Effect of feedback delay and channel gain difference on distributed transmit diversity without receiver phase compensation

In this letter, we investigate the effect of feedback delay on the performance of a dual-hop amplify-and-forward (AF) relay network with beamforming in the presence of multiple interferers over Rayleigh fading channels. Specifically, we derive closed-form expressions for the outage probability (OP) and the symbol error rate (SER). Furthermore, to render insights into the effect of feedback delay and interference on the network performance, asymptotic OP and SER are also presented. These asymptotic expressions are very tight in the high signal-to-noise ratio regime, readily enabling us to obtain the diversity and coding gains of the considered network.

Inspired by the information theoretic results concerning multiuser diversity, we address practical issues in implementing multiuser diversity in a multiple access wireless setting. Considering a channel-assigning strategy that assigns the channel only to the user with the best instantaneous SNR , our emphasis is on the effects of channel feedback delay in downlink transmissions. A finite set of M-ary quadrature amplitude modulation (M-QAM) constellations is adopted and a constant transmit power is assumed in this practical multiuser adaptive modulation scheme. Based on the closed-form expressions for average bit error rate (BER) and average data rate, we illustrate the impact of channel feedback delay on the achievable multiuser diversity gain with the number of users. Simple and accurate asymptotic approximations are also provided in the limit of large numbers of users. Focusing on different applications, we propose two optimization criteria for the switching thresholds, based on either an average BER, or an outage probability constraint. Two novel constant power, variable rate M-QAM schemes that are less sensitive to feedback delay are proposed using the optimal switching thresholds, which are derived to maximize the average data rate subject to these two constraints, respectively. To obtain a certain degree of fairness among the users, we also consider a fair channel-assigning strategy that assigns the channel to only the user with the greatest normalized SNR.

Allocating wireless resources often relies on the accurate feedback of channel state information (CSI). In this paper, we study how strongly a multiuser OFDM downlink with single-cell scheduling and channel estimation suffers from feedback delay. Unlike previous work, we study this degradation for optimal joint power and rate allocation under fairness constraints. Comparing the performance of the ideal case to delayed CSI shows that (i) adjusting the schedulers fairness cannot mitigate the strong performance loss due to feedback delay but that (ii) simple linear channel prediction is a powerful tool to do so.

In this paper, the effect of feedback delays on the performance of multiple-input multiple-output antenna amplify-and-forward relay networks with the best transmit/receive antenna pair selection over Rayleigh fading is studied. The cumulative distribution function and the moment generating function of the end-to-end signal-to-noise ratio (SNR) are derived. Closed-form expressions for the outage probability, average symbol error rate (SER), and the SNR moments are also derived. To gain further insights, the asymptotic outage probability, average SER, diversity order, and coding gain are presented. Numerical results and Monte-Carlo simulations are provided to illustrate the detrimental effects of feedback delays on the system performance and to verify the accuracy of our analysis.

In this paper, the outage performance of multiuser multiple-input single-output (MISO) systems exploiting joint spatial and multiuser diversities is investigated for Rayleigh fading channels with outdated feedback. First, we derive closed-form exact outage probabilities for the joint diversity schemes that combine user scheduling with different spatial diversity techniques, including: 1) transmit maximum-ratio combining (TMRC); 2) transmit antenna selection (TAS); and 3) orthogonal space-time block coding (OSTBC). Then the asymptotic outage probabilities are analyzed to gain more insights into the effect of feedback delay. It is observed that with outdated feedback, the asymptotic diversity order of the multiuser OSTBC (M-OSTBC) scheme is equal to the number of transmit antennas at the base station, while that of the multiuser TMRC (M-TMRC) and the multiuser TAS (M-TAS) schemes reduce to one. Further by comparing the asymptotic outage probabilities, it is found that the M-TMRC scheme outperforms the M-TAS scheme, and the M-OSTBC scheme can perform best in the outage regime of practical interest when the feedback delay is large. Theoretical analysis is verified by simulation results.

This paper investigates the outage probability of the multiuser transmit antenna selection/maximal-ratio combining (TAS/MRC) system over Rayleigh fading channels with outdated feedback. The exact outage probability is first derived. Then the asymptotic outage probability is analyzed to gain more insights into the effect of feedback delay. The analytical results show that: 1) increasing the number of users has the same effect on the outage probability as increasing the number of transmit antennas at the base station; 2) with outdated feedback, the asymptotic diversity order of the multiuser TAS/MRC system reduces to the number of receive antennas at the users. Theoretical analysis is verified by simulation results.

SUMMARYThe quality of channel state information at the transmitter (CSIT) is critical to MIMO beamforming systems. However, in practical wireless systems, CSIT suffers from imperfections originating from quantization effects, feedback error and feedback delay. In this paper, we study the impact of feedback error and delay on the symbol error rate of MIMO beamforming systems with finite rate feedback. The feedback channel is modeled as a uniform symmetric channel. We derive an symbol error rate upper bound that is tight for a good beamformer. We also quantify the diversity gain and array gain loss due to the feedback error and delay. The codebook design method that is applicable to the beamforming systems with error or delay feedback is discussed. Both analytical and simulation results show that feedback error and delay will make the system behave badly at high signal‐to‐noise ratios. Copyright © 2012 John Wiley & Sons, Ltd.

The authors investigate deployment of link adaptation techniques to enhance the performance of real-time video communications over time-varying error-prone environments. A novel link adaptation algorithm is proposed and analysed. Two approaches for link adaptation are investigated. The first approach aims to optimise video quality for a fixed channel allocation. The design criterion of the second approach is to maximise the overall access network throughput while maintaining the required video quality. The effectiveness of the algorithms is demonstrated for MPEG-4 coded video transmissions over simulated EGPRS networks. In addition, the effects of feedback delay, a noisy feedback channel and bursty channel errors on algorithm performance are investigated.

We investigate the effect of delay in feedback on the oscillation characteristics (amplitude and frequency) of a string generator, which, as is well known, works in a self-induced oscillation mode and is a part of a string accelerometer (a device for measuring the acceleration of ballistic missiles, launch vehicles, and other moving objects). A mathematical model of the dynamics of a string generator is taken in the form of a quasilinear second-order hyperbolic equation with constant delay with respect to one of independent variables (time). For the analysis of the mathematical model, we use the one-frequency asymptotic Krylov-Bogolyubov-Mitropol'skii method (its first and second approximations) of nonlinear mechanics. We show that an increase in the delay in the nonlinear feedback amplifier results in a decrease in the frequency of self-induced oscillations, which transforms the string generator into a low-frequency device.

Understanding barriers to organizational learning is central to understanding firm performance. We investigate the role of time delays between taking an action and observing the results in impeding learning. These delays, ubiquitous in real‐world settings, are relevant to tradeoffs between long term and short term. We build four learning heuristics, with different levels of complexity and rationality, and analyze their performance in a simple resource allocation task. All reliably converge to the optimal solution when there are no/short delays, and when those delays are correctly assessed. However, learning is slowed significantly when decision makers err in assessing the length of the delay. In many cases, the decision maker never finds the optimal solution, wandering in the action space or converging to a suboptimal allocation. Results are robust to the organization's level of rationality. The proposed heuristics can be applied to a range of problems for modeling learning from experience in the presence of delays. Copyright © 2009 John Wiley & Sons, Ltd.

Non-orthogonal multiple access (NOMA) guarantees good spectral efficiency and better enhance system radio capacity. However, the deployment of NOMA is not easy due to complexity of successive interference cancellation (SIC). Thus, it is advisable to divide users into orthogonal frequency groups and adopt a Conventional NOMA (C-NOMA) pairing within each group (hybrid NOMA). Knowing that C-NOMA uses the channel gain difference and the power allocation to increase the data rate of the pair, in a dense user environment, this channel gain difference narrows further. To do this, the users are grouped in such a way as to exploit the intergroup gap in order not only to avoid the formation of very small channel gain pairs, but also improved the data throughput of low gain groups. In this paper, we examine the user pairing scheme that we will call D-NOMA (Distributed NOMA), in a uniform deployment scenario, to distribute the data throughput in the NOMA sets, to exploit the intergroup gap and facilitate a controlled data throughput distribution of NOMA weak pairs more precisely. The results show that about 50% of D-NOMA pairs of small channel gain difference benefit from a data rate higher than C-NOMA, and 25% of D-NOMA pairs of small channel gain difference benefit from a higher data rate than conventional Divide-and-Next-Largest-difference based User Pairing Algorithm (D-NLUPA).

We investigate the joint effects of feedback delay and channel estimation errors (CEE) over Nakagami- m fading channels for two-hop amplify-and-forward (AF) relaying systems with transmit beamforming (TB) and relay selection (RS). We derive new closed-form expressions for the system outage performance including the exact analysis and informative high SNR asymptotic approximations, which indicate that TB feedback delay reduces the achievable diversity order to one, regardless of Nakagami- m fading parameters. Whereas RS delay reduces the diversity order to a case without relay selection and CEE merely result in coding gain loss, numerical results verify the theoretical analysis and illustrate that the outage performance is more sensitive to the TB feedback delay.

In our earlier work, we described an optimization problem and corresponding scheduling algorithm aimed at obtaining maximum throughput guarantees in wireless networks. To further improve the short-term performance, we also proposed two adaptive versions of the optimal algorithm. Results from the simulations showed that the adaptive algorithms perform significantly better than other well-known scheduling algorithms in networks based on Mobile WiMAX, HSDPA, LTE and WINNER I. However, there were several idealistic assumptions in that analysis, the most important of which is that each user estimates its carrier-to-noise ratio (CNR) perfectly, and there is no feedback delay. In practice however, the channel estimation is not perfect, and there is always some delay in the feedback channel. In this paper, we assume that a maximum a posteriori (MAP) predictor is employed for the CNR, so that the system takes the feedback delay and the channel noise into account. We then investigate the effect of imperfect channel prediction and delay on the throughput guarantees promised to all the users in the wireless network. A procedure to reduce the probability of outage in case of imperfect channel prediction is also proposed.

Orthogonal frequency-division multiple access (OFDMA) systems divide the available bandwidth into orthogonal subchannels and exploit multiuser diversity and frequency selectivity to achieve high spectral efficiencies. However, they require a significant amount of channel state feedback for scheduling and rate adaptation and are sensitive to feedback delays. We develop a comprehensive analysis for OFDMA system throughput in the presence of feedback delays as a function of the feedback scheme, frequency-domain scheduler, and rate adaptation rule. Also derived are expressions for the outage probability, which captures the inability of a subchannel to successfully carry data due to the feedback scheme or feedback delays. Our model encompasses the popular best- <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> and threshold-based feedback schemes and the greedy, proportional fair, and round-robin schedulers that cover a wide range of throughput versus fairness tradeoff. It helps quantify the different robustness of the schedulers to feedback overhead and delays. Even at low vehicular speeds, it shows that small feedback delays markedly degrade the throughput and increase the outage probability. Further, given the feedback delay, the throughput degradation depends primarily on the feedback overhead and not on the feedback scheme itself. We also show how to optimize the rate adaptation thresholds as a function of feedback delay.

In this paper, we first address the effects of the feedback delay on a variable-rate variable-power adaptive modulation MIMO system that is designed under a perfect channel state information (CSI) assumption. Closed-form expressions for the average bit error rate (BER) and average spectral efficiency (ASE) are derived. Based on that, simple but effective adaptive modulation designs using the outdated instantaneous CSI and time correlation coefficient are proposed based on the signal-to-interference and noise ratio (SINK) and BER analysis. Analytical and simulation results show that these designs provide good trade-offs between the ASE and BER in an adaptive way, and make the adaptive MIMO system much more robust to the CSI imperfection