Presence Of Imperfect Channel State Information Research Articles

Energy and spectral efficient Doppler diversity transmissions in high-mobility systems with imperfect channel estimation

This paper studies energy and spectral efficient Doppler diversity transmissions in the presence of imperfect channel state information (CSI). Fast time-varying fading in high-mobility communication systems introduces Doppler diversity that can benefit system performance. On the other hand, it is more difficult to estimate and track fast time-varying channel; thus, channel estimation errors might seriously degrade system performance in high-mobility systems. The trade-offs between channel estimation errors and Doppler diversity are studied by using two precoding schemes, a simple repetition code, and a rate 1 Doppler domain multiplexing (DDM) scheme. The repetition code can achieve the maximum Doppler diversity at the cost of a lower spectral efficiency, and the DDM scheme can achieve the energy and spectral efficient Doppler diversity transmissions. Unlike many other Doppler diversity systems that assume perfect CSI, we explicitly consider the impacts of imperfect CSI on the design and performance of both precoding schemes. Optimum and suboptimum receivers for both schemes are developed by studying the statistical properties of channel estimation errors. The analytical error probabilities of the receivers are expressed as functions of a number of system parameters, such as the maximum Doppler spread, the percentage of pilot symbols for channel estimation, the energy allocation between the pilot and data symbols, etc. The analytical and simulation results indicate that both precoding schemes can achieve the maximum Doppler diversity order through the optimization of the various parameters, even in the presence of imperfect CSI.

Performance Bound Analysis on Transmit Antennas Selection Systems Considering Erroneous Channel Information

Abstract We consider multiple-inputs-single-output (MISO) systems equipped with N transmit and single receive antennas, and concentrate on transmit antenna selection (TAS) for flat Rayleigh fading channels. We assume perfect channel state information (CSI) at receiver and imperfect CSIs through an feedback link at transmitter. The metric of TAS are those with the largest instantaneous signal-to- noise ratio (SNR), the best 2 out of N available transmit antennas always are selected. We use Alamouti encoding scheme and derive the probability density function (PDF) of Frobenius norm of column vector of the channel matrix. Using the known PDF we can derive the joint PDF of order statistics channel for the subseti, j. Assuming that the transmitted signals employ Mary phase-shift keying (MPSK) constellation, we consider the impact of imperfect antenna selection subsets on system performance, and explicitly derive a closed-form BER expression of Chernoff upper bounds (CUB). For two special cases with 2 out of N =3 and 4 possible transmit antennas, we analyses asymptotic performance of selected subsets. Numerical and simulating results show that we can achieve full spatial diversity with antenna selection in the presence of imperfect CSI and the largest ordinal number antenna selected as if all the transmit antennas were used; there may be some loss in the diversity order without the best transmit antenna.

Performance Analysis of Interference Alignment Under CSI Mismatch

With interference alignment (IA), the achievable degrees of freedom (DoFs) in wireless networks can be linearly scaled up with the number of users. However, to attain the full DoF, the availability of perfect network channel state information (CSI) is mandatory, which is not pragmatic in general. In this paper, we quantify the performance of IA under CSI mismatch where the variance of the CSI measurement error depends on the signal-to-noise ratio (SNR). We show that when this error variance is proportional to the inverse of the SNR, the full DoF is achievable, and an upper bound on asymptotic mean loss in sum rate compared with the perfect CSI case is derived. We also derive a bound on the achievable DoF when the CSI error variance is proportional to the inverse of the SNR to a power of a constant. Furthermore, we investigate the effect of CSI mismatch on the performance of the maximum signal-to-interference-plus-noise ratio (Max-SINR) algorithm. We show that with perfect CSI, the Max-SINR algorithm outperforms interference leakage minimization algorithms, but with the presence of imperfect CSI, its comparative improvement becomes negligible. We then propose an adaptive Max-SINR algorithm that can notably improve the performance of the original Max-SINR algorithm under CSI mismatch.

Discrete-rate adaptive modulation with variable threshold for distributed antenna system in the presence of imperfect CSI

Discrete-rate adaptive modulation (AM) scheme for distributed antenna system (DAS) with imperfect channel state information (CSI) is developed, and the corresponding performance is investigated in composite Rayleigh channel. Subject to target bit error rate (BER) constraint, an improved fixed switching threshold (FST) for the AM scheme is presented by means of tightly-approximate BER expression, and it can avoid the performance loss from conventional FST. Based on the imperfect CSI, the variable switching threshold (VST) is derived by utilizing the maximum a posteriori method. This VST includes the improved FST as a special case, and may lower the impact of estimation error on the performance. By the switching thresholds, the spectrum efficiency (SE) and average BER of the system are respectively derived, and resulting closedform expressions are attained. With these expressions, the system performance can be effectively evaluated. Simulation results show that the derived theoretical SE and BER can match the simulations well. Moreover, the AM with the presented FST has higher SE than that with the conventional one, and the AM with VST can tolerate the large estimation error while maintaining the target BER.

Egoistic vs. altruistic beamforming in multi-cell systems with feedback and back-haul delays

Base station cooperation is an attractive technique to increase the spectral efficiency of multi-cell systems. One of the challenges in multi-cell systems is obtaining accurate channel state information (CSI) at the base station. One source of CSI inaccuracy is the delay incurred in obtaining CSI and exchanging it among base stations. The presence of delay is inevitable when CSI is exchanged over the back-haul. In addition, CSI is commonly obtained using limited feedback techniques which further contribute to its inaccuracy. In this paper, we re-visit the comparison between competitive (egoistic) and cooperative (altruistic) beamforming strategies in the presence of imperfect CSI. The impact of CSI inaccuracy due to delay and finite codebook size on the achieved sum rate is analyzed. Closed-form expressions for a lower bound and a first-order approximation of the average sum rates achieved by these beamforming strategies are derived. Using the closed-form expressions, a mode switching criterion is proposed to switch between competitive and cooperative beamforming based on the signal-to-noise ratio (SNR), delay, Doppler frequency and codebook size. It is shown that competitive beamforming is preferred in the limit of low SNR irrespective of the quality of CSI, while cooperative beamforming is preferred only at high SNR and low Doppler frequencies, confirming that base station cooperation is not always advantageous.

Relay Beamforming Design with SIC Detection for MIMO Multirelay Networks with Imperfect CSI

In this paper, we consider a dual-hop multiple-input-multiple-output (MIMO) wireless multirelay network, in which a source-destination pair, both equipped with multiple antennas, communicates through multiple half-duplex amplify-and-forward (AF) relay terminals, which are also with multiple antennas. Since perfect channel-state information (CSI) is difficult to obtain in a practical multirelay network, we consider imperfect CSI for all channels. We focus on maximizing the signal-to-interference-plus-noise ratio (SINR) at the destination. We propose a novel robust linear beamforming at the relays, based on the QR decomposition filter at the destination node, which performs successive interference cancellation (SIC). Using the law of large numbers, we obtain the asymptotic rate in the presence of imperfect CSI, upon which the proposed relay beamforming is optimized. Simulation results show that the asymptotic rate matches with the ergodic rate well. Analysis and simulation results demonstrate that the proposed beamforming outperforms the conventional beamforming schemes for any power of CSI errors and SNR regions.

QoS Guarantees in AF Relay Networks with Multiple Source-Destination Pairs in the Presence of Imperfect CSI

A relay network approach is proposed that allows multiple source-destination pairs to communicate simultaneously. The communication is enabled by a multi-antenna amplify-and-forward relay and is implemented in two slots; in the first slot, the sources transmit, and in the second slot, the relay forwards the received signals after processing them through a Zeroforcing Beamforming (ZFBF) matrix. The relay determines the ZFBF matrix so that the transmit power is minimized while the SINR of each destination meets a predefined constraint. Initially, the design is based on perfect channel state information (CSI). Imperfect CSI results in interference at the destinations. This effect can be controlled by increasing the number of relay antennas, or by optimally selecting the antennas to be used. Antenna selection schemes are proposed, which minimize the outage probability, or the destination interference. Also, an iterative scheme is proposed, whereby the amplitudes of the beamforming weights of all source-destination pairs are iteratively increased so that the worst case SINRs meet the requirements of the destinations. It is shown that this approach, coupled with antenna selection, greatly reduces the outage probability.

Energy-Aware Power Allocation in Cooperative Communication Systems with Imperfect CSI

Energy-aware power allocation in cooperative communication systems depends on the availability of channel state information (CSI), which is often imperfect in practice. This paper proposes energy-aware, optimal power allocation schemes for an amplify-and-forward cooperative communication system in the presence of imperfect CSI, to i) minimize the total transmit power; ii) maximize the end-to-end signal-to-noise ratio (SNR). Energy awareness is incorporated in the schemes either by avoiding over-provisioning of quality-of-service (QoS) or, by preventing unsuccessful transmissions, depending on the application. In both the schemes, the source and relay nodes share a fixed total transmit power budget, and transmission is allowed only if the minimum required end-to-end SNR can be achieved with the available power budget. Closed-form expressions for the source and relay optimal transmit powers are derived for both these schemes. Performance of the systems under the proposed schemes are investigated through simulations.

Resource Allocation for Selective Relaying Based Cellular Wireless System with Imperfect CSI

In this paper, we propose robust power allocation and admission control schemes for providing probabilistically constrained quality of service (QoS) in selective relaying based decode-and-forward (DF) cooperative cellular systems. The proposed schemes are robust against imperfect channel state information (CSI) in slow fading while optimizing the total uplink transmit power in these cooperative wireless networks. At first, we derive novel closed-form solutions for the optimization problem, where the objective is to minimize total uplink transmit power while meeting the probabilistic QoS guarantees for a given number of admitted users. This is achieved by approximating the probabilistic optimization problem into a convex deterministic form and then by deriving closed form analytical solutions for power allocation using Karush-Kuhn-Tucker (KKT) conditions. The closed-form property of these solutions allows us later to develop a very low-complexity suboptimal algorithm for joint admission control and power allocation in presence of imperfect CSI and selective relaying. We also conduct comprehensive simulation experiments to demonstrate the effectiveness of our proposed schemes and to highlight the benefits gained from considering channel estimation errors in resource allocation for cooperative cellular systems.

Finite-signal-to-noise ratio diversity-multiplexing-rate trade-off in limited feedback beamforming systems with imperfect channel state information

The problem of diversity-multiplexing-rate trade-off (DMRT) in limited feedback beamforming systems is addressed here. A major difference from previous works is that the authors consider the trade-off in finite-signal-to-noise ratio (SNR) regime. Under this condition, the feedback rate has a great impact on the conventional diversity-multiplexing relationship. Hence, the release of the trade-off among diversity, multiplexing and feedback rate has a practical benefit to the design and adoption of space–time signals in limited feedback beamforming systems. Asymptotical analysis shows that the obtained trade-off is consistent with the conventional one when feedback rate equals to zero and the SNR approaches infinity. Furthermore, considering the channel dynamics, the authors investigate the effect of imperfect channel state information (CSI) caused by channel estimation error and feedback delay on the DMRT. It is found that in the presence of imperfect CSI, besides the system parameters, such as the number of transmit and receive antennas, maximum diversity order and multiplexing gain are also limited by SNR and correlation coefficient between the obtained CSI and the real CSI. Finally, our theoretical claims are validated by the numerical results.

Performance Analysis of Multiuser Downlink Space-Time Scheduling for TDD Systems With Imperfect CSIT

This paper studies the effect of imperfect channel state information (CSIT) on the performance of multiple-antenna downlink scheduling for time-division-duplex system. The base station is equipped with n/sub T/ transmit antennas and there are K mobiles in the system, each with single receive antenna. We propose an analytical framework to study the multiantenna downlink scheduling problem in the presence of imperfect CSIT at the base station. We found that with ideal CSIT, the space-time scheduler can achieve significant system capacity with respect to n/sub T/ due to increased spatial channels. However, at moderate CSIT estimation error, the system performance using the ideal scheduling algorithm (designed for perfect CSI) saturates quickly with respect to n/sub T/ and signal-to-noise ration (SNR) increases. This is because in the presence of imperfect CSIT, the scheduled data rate of a user may exceed the actual channel capacity and resulting in packet transmission outage. To realize the potential spatial multiplexing gain over n/sub T/ and SNR, we propose an analytical framework to take into account of the packet transmission outage and propose scheduling solutions matching the imperfect CSIT situations. We found that, by considering the statistics of CSIT errors into the design, the proposed schemes provide significant system performance enhancement.