Effect of delay on uncertainty feedback systems (Corresp.)

Recent work on feedback communications systems is predicated on negligible delay in the forward and the feedback channels. The effect of delay on binary feedback systems of the type considered by Turin and Horstein is studied. Both sequential and nonsequential detection at the receiver are considered. It is shown that if the round-trip delay is small relative to the detection time at the receiver, uncertainty feedback offers considerable advantage. However, for the class of signals considered, the presence of delay precludes operation at channel capacity with zero probability of error.     

Optimal signal design for sequential signaling over a channel with feedback

Turin [1] has studied the problem of optimal sequential detection over a channel with feedback when the signals used are subject to peak and average power constraints. With special additional constraints on the signals he was able to obtain a series solution for the first passage probability density and hence find optimal signals when the ratio of peak power to average power was infinity or one. Horstein,[2] concurrently with this study, was able to find optimal signals for arbitrary ratios of peak to average power when the signals were subject to the same special constraints. This paper presents a simpler and more direct approach for obtaining optimal signals which minimize the expected time to decision for arbitrary peak power constraints and various average power constraints. Explicit closed form solutions are derived for the expected energies and times to decision without having to first obtain the probability distribution of the first passage time. No special constraints are required on the signals. For communication with white noise in the feedback link, optimal stationary signals are found for peak and average power constraints. It is shown that communication rates up to but strictly less than channel capacity are possible with noisy feedback. However, it is also noted that for the schemes considered here, the stationary signals and white noise in the feedback link imply infinite feedback power.     

Binary communication over the Gaussian channel using feedback with a peak energy constraint

We consider binary communication over the additive white Gaussian noise channel with no bandwidth constraint on the channel input signals, assuming the availability of a noiseless delayless feedback link. Although the signals at timetcan depend on the noise at timestau < tand are therefore random functions, we require that the signal energy never exceed a fixed level. We show that the optimal probability of error is attainable without the use of the feedback channel by using antipodal signals.     

Comparison of sequential and nonsequential detection systems with uncertainty feedback

In a previous paper, we found optimal signals for, and evaluated the performance of, a binary sequential detection system in which the detector constantly feeds back to the transmitter its "state of uncertainty" concerning what is being sent. In the present paper, we consider a similar system, which uses a nonsequential detector. Comparison of the results of the two papers shows that: 1) when the prescribed peak-to-average power ratio is small, the sequential system operates with a6-dB average-power advantage over the nonsequential system; 2) when the prescribed peak-to-average power ratio is large, the sequential system operates with a6-dB peak-power advantage over the nonsequential system. In both systems, the performance improves rapidly as the peak-power constraint is relaxed, i.e., as the prescribed peak-to-average power ratio is increased.     

Signal design for sequential detection systems with feedback

We consider a coherent white Gaussian channel, through which one of two signals is sent to a receiver which operates as a sequential detector. A noiseless delayless feedback link is assumed, which continuously informs the transmitter of the state of the receivers uncertainty concerning which signal was sent, and which also synchronizes the transmitter when the receiver has reached a decision. The transmitter, in turn, uses the output of the feedback link to modify its transmission so as to hasten the receiver's decision. The following problem is posed: Given average- and peak-power constraints on the transmitter and a prescribed error probability for the receiver, what signal waveforms should the transmitter use in order to minimize the average transmission time, and how should it utilize the fedback values of the receiver's uncertainty to modify these waveforms while transmission is in progress? We give partial solutions to these questions. In particular, we have shown that if the peak-to-average power ratio is allowed to be sufficiently large, substantial improvement of performance may be achieved through the use of uncertainty feedback.     

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

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.     

Maximum-SNR spatial-temporal formatting designs for MIMO channels

We consider a communication scenario involving an m /spl times/ n multiple input multiple output (MIMO) flat fading channel whose input is a symbol stream multiplied prior to transmission by an n /spl times/ n spatial-temporal formatting matrix X and whose output is fed into an m /spl times/ n linear combiner Z. We show how to choose the matrices X and Z to maximize the signal-to-noise ratio (SNR) of the linear combiner output data that are used for detection, under the total power constraint (TPC), the elemental power constraint (EPC), or the total and elemental power constraint (TEPC). The TEPC design (considered here for the first time) is shown to include the TPC and EPC designs (previously considered by the authors) as special cases and, hence, to provide a theoretically and practically interesting unifying framework. We make use of this framework to discuss various tradeoffs of the three space-time formatting designs considered, such as transmission rate and requirements for channel state information at the transmission side. Additionally, we show that the EPC design, which is the only one of the aforementioned designs that does not require channel information at the transmission side, is also the maximum SNR design in the worst channel case under a TPC.     

Model-based pilot and data power adaptation in psam with periodic delayed feedback

We consider the optimum design of pilot-symbolassisted modulation (PSAM) schemes with feedback. The received signal is periodically fed back to the transmitter through a noiseless delayed link and the time-varying channel is modeled as a Gauss-Markov process. We optimize a lower bound on the channel capacity which incorporates the PSAM parameters and Kalman-based channel estimation and prediction. The parameters available for the capacity optimization are the data power adaptation strategy, pilot spacing and pilot power ratio, subject to an average power constraint. Compared to the optimized open-loop PSAM (i.e., the case where no feedback is provided from the receiver), our results show that even in the presence of feedback delay, the optimized power adaptation provides higher information rates at low signal-to-noise ratios (SNR) in mediumrate fading channels. However, in fast fading channels, even the presence of modest feedback delay dissipates the advantages of power adaptation.     

Distributed Detection in Wireless Sensor Networks Using A Multiple Access Channel

Distributed detection in a one-dimensional (1-D) sensor network with correlated sensor observations, as exemplified by two problems-detection of a deterministic signal in correlated Gaussian noise and detection of a first-order autoregressive [AR(1)] signal in independent Gaussian noise, is studied in this paper. In contrast with the traditional approach where a bank of dedicated parallel access channels (PAC) is used for transmitting the sensor observations to the fusion center, we explore the possibility of employing a shared multiple access channel (MAC), which significantly reduces the bandwidth requirement or detection delay. We assume that local observations are mapped according to a certain function subject to a power constraint. Using the large deviation approach, we demonstrate that for the deterministic signal in correlated noise problem, with a specially chosen mapping rule, MAC fusion achieves the same asymptotic performance as centralized detection under the average power constraint (APC), while there is always a loss in error exponents associated with PAC fusion. Under the total power constraint (TPC), MAC fusion still results in exponential decay in error exponents with the number of sensors, while PAC fusion does not. For the AR signal problem, we propose a suboptimal MAC mapping rule which performs closely to centralized detection for weakly correlated signals at almost all signal-to-noise ratio (SNR) values, and for heavily correlated signals when SNR is either high or low. Finally, we show that although the lack of MAC synchronization always causes a degradation in error exponents, such degradation is negligible when the phase mismatch among sensors is sufficiently small     

Optimization of SNDR for amplitude-limited nonlinearities

Many components used in communication systems are nonlinear and have a peak power or peak amplitude constraint. Nonlinearity generates distortions and thus signal-to-noise-and-distortion ratio (SNDR) is an appropriate performance measure. In this paper, we are interested in finding the nonlinear mapping that maximizes the SNDR subject to the peak amplitude constraint. The answer is a soft limiter with gain calculated based on the noise power and the probability density function of the input amplitude. We also investigate a bounding relationship between the SNDR and capacity of the nonlinear channel. The results of this paper can be applied for efficient transmission of high peak-to-average power ratio signals or for optimal linearization of nonlinear devices.     

Carrier detection of PSK signals

This paper reports on a theoretical study of the detection of the 2f and 4f carrier components of phase-shift keying (PSK) signals produced by passing signal and noise through a nonlinear device. Unbalanced quadrature PSK (QPSK) signals, i.e., QPSK signals with unequal power in the two channels, are studied. The complete range of channel power ratio is covered, with equal emphasis on the general unbalanced case and the two limiting cases of binary PSK and (balanced) QPSK. Analytic expressions are derived for the detected SNR of carrier harmonics 2f and 4f as a function of SNR, channel power ratio, and normalized input bandwidth. The results apply equally well to PSK data signals and direct-sequence spread-spectrum signals. Measurements confirm every aspect of the theory. The least detectable signal type is balanced QPSK, which is detectable (at 4f) at a threshold SNR ranging from -2 to -13 dB as the detection process gain (chip or data rate/detection bandwidth) is varied from 40 to 80 dB     

Power allocation for multi-antenna systems with space-time block coding in the presence of estimation error and delayed feedback

Based on imperfect channel state information with channel estimation error at the receiver and delayed feedback at the transmitter, a suboptimal power allocation (PA) scheme to minimize bit error rate (BER) under a power constraint is developed for beamforming multi-antenna systems with space-time block coding. The proposed scheme is based on a so-called compressed signal-to-noise ratio criterion, where a single compressed factor is utilized, and it can be used to generalize some existing schemes by setting the compressed factor to different forms. A closed-form compressed factor is derived to minimize the BER, and the resultant close-form expression of power allocation is attained. This closed-form expression is computational efficient and can obtain the BER performance close to the existing optimal approach which requires numerical search. Simulation results show that the proposed scheme can provide BER lower than the equal power allocation scheme. However, due to the impact of both estimation error and delayed feedback, it has performance degradation when compared to the PA scheme with estimation error or delayed feedback only.     

Power control in feedback communications over a fading channel

Pilot symbol assisted modulation and a minimum mean-square error (MMSE) channel predictor are used to employ feedback MMSE power control over a frequency nonselective slow Rayleigh fading channel. Feedback is assumed to be noiseless and delayless. First, the performance of the pilot symbol system using MMSE power control is derived in the case of the frame size of two. Lag error is noticed to cause severe performance degradation, even when the channel is very slowly fading. In order to decrease the lag error and to get a good system performance, the number of estimator coefficients is found to become quite large. The operating strategy of MMSE power control is studied by Monte Carlo simulations and compared to various strategies presented in the literature. Spectral efficiency of the pilot symbol system is increased by transmitting more than one data symbol in a given frame. Finally, the performance of the pilot symbol system using MMSE power control is derived in the case of an optimal frame size     

Progressive Linear Precoder Optimization for MIMO Packet Retransmissions Exploiting Channel Covariance Information

This work investigates the design of linear precoders for ARQ packet retransmissions in multi-input multi-output (MIMO) systems. We consider transmitter precoder design based on partial MIMO channel information in the form of their covariance feedback. Our objective is to maximize the ergodic mutual information provided by multiple (re)transmissions of a packet subject to transmission power constraint. We propose a set of near-optimal successive linear ARQ precoders for flat fading MIMO channels. This progressive linear ARQ precoder combines the appropriate power loading and the reverse-order pairing of singular values in the current retransmission with previous transmissions. This reverse-order pairing is a special feature unique to our sequential ARQ preceding approach with demonstrated performance gains.     

Sequential decision feedback with a MAP strategy (Corresp.)

A computer simulation technique is used to evaluate the performance of the MAP strategy for sequential block orthogonal signaling over a Gaussian channel with noiseless and delayless feedback. The system performance is given in terms of the character error probability. The obtained results are compared with those derived using other suboptimum strategies previously proposed.     

一种新的时变衰落信道下MIMO系统的功率分配与自适应调制算法

本文提出一种在时变衰落信道下,MIMO系统的功率分配和自适应调制方法.该方法采用空域注水定理,在发送端天线的平均功率受限的条件下,按照信道传输矩阵的奇异值对发端的多天线进行最优功率分配和自适应MQAM调制.本文从频谱效率方面对其性能进行分析.给出了信道估计的误差和反馈时延对该方法的影响.理论分析和仿真结果表明,该方法实现简单,且与传统的总功率受限的自适应调制方法相比,具有更高的频谱效率.     

Globally Constrained Power Control Across Multiple Channels in Wireless Data Networks

We investigate multi-channel transmission schemes for packetized wireless data networks. The transmitting unit transmits concurrently in several orthogonal channels (for example, distinct FDMA bands or CDMA codes) with randomly fluctuating interference and there is a global constraint on the total power transmitted across all channels at any time slot. Incoming packets to the transmitter are queued up in separate buffers, depending on the channel they are to be transmitted in. In each time slot, one packet can be transmitted in each channel from its corresponding queue. The issue is how much power to transmit in each channel, given the interference in it and the packet backlog, so as to optimize various power and delay costs associated with the system. We formulate the general problem taking a dynamic programming approach. Through structural decompositions of the problem, we design practical novel algorithms for allocating power to various channels under the global power constraint.     

On the reliability function of the ideal Poisson channel withnoiseless feedback

A coding scheme for the channel under peak power and average power constraints on the input is presented, and its asymptotic error exponent is shown to coincide, at all rates below capacity, with the sphere packing error exponent, which, for the case at hand, is known to be unachievable without feedback for rates below the critical rate. An upper bound on the error exponent achievable with feedback is also derived and shown, under a capacity reducing average power constraint, to coincide with the error exponent achieved by the proposed coding scheme; in such a case the coding scheme is asymptotically optimal. Thus, the ideal Poisson channel, limited by a capacity-reducing average power constraint, provides a nontrivial example of a channel for which the reliability function is known exactly both with and without feedback. It is shown that a slight modification of the coding scheme to one of random transmission time can achieve zero-error probability for any rate lower than the ordinary average-error channel capacity     

Nonsymmetric sources and optimum signal selection

There are some applications where the information source is nonsymmetric. Here, it is shown that differential pulse code modulation (DPCM) of video signals results in a nonsymmetric source. Previous works on 2-D signal design have been focused around equally likely sources. In this paper, an iterative algorithm for minimum error signal design subject to average power (or peak power) constraint is presented. Then, design of minimum cost signal sets is addressed, and application to a DPCM system for picture transmission is developed. Comparisons are made between the nonsymmetric and symmetric signal design in one case and between minimum error signal design and minimum cost signal selection in the other case, for the transmission of DPCM-coded signals. It is seen that nonsymmetric signal design gains significant improvements over the equally likely signal selection when the channel is noisy. Minimum cost signal design also demonstrated some improvement relative to minimum error signal selection over noisy channels     

Turbo space-time equalization of TCM for broadband wireless channels

This paper presents a space-time turbo (iterative) equalization method for trellis-coded modulation (TCM) signals over broadband wireless channels. For fixed wireless systems operating at high data rates, the multipath delay spread becomes large, making it impossible to apply trellis-based equalization methods. The equalizer proposed here consists of a broadband beamformer which processes antenna array measurements to shorten the observed channel impulse response, followed by a conventional scalar turbo equalizer. Since the applicability of trellis-based equalizers is limited to additive white noise channels, the beamformer is required to preserve the whiteness of the noise at its output. This constraint is equivalent to requiring that the finite-impulse response (FIR) beamforming filters must have a power complementarity property. The power complementarity property imposes nonnegative definite quadratic constraints on the beamforming filters, so the beamformer design is expressed as a constrained quadratic optimization problem. The composite channel impulse response at the beamformer output is shortened significantly, making it possible to use a turbo equalizer for the joint equalization and decoding of trellis modulated signals. The proposed receiver structure is simulated for two-dimensional TCM signals such as 8-PSK and 16-QAM and the results indicate that the use of antenna arrays with only two or three elements allows a large decrease in the channel signal-to-noise ratio needed to achieve a 10/sup -4/ bit-error rate.