Maximum likelihood estimation of the K factor in Ricean fading channels

Estimation of the K factor in a Ricean fading channel is studied. Unlike most previous estimators which employ exclusively samples of the fading envelope, new maximum likelihood estimators that use samples of both the fading envelope and the fading phase, or samples of the fading phase only, are derived and examined. Simulation results show that these estimators have good performances when operating in a Ricean fading channel, and in some cases outperform envelope-sample-based estimators.     

SNR estimation in time-varying fading channels

Signal-to-noise ratio (SNR) estimation is considered for phase-shift keying communication systems in time-varying fading channels. Both data-aided (DA) estimation and nondata-aided (NDA) estimation are addressed. The time-varying fading channel is modeled as a polynomial-in-time. Inherent estimation accuracy limitations are examined via the Cramer-Rao lower bound, where it is shown that the effect of the channel's time variation on SNR estimation is negligible. A novel maximum-likelihood (ML) SNR estimator is derived for the time-varying channel model. In DA scenarios, where the estimator has a simple closed-form solution, the exact performance is evaluated both with correct and incorrect (i.e., mismatched) polynomial order. In NDA estimation, the unknown data symbols are modeled as random, and the marginal likelihood is used. The expectation-maximization algorithm is proposed to iteratively maximize this likelihood function. Simulation results show that the resulting estimator offers statistical efficiency over a wider range of scenarios than previously published methods.     

Microdiversity on Rician fading channels

The performance of an L-branch equal gain (EG) combiner on slow and nonselective Rician fading channels is analyzed. Two performance criteria are considered; the probability distribution of signal-to-noise power ratio (SNR) at the output of the EG combiner and the average bit error rate (BER). Matched filter receivers are considered for two binary modulation formats, coherent phase shift keying (CPSK) and noncoherent frequency shift keying (NCFSK). Results using both maximal ratio combining (MRC) and selection diversity combining (SC) are presented for comparison. Our results show that from a feasibility and practical tradeoffs point of view, the performance of an EG combiner may be as good as that of a MR combiner. The effects of gain unbalance between branches of the EG combiner on the probability distribution of SNR and on the bit error rates are also investigated. The Rician fading model may be used to model bath the microcellular environment and the mobile satellite fading channel. Hence, the results of this paper may be useful in both of these areas. Furthermore, in the development of the analysis, we present an efficient method for computing the distribution of sums of Rician random variables. This may be useful for other problems involving Rician fading. The suitability of modeling a Rician fading environment by a properly chosen Nakagami model is examined. A formula for determining the corresponding values of Rician parameter K and Nakagami parameter m is also assessed     

Combining PSA fading estimation techniques for TCM and diversity reception in Rician fading channels

In this paper, a novel pilot‐symbol‐aided (PSA) technique is proposed for fading estimation in the land mobile satellite fading channels. The proposed technique combines the fading estimates obtained from a bandwidth‐efficient technique and a conventional technique according to the signal‐to‐noise ratios (SNRs) of the fading estimates. To enhance the transmission quality, trellis‐coded modulation (TCM) and diversity reception are employed in the system, and the combined estimates are subsequently used to correct the channel fading effects, to weight the signals from different diversity branches, and to provide channel state information to the Viterbi decoder. Monte Carlo computer simulation has been used to study the bit‐error‐rate (BER) performance of the proposed technique on trellis‐coded 16‐ary quadrature amplitude modulation in the frequency non‐selective Rician fading channels. Results have shown that the proposed PSA technique requires a very low bandwidth redundancy to provide satisfactory BER performance at low SNRs, and thus is suitable for use with TCM and diversity reception to achieve both bandwidth and power‐efficient transmission. Copyright © 2002 John Wiley & Sons, Ltd.     

Maximum likelihood sequence estimation of differentially encoded PSK signals transmitted over Rayleigh frequency-flat fading channels

The problem of maximum likelihood (ML) detection of differentially encodedM-PSK signals on Rayleigh fading channels is investigated. It is shown that the solution to this problem can be easily related to previous results [1] and leads to the implementation of a receiver structure based on the Viterbi algorithm and employing per-survivor processing. The error rate performance of this receiver is evaluated by means of computer simulations for both coded and uncoded systems.     

Effect of channel estimation errors on MRC diversity in Rician fading channels

We study the effect of imperfect channel estimation (ICE) on the performance of M-ary phase shift keying (M-PSK) with maximum ratio combining (MRC) in generalized Rician fading channels. First, we derive the error probability formulas for M-PSK with MRC and ICE in arbitrary Rician fading channels. Furthermore, we derive the effective receiver output signal-to-noise ratio (SNR) statistics and the outage probability, and analytically quantify the average SNR loss of M-PSK caused by ICE, assuming independent diversity branches. Finally, we point out a major approximation in a popular approach used in the literature to evaluate the adverse effect of ICE.     

Mobile speed estimation for broadband wireless communications over Rician fading channels

In this paper, a new algorithm is proposed to estimate mobile speed for broadband wireless communications, which often encounter large number of fading channel taps causing severe intersymbol interference. Different from existing algorithms, which commonly assume that the fading channel coefficients are available for the speed estimators, the proposed algorithm is based on the received signals which contain unknown transmitted data, unknown frequency selective fading channel coefficients possibly including line-of-sight (LOS) components, and random receiver noise. Theoretical analysis is first carried out from the received signals, and a practical algorithm is proposed based on the analytical results. The algorithm employs a modified normalized auto-covariance of received signal power to estimate the speed of mobiles. The algorithm works well for frequency selective Rayleigh and Rician channels. The algorithm is very resistant to noise, it provides accurate speed estimation even if the signal-to-noise ratio (SNR) is as low as 0 dB. Simulation results indicate that the new algorithm is very reliable and effective to estimate mobile speed corresponding to a maximum Doppler up to 500 Hz. The algorithm has high computational efficiency and low estimation latency, with results being available within one second after communication is established.     

Accurate Simulation of multiple cross-correlated Rician fading channels

The computer generation of multiple cross-correlated Rician fading channels is investigated. We prove that the output sequences of existing multichannel fading simulators are restricted to have cross-correlation statistics that have the same functional form as the component autocorrelation functions. To overcome this limitation, vector autoregressive stochastic models are proposed for the generation of multiple Rician fading processes with specified realizable autocorrelation and cross-correlation statistics. This capability is desirable, for example, to permit realistic performance assessments of space-time modem designs by enabling the simulation of space-time-selective wireless channel models. The utility of the simulation approach is demonstrated by the accurate synthesis of some bandlimited multichannel Rayleigh and Rician processes.     

Performance of decorrelating receivers in multipath Rician fading channels

This letter focuses on the performance analysis of the decorrelating receiver in multipath Rician faded CDMA channels. M-ary QAM scheme is employed to improve the spectral efficiency. Approximate expressions are first derived for the two performance indexes: the average symbol error rate (SER) and the average bit error rate (BER) when the decorrelating-first receiver perfectly knows the channel information of the user of interest. To achieve desirable closed-form expressions of the SER and the BER, we exploit results in large system analysis and make assumptions of a high signal-to-interference ratio (SIR) and/or a small Rician K-factor. To measure the receiver performance in the practical scenario, we further derive expressions to approximate the average SER and BER of the decorrelating-first scheme with channel uncertainty. Simulation results demonstrate that the analytical results can also be employed to evaluate the performance of the combining-first receiver.     

Worst-case partial-band noise jamming of Rician fading channels

Analyses of worst-case partial-band noise jamming of binary digital modulation are presented. Both noncoherent detection and differentially coherent detection over slowly varying, frequency-nonselective Rician fading channels are considered. The analysis bridges the gap between earlier works by Viterbi and Jacobs (1975) and by Omura (1981) for the limiting cases of Gaussian and Rayleigh channels, respectively. The results complement those by Crepeau (1990) for noncoherent binary transmission over the Nakagami fading channel. However, the Rician channel model has more physical significance since the parameter k is the ratio of scattered and specular powers. It is shown that a partial-band (partial-time) jamming strategy is optimum for all Rician channels with k<1 if the signal-to-jamming power ratio is sufficiently high. On the other hand, a full-band jamming strategy is the optimal strategy for k⩾1. Results for the Gaussian and Rayleigh channels can be derived from the present analysis in the limit as k=0 and k→∞, respectively     

Linear diversity analyses for M-PSK in Rician fading channels

Symbol and bit error rates of M-ary differentially encoded/differentially decoded phase-shift keying (MDPSK) and coherent M-ary phase-shift keying (M-PSK) over slow, flat, Rician fading channels are derived when linear diversity combining is applied to combat degradation due to fading. These closed-form solutions are general enough to cover several cases of nondiversity, additive white Gaussian noise (the nonfading mode), Rayleigh fading, mixtures of Rayleigh and Rician fading (the mixed mode), and Rician fading. The results presented here can also be applied to predict the error-rate performance when recent transmit diversity techniques are employed. The solutions for the nonuniform fading profile are included as well. Error probabilities are graphically displayed for both modulation schemes.     

CRBs and MLEs for SNR estimation of noncoherent BFSK signals in Rayleigh fading channels

Crame/spl acute/r-Rao bound expressions are derived for data and non-data-aided SNR estimation of noncoherent BFSK signals in flat Rayleigh fading channels, and maximum-likelihood estimators for the data-aided and the non-data-aided cases are provided. The performance of the estimators is verified by simulation.     

Performance of MHPM in Rician and Rayleigh fading mobile channels

This paper evaluates the error probability of the rectangular frequency pulse multi-h modulation (MHPM) scheme in slowly-fading, frequency-nonselective or frequency-selective Rician and Rayleigh channels. The evaluation is performed with a method combining analysis and computer simulation. Performance degradations are evaluated for various direct-to-reflected signal ratio, Doppler shifts, and relative time delays in Rician fading channels. Compared with minimum shift keying (MSK), MHPM schemes appear to have retained their coding gains     

Maximum likelihood sequence estimation of CPM signals transmittedover Rayleigh flat-fading channels

A method for the sequential updating of log-likelihood functions for maximum-likelihood sequence estimation is presented. It is shown that, in a general case, this method can be implemented using Kalman filtering techniques. For the special case of Rayleigh flat fading and continuous phase modulation (CPM) signaling, this approach is shown to lead to an attractive receiver structure. This type of receiver, called the linear predictive receiver, can be implemented in the form of the Viterbi algorithm with the trellis updates being computed using a bank of finite pulse response (FIR) filter and square operations. Simulation results are presented that demonstrate the superiority of the linear predictive receiver over receivers employing differential detection, in the presence of fast fading. It is shown that the optimal linear predictive receiver does not possess an irreducible error rate for a class of Rayleigh fading channels used to model terrestrial mobile channels     

Analysis of nonlinear combiner in Rician fading channels withimpulse noise

An efficient method for evaluating the performance of the nonlinear combiner in L-branch frequency non-selective Rician fading channels with impulse noise is derived and verified by simulations. Analysis shows that the nonlinear combiner is robust against impulse noise and fading     

On the average output SNR in selection combining with three correlated branches over Nakagami-m fading channels

An exact and rapidly converging infinite series for the average output signal-to-noise ratio in a triple selection diversity system, over correlated Nakagami-m fading channels, is presented. Numerical results are presented to illustrate the proposed approach and to point out the effect of the fading correlation to the performance of the combiner, as well as the improvement achieved by the triple selection combining compared to the dual diversity case.     

Trellis coded modulation schemes for shadowed Rician fading channels

The Canadian mobile satellite (MSAT) channel has been modelled as the sum of lognormal and Rayleigh components to represent foliage attenuation and multipath fading, respectively. The paper derives a Chernoff based error bound on the performance of trellis coded modulation (TCM) schemes operating on this channel.<>     

Fade margin calculation for channels impaired by Rician fading

Excess path loss due to multipath severely restricts the performance of power limited mobile networks such as those using satellite-aided links. To reduce multipath related losses, the higher elevation angle of the spacecraft can be exploited by utilizing mobile antennas which reduce the strength of the multipath reflections in favor of the line-of-sight signal. The presence of a strong and stable path in a fading link will change the envelope statistics of the received waveform from Rayleigh to a more favorable Rician distribution. It is determined that the excess path loss, or fade margin, of a Rician channel when coherent detection of binary phase shift keying (BPSK) or quaternary phase shift keying (QPSK) signals is considered. The results are presented parametrically such that they can be applied to a wide range of propagation characteristics from heavy fading to nonfading situations. Furthermore, similar results are also given for the case where only limited coverage is provided.     

TCMP-a modulation and coding strategy for Rician fading channels

The authors describe TCMP, a novel modulation strategy for Rician fading channels that multiplexes a time domain pilot sequence with trellis-coded data to permit coherent detection. This technique is shown to provide remarkably robust performance in the presence of fading. It is also shown that, when choosing trellis codes for fading channels, time diversity is of greater important than asymptotic coding gain. The motivation for studying this strategy is to find signaling schemes for transmitting data at a 4.8 kb/s rate over a mobile satellite channel with 5-kHz channel spacing