit diversity schemes decreases the performance when compared to a closed-loop system where the transmitter has access to complete CSI. In this paper, we analyze the effect of quantization of CSI and deduce approximate capacity formulae for closed-loop transmit diversity schemes that are generalizations of the closed-loop schemes included in UTRA FDD specification. Moreover, we calculate approximation error and show by simulations that our approximation is tight for flat Rayleigh fading environments with and without fast transmit power control.     

Analytical modelling of multiservice switching networks with multiservice sources and resource management mechanisms

In this paper, we presents an analytical link capacity and outage performance analysis of downlink multiuser diversity (MUD) in multiple-input multiple-output (MIMO) system employing maximal-ratio combining (MRC) with transmit antenna selection (TAS) in the presence of imperfect channel state information (CSI) due to feedback delay over Rayleigh fading channels. The unified achievable analysis is appropriate for MUD–MIMO with TAS/MRC systems in which effective output signal-to-noise ratio (SNR) is specified as highest order statistic of chi-square distribution. Based on this framework, the closed-form channel capacity and outage probability expressions are examined for the MUD–MIMO exploiting TAS/MRC with normalized SNR based scheduling in heterogeneous wireless networks. Further, we derive approximate upper bound capacity as well as capacity at high SNR and low SNR region under delayed feedback CSI. The upper and lower bound of outage probability under delayed feedback CSI is also evaluated. Thereafter the impact of feedback delay and antenna structures with significance on the consideration of MUD on the performance of the system has been analyzed.     

Optimum Receiver for a Realistic Transmit–Receive Diversity System in Correlated Fading

A transmit–receive diversity system in correlated Rayleigh fading in which the receiver estimates the channel through pilot symbols, and feeds this information back to the transmitter through a feedback path, is considered. The imperfect channel state information (CSI) is used by the transmitter to obtain the transmit weight vector for data transmission. The optimum receiver in the maximum-likelihood (ML) sense obtained from the conditional distribution of the received signal vector, conditioned on the imperfect CSI and the transmit weight vector, is derived for the system. For the case of $M$-ary phase-shift keying (MPSK), an analytical expression for the conditional symbol error probability (SEP), conditioned on the channel estimate and the transmit weight vector, is obtained, with the transmit weight vector chosen to minimize this conditional SEP. For the receive-only and transmit-only correlation scenarios with ill-conditioned eigenvalues of the receive and transmit covariance matrices (that is, some of the eigenvalues are very small), we derive expressions for the diversity gain. Numerical results are presented to compare the performance of our receiver with that of a conventional receiver in case of exponentially correlated fading. These results show that the optimum receiver typically has about a 0.5-dB gain over a conventional receiver when the correlation coefficient exceeds 0.5 and the number of receive antennas is much larger than the number of transmit antennas.      

A semiblind method for transmit antenna arrays in CDMA systems

Using a transmit antenna array (TAA), the downlink beamforming is able to improve the performance of wireless communication systems. We propose a semiblind downlink beamforming method based on channel reciprocity of the wireless channels for code-division multiple-access (CDMA) systems equipped with TAA. In the proposed semiblind method, it is shown that the feedback delay can result in performance degradation under a time-varying fading channel environment. Hence, the performance of the semiblind method is satisfactory only when the maximum Doppler frequency is low or the feedback delay is not significant. To overcome this difficulty, the channel prediction is considered. Using the channel predictor, the semiblind method can provide a reasonable performance for a moderate maximum Doppler frequency (about a few hundred hertz). For theoretical performance analysis, upper, and lower bounds of the bit error probability under a fading channel environment are derived     

Multi-Antenna Downlink Channels with Limited Feedback and User Selection

We analyze the sum-rate performance of a multi- antenna downlink system carrying more users than transmit antennas, with partial channel knowledge at the transmitter due to finite rate feedback. In order to exploit multiuser diversity, we show that the transmitter must have, in addition to directional information, information regarding the quality of each channel. Such information should reflect both the channel magnitude and the quantization error. Expressions for the SINR distribution and the sum-rate are derived, and tradeoffs between the number of feedback bits, the number of users, and the SNR are observed. In particular, for a target performance, having more users reduces feedback load.     

Opportunistic Feedback for Multiuser MIMO Systems With Linear Receivers

A novel multiuser scheduling and feedback strategy for the multiple-input multiple-output (MIMO) downlink is proposed in this paper. It achieves multiuser diversity gain without substantial feedback requirements. The proposed strategy uses per-antenna scheduling at the base station, which maps each transmit antenna at the base station (equivalently, a spatial channel) to a user. Each user has a number of receive antennas that is greater than or equal to the number of transmit antennas at the base station. Zero-forcing receivers are deployed by each user to decode the transmitted data streams. In this system, the base station requires users' channel quality on each spatial channel for scheduling. An opportunistic feedback protocol is proposed to reduce the feedback requirements. The proposed protocol uses a contention channel that consists of a fixed number of feedback minislots to convey channel state information. Feedback control parameters including the channel quality threshold and the random access feedback probability are jointly adjusted to maximize the average throughput performance of this system. Multiple receive antennas at the base station are used on the feedback channel to allow decoding multiple feedback messages sent simultaneously by different users. This further reduces the bandwidth of the feedback channel. Iterative search algorithms are proposed to solve the optimization for selection of these parameters under both scenarios that the cumulative distribution functions of users are known or unknown to the base station     

Effect of imperfect channel estimation on transmit diversity in CDMA systems

In this paper, the effect of imperfect channel estimation on the transmit diversity based on space-time block coding for the downlink of a direct-sequence code-division multiple-access system is studied. Two transmit antenna and one receiving antennas are employed. However, the results of this paper can be extended to the system with more receiving antennas. Each channel is modeled as frequency-selective Rayleigh fading and the pair of channels corresponding to two transmit antennas are mutually independent. Both spatial diversity gain and multipath diversity gain are obtained in the system. The system performance is evaluated in terms of bit-error rate under the perfect and imperfect channel estimation. A pilot-assisted channel-estimation scheme with one common spreading code sequence is exploited. It is shown that the inaccurate channel estimates suffering from multiple access and multipath interference significantly degrade the system performance and can be effectively improved by use of a simple low-pass filter. The investigation of the power ratio of pilot to data channels illustrates that the base station should dynamically adjust the transmit power of the pilot channel according to the varying system configurations in order to achieve the best performance.     

SR ARQ for adaptive modulation systems combined with selection transmit diversity

Adaptive automatic repeat request (ARQ) schemes are quite effective for throughput enhancement in time-varying mobile channel environments. In this paper, both throughput and packet error rate are analyzed for a selective-repeat ARQ scheme based on a constant-power variable-rate adaptive M-QAM system combined with selection transmit diversity over multiple-input multiple-output Markovian-Nakagami channels. In this analysis, the impact of using outdated and/or imperfect channel state information on the performance of the system is considered.     

Antenna combining for the MIMO downlink channel

A multiple antenna downlink channel where limited channel feedback is available to the transmitter is considered. In a vector downlink channel (single antenna at each receiver), the transmit antenna array can be used to transmit separate data streams to multiple receivers only if the transmitter has very accurate channel knowledge, i.e., if there is high-rate channel feedback from each receiver. In this work it is shown that channel feedback requirements can be significantly reduced if each receiver has a small number of antennas and appropriately combines its antenna outputs. A combining method that minimizes channel quantization error at each receiver, and thereby minimizes multi-user interference, is proposed and analyzed. This technique is shown to outperform traditional techniques such as maximum-ratio combining because minimization of interference power is more critical than maximization of signal power in the multiple antenna downlink. Analysis is provided to quantify the feedback savings, and the technique is seen to work well with user selection and is also robust to receiver estimation error.     

New transmit schemes and simplified receivers for MIMO wireless communication systems

In this paper, optimized transmit schemes for multiple-input multiple-output (MIMO) systems with simplified receivers are proposed for the downlink of high-speed wireless communication systems. In these systems, MIMO signal preprocessing is performed at the transmitter or base station with the receiver at the mobile station having a simplified structure that requires only limited signal processing. An important potential application for our transmit MIMO techniques is in the downlink of high-speed wireless communication systems with Vertical Bell Laboratories Layered Space-Time (V-BLAST) or a similar technique utilized in the uplink, creating a high-speed duplex system with a simplified mobile station transceiver structure. Two approaches are introduced and these depend on whether or not receive diversity is employed at the receiver. Both methods require that channel state information be available at the transmitter. In addition, some important associated issues such as peak-to-average power ratio requirements at the transmitter and robustness to downlink channel errors are also investigated and various solutions are proposed. Simulation results are provided and these show that performance improvement can be achieved when compared with other MIMO transmit schemes.     

Performance Analysis of Dual-Hop AF Relay Networks in the Presence of Channel Estimation Errors and Feedback Delay

In this letter, we investigate the performance of multiple-input multiple-output two hop beamforming amplify-and-forward (AF) relay networks under imperfect channel state information (CSI) including channel estimation errors (CEE) and feedback delay (FD). To quantify the effect of imperfect CSI on our considered network, we derive the closed-form expression for the outage probability. To gain more insight, we also present an asymptotic analysis which provides the details of the diversity order and array gain. Through our works, one can see the effect of CEE and FD on the system as well as the benefits of deploying multiple antennas at the terminals. Numerical and simulation results are provided to verify the analysis and compare the performance of the considered network for two different models for channel estimation error.     

Unquantized and uncoded channel state information feedback in multiple-antenna multiuser systems

We propose a channel state information (CSI) feedback scheme based on unquantized and uncoded (UQ-UC) transmission. We consider a system where a mobile terminal obtains the downlink CSI and feeds it back to the base station using an uplink feedback channel. If the downlink channel is an independent Rayleigh fading channel, then the CSI may be viewed as an output of a complex independent identically distributed Gaussian source. Further, if the uplink feedback channel is an additive white Gaussian noise channel, and the downlink CSI is perfectly known at the mobile terminal, it can be shown that UQ-UC CSI transmission (that incurs zero delay) is optimal in that it achieves the same minimum mean-squared error distortion as a scheme that optimally (in the Shannon sense) quantizes and encodes the CSI, while theoretically incurring infinite delay. Since the UQ-UC transmission is suboptimal on correlated wireless channels, we propose a simple linear CSI feedback receiver that can be used to improve the performance of UQ-UC transmission while still retaining the attractive zero-delay feature. We provide bounds on the performance of such UQ-UC CSI feedback and study its impact on the achievable information rates. Furthermore, we explore its application and performance in multiple-antenna multiuser wireless systems, and also propose a corresponding pilot-assisted channel-state estimation scheme.     

Robust Optimal Cross-Layer Designs for TDD-OFDMA Systems with Imperfect CSIT and Unknown Interference: State-Space Approach Based on 1-bit ACK/NAK Feedbacks

Cross-layer designs for OFDMA systems have been shown to offer significant gains of spectral efficiency by exploiting the multiuser diversity over the temporal and frequency domains. In this paper, we shall propose a robust optimal cross-layer design for downlink TDD-OFDMA systems with imperfect channel state information at the base station (CSIT) and unknown interference in slow fading channels. Exploiting the ACK/NAK (1-bit) feedbacks from the mobiles, the proposed cross-layer design does not require knowledge of the CSIT error statistics or interference statistics. To take into account of the potential packet error due to the imperfect CSIT and unknown interference, we define average system goodput (which measures the average b/s/Hz successfully delivered to the mobile) as our optimization objective. We formulate the cross-layer design as a state-space control problem. The optimal power, optimal rate and optimal user allocations are determined as the output equations from the system states based on dynamic programming approach. Simulation results illustrate that the performance of the proposed closed-loop cross-layer design is very robust with respect to imperfect CSIT, unknown interference, model mismatch as well as channel variations due to Doppler.     

Predictive downlink beamforming for wideband CDMA over Rayleigh-fading channels

A new approach to adaptive downlink beamforming to combat fast Rayleigh fading is presented. In this approach, the antennas at the base transceiver station form transmit beam patterns according to the prediction of downlink channels. The channel prediction is a linear prediction based on the autoregressive model, which is downsampled to extend the memory span given fixed model order. For a wideband code-division multiple-access downlink, pre-RAKE transmission is employed to achieve the multipath diversity gain. In particular, we combine pseudoinverse directions of arrival beamforming with pre-RAKE transmission to alleviate self-interference. The beamforming weights are adjusted within a downlink frame to compensate the predicted fading. We give measures of the prediction and beamforming performance and evaluate the impact of prediction errors on the downlink. Ray tracing simulations in a three-dimensional urban physical model show that the predictive downlink beamforming outperforms the conventional beamforming over Rayleigh-fading channels.     

Performance analysis of coherent TCM systems with diversityreception in slow Rayleigh fading

Coherent trellis-coded modulation (TCM) systems employing diversity combining are analyzed. Three different kinds of combining are considered: maximal ratio, equal gain, and selection combining (SC). First, the cutoff rate parameter is derived for equal gain combining (EGG) and SC assuming transmission over a fully interleaved channel with flat slow Rayleigh fading, which permits comparison with previously derived results for maximal ratio combining (MRC). Then, tight upper bounds on the pairwise error probabilities are derived for all three combining techniques. These upper bounds are expressed in product form to permit bounding of the bit error rate (BER) via the transfer function approach. In each case, it is assumed that the diversity branches are independent and that the channel state information (CSI) can be recovered perfectly. Also included is an analysis of MRC when the diversity branches are correlated-the cutoff rate and a tight upper bound on the pairwise error probability are derived. It is shown that with double diversity a branch correlation coefficient as high as 0.5 results in only slight performance degradation     

A transmitter diversity scheme for wideband CDMA systems based onspace-time spreading

We present a transmit diversity technique for the downlink of (wideband) direct-sequence (DS) code division multiple access (CDMA) systems. The technique, called space-time spreading (STS), improves the downlink performance by using a small number of antenna elements at the base and one or more antennas at the handset, in conjunction with a novel spreading scheme that is inspired by space-time codes. It spreads each signal in a balanced way over the transmitter antenna elements to provide maximal path diversity at the receiver. In doing so, no extra spreading codes, transmit power or channel information are required at the transmitter and only minimal extra hardware complexity at both sides of the link. Both our analysis and simulation results show significant performance gains over conventional single-antenna systems and other open-loop transmit diversity techniques. Our approach is a practical way to increase the bit rate and/or improve the quality and range in the downlink of either mobile or fixed CDMA systems. A STS-based proposal for the case of two transmitter and single-receiver antennas has been accepted and will be included as an optional diversity mode in release A of the IS-2000 wideband CDMA standard