Maximum likelihood (ML) amplitude and noise variance estimation without having to jointly estimate the frequency and the phase and based only on information from the noisy received signal magnitude, is studied for a single sinusoid in complex additive white Gaussian noise. This estimation problem is equivalent to the classic problem of parameter estimation for the Rician distribution. While solving the likelihood equation is impossible in general, we propose a new approach based on a large argument approximation. For the case with known noise variance, a closed-form ML amplitude estimator is obtained, which outperforms the conventional root-mean-square estimator. For the case with unknown noise variance, the closed-form joint amplitude and noise variance estimators obtained do not require prior knowledge of one another.

We consider phase-based estimators for chirp parameters due to their high computational efficiency for implementation. Their performances can approach the Cram\'{e}r-Rao lower bound for high signal-to-noise ratio (SNR). One challenge for the phase-based estimators is the performance loss at low SNR because the reliability of phase unwrapping and the accuracy of the phase noise model decrease seriously at low SNR. We here propose a signal recovery method to enhance the SNR for phase-based estimators. The method first uses an adaptive filter to recover the chirp signal from the noisy received signals. Then, the reconstructed chirp signal is used as the input to the traditional phase-based estimators for parameter estimation. The significantly enhanced SNR at the output of the filter brings much improved estimation performance. A robust algorithm is also proposed to achieve good performance over a range of values of chirp parameters of interest. Our simulation results show that significantly improved performance can be obtained by using the signal recovery method for the phase-based estimators.

Phase-based frequency estimators over frequency-selective fading channels are examined. The implementation complexity of phase-based estimators is low due to their explicit structures which require no numerical search. The statistical information of the measurement phase noise (MPN) is crucial for phase-based estimators. The exact probability density function of the MPN over frequency-selective fading channels is first derived. Then, two approximations are proposed to further reduce the computational complexity of the estimators. In our new phase models, the magnitudes of received signal samples enter in determining the covariance of the MPN, and give adaptive weights to the phase measurements. In contrast, only phase information is exploited in the traditional phase-based frequency estimators due to the approximate MPN model used. Our simulation results demonstrate that better performance can be achieved by using our improved MPN models over frequency selective fading channels. Finally, the effects of the periodic length of the training sequence on the performance of frequency estimation are studied.

In we developed a Viterbi algorithm for efficient detection ofM-ary phase-shift keyed (MPSK) sequences received over the additive, white, Gaussian noise (AWGN) channel with an unknown carrier phase. Its performance approaches that of coherent detection, but the observation interval for forming the decision metric is fixed and chosen based on prior statistical knowledge of the carrier phase characteristics. Thus, the metric is non-adaptive, and cannot be optimized when a priori statistical knowledge of the carrier phase is not available. The work here renders it adaptive by developing a recursive metric that is adapted on-line based on the received signal, without prior knowledge of the carrier phase characteristics. An adaptive filter is used to generate the phasor reference on-line, by extending that in to sequence detection for generalM-ary quadrature amplitude modulation (MQAM). Comparison between the proposed adaptive, recursive metric and those in the literature is provided. Simulation results using a random-walk carrier phase model show the superior performance of the adaptive sequence detector over the original nonadaptive sequence detector of.

We consider the maximum likelihood (ML) receiver design, performance analysis and code design for space-time trellis codes (STTC) over non-identical, rapid fading channels with imperfect channel state information (CSI). The exact pairwise error probability (PEP) and PEP bounds for the ML receiver are obtained. A new code design criterion exploiting the statistical information of the channel estimates is proposed, which can minimize the performance loss caused by channel estimation error. New codes are obtained via an iterative search algorithm with reduced complexity. Under actual channel estimation conditions, our codes perform better than the existing codes in the literature which are designed on the assumption of identical channels, and perfect CSI at the receiver. More performance gain can be achieved by our codes when the degree of imbalance among the links is higher.

The performance analysis of space-time trellis codes over rapid nonselective Rayleigh fading channels with imperfect channel state information is considered. A pilot-symbol-assisted-modulation scheme is used for channel estimation. The parameters used in this scheme, i.e., pilot spacing and Wiener filter length are chosen in a tradeoff between estimation accuracy, transmission rate/pilot overhead, and receiver complexity. A simple maximum likelihood receiver for M-ary phase shift keying modulation is derived. An exact closed-form pairwise error probability (PEP) expression and explicit PEP bounds are presented. It is shown that the performance loss caused by channel estimation errors increases mainly with the channel fade rate.

We consider a multi-antenna system using space- time trellis codes (STTC) over independent, non-identically distributed, rapid, Rayleigh fading channels with pilot-symbol- assisted-modulation channel estimation. The maximum likelihood (ML) receiver structure that incorporates the imperfect channel state information (CSI) from the pilot channel measurements, is derived. The exact pairwise error probability (PEP) and PEP bounds for the ML receiver are obtained. Using the explicit PEP bounds obtained, a new pilot power allocation scheme is proposed to improve the performance of STTC at no additional cost of bandwidth or power.

In this paper, we provide a new, practical design criterion for space-time trellis codes over rapid fading channels with imperfect channel state information (CSI) at the receiver. This criterion exploits the statistical information of the channel estimates in code design. The minimum error performance can be achieved by optimally distributing the symbol-wise Euclidean distance based on the variances of the channel estimates. New codes designed with imperfect CSI are obtained using an iterative algorithm with reduced complexity. Simulation results show that in the presence of channel estimation errors, the codes designed based on our criterion assuming imperfect CSI have improved bit error probability performance compared with existing codes that were designed under the perfect CSI assumption. It is also shown that the effect of channel estimation on code design increases with the channel fade rate and the number of transmit antennas