On the asymptotic capacity of stationary Gaussian fading channels

We consider a peak-power-limited single-antenna flat complex-Gaussian fading channel where the receiver and transmitter, while fully cognizant of the distribution of the fading process, have no knowledge of its realization. Upper and lower bounds on channel capacity are derived, with special emphasis on tightness in the high signal-to-noise ratio (SNR) regime. Necessary and sufficient conditions (in terms of the autocorrelation of the fading process) are derived for capacity to grow double-logarithmically in the SNR. For cases in which capacity increases logarithmically in the SNR, we provide an expression for the "pre-log", i.e., for the asymptotic ratio between channel capacity and the logarithm of the SNR. This ratio is given by the Lebesgue measure of the set of harmonics where the spectral density of the fading process is zero. We finally demonstrate that the asymptotic dependence of channel capacity on the SNR need not be limited to logarithmic or double-logarithmic behaviors. We exhibit power spectra for which capacity grows as a fractional power of the logarithm of the SNR     

Performance analysis of HARQ protocols with link adaptation on fading channels

This work considers hybrid automatic repeat request (HARQ) protocols on a fading channel with Chase combining and deals with both Rayleigh and Nakagami-m fading. We derive the packet loss probability and the throughput for HARQ both for a slow-varying and a fast-varying channel. We then consider link adaptation with complete channel state information (CSI) for which the instantaneous signal-to-noise ratio (SNR) is known and with incomplete CSI for which only the average SNR is known. We derive analytical formulae of the long-term throughput. These formulae are simple enough to be used for higher level simulations. We show that the throughput is slightly higher on a slow-varying channel but at the expense of a higher loss probability.     

Distribution functions of selection combiner output in equally correlated Rayleigh, Rician, and Nakagami-m fading channels

We develop a novel approach to derive the cumulative distribution functions (cdfs) of the selection-combining (SC) output signal-to-noise ratio (SNR) in equally correlated Rayleigh, Ricean, and Nakagami-m fading channels. We show that a set of equally correlated channel gains can be transformed into a set of conditionally independent channel gains. Single-fold integral expressions are, therefore, derived for the cdfs of the SC output SNR. Infinite series representations of the output cdfs are also provided. New expressions are applied to analyze the average error rate, the outage probability, and the output statistics of SC. Numerical and simulation results that illustrate the effect of fading correlation on the performance of L-branch SC in equally correlated fading channels are provided.     

Performance of generalized selection combining over Weibull fading channels

The literature is relatively sparse in performance analysis of diversity combining schemes over Weibull fading channels, despite the fact that the Weibull distribution is often found to be suitably fit for empirical fading channel measurements. In this paper, we capitalize on some interesting results due to Lieblein on the order statistics of Weibull random variables to derive exact closed‐form expressions for the combined average signal‐to‐noise ratio (SNR) as well as amount of fading (AF) at a generalized selection combining (GSC) output over Weibull fading channels. We also use some simple AF‐based mappings between the fading parameters of the Weibull distribution and those of the Nakagami, Rice, and Hoyt distributions to obtain the approximate but accurate average SNR and AF of GSC over these types of channels. The mathematical equations are validated and illustrated by some numerical examples for scenarios of practical interest. Copyright © 2006 John Wiley & Sons, Ltd.     

Asymptotic error-rate behavior for noncoherent on-off keying in thepresence of fading

This article investigates the asymptotic error-rate behavior for the noncoherent on-off keying (OOK) signaling scheme in different fading environments and at both extremes of the signal-to-noise ratio (SNR). A transcendental equation to compute the optimum threshold level of noncoherent OOK operating over a Rician fading channel is derived. The optimum threshold level and its corresponding ratio of the mark and space error probabilities in additive white Gaussian noise (AWGN). Rayleigh, and Rician channels are tabulated as a function of the SNR. Geist (see ibid., vol.42, p.225, 1994) has shown that mark and space errors contribute equally to the average error probability in an AWGN channel when the SNR is large with optimum threshold setting. We show that mark errors predominate when the SNR is small and/or in fading channels     

Degrees of freedom in some underspread MIMO fading channels

Consider a multiple-input multiple-output (MIMO) fading channel in which the fading process varies slowly over time. Assuming that neither the transmitter nor the receiver have knowledge of the fading process, do multiple transmit and receive antennas provide significant capacity improvements at high signal-to-noise ratio (SNR)? For regular fading processes, recent results show that capacity ultimately grows doubly logarithmically with the SNR independently of the number of transmit and receive antennas used. We show that for the Gauss-Markov fading process in all regimes of practical interest the use of multiple antennas provides large capacity improvements. Nonregular fading processes show completely different high-SNR behaviors due to the perfect predictability of the process from noiseless observations. We analyze the capacity of MIMO channels with nonregular fading by presenting a lower bound, which we specialize to the case of band-limited slowly varying fading processes to show that the use of multiple antennas is still highly beneficial. In both cases, regular and nonregular fading, this capacity improvement can be seen as the benefit of having multiple spatial degrees of freedom. For the Gauss-Markov fading model and all regimes of practical interest, we present a communication scheme that achieves the full number of degrees of freedom of the channel with tractable complexity. Our results for underspread Gauss-Markov and band-limited nonregular fading channels suggest that multiple antennas are useful at high SNR.     

改进的Summer算法及其在Turbo译码中的应用

由于Summer信噪比算法采用的信道模型为AWGN信道,他对衰落信道并不适用。通过在接收信号中增加了衰落因子,提出了一种能够应用于Nakagami衰落信道的改进Summer信噪比估计算法。仿真表明,运用改进的算法获得的信道信噪比信息非常接近实际的信噪比信息,同时,改进的Summer在线估计器使得Turbo译码性能得到明显的改善,而且不影响Turbo译码过程的总复杂度。     

How much training is needed in multiple-antenna wireless links?

Multiple-antenna wireless communication links promise very high data rates with low error probabilities, especially when the wireless channel response is known at the receiver. In practice, knowledge of the channel is often obtained by sending known training symbols to the receiver. We show how training affects the capacity of a fading channel-too little training and the channel is improperly learned, too much training and there is no time left for data transmission before the channel changes. We compute a lower bound on the capacity of a channel that is learned by training, and maximize the bound as a function of the received signal-to-noise ratio (SNR), fading coherence time, and number of transmitter antennas. When the training and data powers are allowed to vary, we show that the optimal number of training symbols is equal to the number of transmit antennas-this number is also the smallest training interval length that guarantees meaningful estimates of the channel matrix. When the training and data powers are instead required to be equal, the optimal number of symbols may be larger than the number of antennas. We show that training-based schemes can be optimal at high SNR, but suboptimal at low SNR.     

On the Performance Analysis of Digital Modulations in Generalized-K Fading Channels

In this paper we present novel expressions for several performance metrics of communication systems operating over a composite fading environment modelled by the generalized-K distribution. Initially, for a generalized-K fading channel with arbitrary values for the small and large-scale fading parameters we derive a closed-form expression for the moment generating function (MGF) of the received signal-to-noise ratio (SNR) and utilize it to obtain the exact average symbol error probability for a variety of digital modulations using the MGF based approach. Then, for integer values of the small-scale fading parameter, we derive a novel closed-form expression for the cumulative distribution function of the received SNR, which is then used to obtain closed-form expressions for the outage probability, the average bit error probability of various digital modulations, and the ergodic capacity of the generalized-K fading channel.     

Finite-state Markov model for Rayleigh fading channels

We form a finite-state Markov channel model to represent Rayleigh fading channels. We develop and analyze a methodology to partition the received signal-to-noise ratio (SNR) into a finite number of states according to the time duration of each state. Each state corresponds to a different channel quality indicated by the bit-error rate (BER). The number of states and SNR partitions are determined by the fading speed of the channel. Computer simulations are performed to verify the accuracy of the model     

Utilizing Space-Time Diversity for Wireless Communications

In this paper we consider the use of multiple antennas for wireless communication over fading channels.The fading we consider is quasi-static flat Rayleigh fading. For such a scenario optimal SNR schemes are derived when the transmitter knows the channel and when the transmitter does not know the channel. But in both cases the receiver has to estimate the channel. When the SNR during channel estimation is reasonably high we derive expressions to show the impact of channel estimation errors on SNR.     

Communication on the Grassmann manifold: a geometric approach tothe noncoherent multiple-antenna channel

We study the capacity of multiple-antenna fading channels. We focus on the scenario where the fading coefficients vary quickly; thus an accurate estimation of the coefficients is generally not available to either the transmitter or the receiver. We use a noncoherent block fading model proposed by Marzetta and Hochwald (see ibid. vol.45, p.139-57, 1999). The model does not assume any channel side information at the receiver or at the transmitter, but assumes that the coefficients remain constant for a coherence interval of length T symbol periods. We compute the asymptotic capacity of this channel at high signal-to-noise ratio (SNR) in terms of the coherence time T, the number of transmit antennas M, and the number of receive antennas N. While the capacity gain of the coherent multiple antenna channel is min{M, N} bits per second per Hertz for every 3-dB increase in SNR, the corresponding gain for the noncoherent channel turns out to be M* (1 - M*/T) bits per second per Hertz, where M*=min{M, N, [T/2]}. The capacity expression has a geometric interpretation as sphere packing in the Grassmann manifold     

Performance Analysis on Channel Estimation with Antenna Diversity of OFDM Reception in Multi-path Fast Fading Channel

Vehicle to everything (V2X) communication supports vehicle to anything communication for vehicle safety and cooperative Intelligent Transport System in vehicular environments. IEEE 802.11p modem has been developed and applied for V2X communication system. V2X radio channel has multipath fast fading due to moving vehicles and surrounded road structure. We proposed a new DFCE-AD which combines DFCE and antenna diversity for OFDM reception and analyzed the performance improvement in multipath fading channel. Through computer simulation, SNR gain of DFCE-AD over DFCE for QPSK modulation is approximately 6 dB at PER?=?10%. In other word, PER of DFCE-AD is improved over that of DFCE by about 20% at SNR?=?10 dB. This result will be applied for the short sized packet and low order OFDM modulation in vehicular multipath fading channel.

     

Minimum selection GSC in independent Rayleigh fading

We analyze the error performance of minimum selection generalized selection combining (MS-GSC), in which the minimum number of diversity branches are selected such that their combined signal-to-noise ratio (SNR) is above a given threshold. A flat Rayleigh fading channel with independent and distinctly distributed branch SNRs is considered. By transforming the ordered instantaneous branch SNRs to their differences, we derive the distribution of the number of selected branches in closed form. We then modify the derivation of this distribution to get the characteristic function (cf.) of the combiner output SNR. This cf. is used to obtain the symbol error probability for different coherent digital modulation schemes.     

莱斯多径衰落信道下OFDM系统的容量方差分析

方差是系统容量的一个重要参数,可以用来估计通信系统的中断容量。该文研究了正交频分复用（OFDM）系统在莱斯衰落信道下的容量方差。首先该文建立了多径莱斯信道的模型并且定义了多径莱斯信道的莱斯因子,基于此信道模型推出了一个OFDM系统容量方差新的数学表达式,此表达式以OFDM系统的子载波数、信噪比、信道的多径时延等为参数。基于此表达式,计算机仿真和数值计算研究了信噪比、多径数目、莱斯因子对OFDM系统容量方差的影响。结果表明:计算机仿真和数值计算基本吻合,验证了所推导数学表达式的正确性;系统容量方差与信噪比成正比,与莱斯因子和信道的多径数目成反比。另外,该文以积分的形式给出了任意两个相关莱斯随机变量的联合概率密度函数。      

Throughput performance of an adaptive ARQ scheme in Rayleigh fading channels

Using a simulation study we analyze the throughput performance of Yao's adaptive ARQ scheme in time-varying channels. The simulation takes into account the Rayleigh amplitude and the fast or the slow fading characteristics of a wireless channel, under a representative M-FSK modulation and Reed-Solomon coding scheme. We show that, for a specific set of design parameters, Yao's adaptive procedure works well for all channel fading rates, except for moderately slow rates. By observing variations of packet error rates at a specified SNR we provide an explanation for these varied behaviors under different channel fading rates.     

Gaussian codes and weighted nearest neighbor decoding in fading multiple-antenna channels

We investigate the fading multiple-antenna channel. The decoder is assumed to possess imperfect channel fading information. A modified nearest neighbor decoder with an innovative weighting factor is introduced and an expression for the generalized mutual information (GMI), the achievable rate, is obtained. We show that under certain conditions the achievable rate is equivalent to that of a fading multiple-antenna Gaussian channel where fading is known to the receiver and is equal to the channel estimation, and where noise is due to both the channel noise and the channel estimation error. We show that for our communication scheme, the minimum mean square error (MMSE) channel estimator is optimal in the sense that it achieves the highest value of GMI, and hence the highest communication rate. Additionally, a training based multiple-input multiple-output (MIMO) scheme in a block-fading channel is investigated and it is shown that the number of degrees of freedom depends on the signal-to-noise ratio (SNR).     

Simple Rate Control for Fluctuating Channels in Ad Hoc Wireless Networks

In the presence of channel fluctuation, rate adaptation is one way to maintain the quality of the link at the desired level. This is especially important in ad hoc wireless networks, where temporary channel fluctuation might create frequent needs for rerouting that would result in severe overhead and adversely affect the performance. We study an unusual method of passive rate adaptation in which some bits are dropped at the receiver end of a link. The symbol-error probability decreases as some bits are dropped. In terms of the mean-square distortion for a real-time analog signal, the tradeoff is between more reliable detection of fewer bits and less reliable detection of more bits. Our scheme achieves smaller mean-square distortion for a certain region of signal-to-noise ratio (SNR) values when compared with the original scheme without rate adaptation. Two examples, uniformly spaced, uncoded pulse amplitude modulation and quadrature amplitude modulation, are studied and compared for both a Gaussian channel and a Rayleigh fading channel. We conclude that our scheme has a larger fading channel than in a Gaussian channel. We also verify that our scheme has a larger applicable region of SNR values when a nonuniform constellation is used, since the important bits are given additional protection.     

Capacity of AM-PSK on partially coherent fading channels

This paper presents numerical capacity curves for two discrete complex channels: (1) a slow-fading Rayleigh channel with discrete carrier tracking by a phase-locked loop (PLL), where the PLL SNR is proportional to the fading amplitude squared, and (2) a fast-fading Rician channel with carrier phase estimation for the line-of-sight path only. Both channel models assume independent fading of successively received symbols. Capacity calculations are performed for equiprobable signaling with 8-ary and 16-ary amplitude-modulated phase-shift-keyed (AM-PSK) constellations. On the Rayleigh channel, the AM-PSK constellations give gains between 2 and 9 dB over PSK, at SNRs between 5 and 40 dB. For the Rician channel, AM-PSK gives a capacity gain over PSK of up to 0.75 bit at high SNR     

Performance of antenna diversity multiuser receivers in CDMA channels with imperfect fading estimation

The performance of antenna diversity coherent and differentially coherent linear multiuser receivers is analyzed in frequency-nonselective Rayleigh fading CDMA channels with memory. The estimates of the complex fading processes are utilized for maximal-ratio combining and carrier recovery of the coherent multiuser receiver. To analyze the impact of channel estimation errors on the receiver performance, error probability is assessed directly in terms of the fading rate and the number of active users, showing the penalty imposed by imperfect channel estimation as well as the fading-induced error probability floor. The impact of fading dynamics on the differentially coherent decorrelating receiver with equal-gain combining is quantified. While performance of multiuser receivers at lower SNR is determined by both the fading dynamics and the number of active CDMA users, performance at higher SNR is given by an error probability floor which is due to fading only and has the same value as in a single-user case. The comparison of the two receiver structures indicates that the coherent decorrelating receiver with diversity reception may be preferable to the differentially coherent one in nonselective fading CDMA channels with memory.