We propose a digital carrier recovery loop employing both a frequency detector and a phase detector for M-ary phase shift keying (MPSK) systems. A new frequency error correction function is also derived to increase the acquisition range. It is shown through computer simulation that the proposed scheme can reduce the acquisition time at large frequency offsets, unlike the existing ones.

In this letter, we elucidate the ergodic capacity of multiple-input multiple-output (MIMO) systems with M-ary phase-shift keying (MPSK) modulation and time-multiplexed pilots in frequency-flat Rayleigh fading environment. With linear minimum mean square error (LMMSE) channel estimation, the optimal pilots design is presented. For mathematical tractability, we derive an easy-computing closed-form lower bound of the channel capacity. Based on the lower bound, the optimal power allocation between the data and pilots is also presented in closed-form, and the optimal training length is investigated by numerical optimization. It is shown that the transmit scheme with equal training and data power and optimized training length provides suboptimal performance, and the transmit scheme with optimized training length and training power is optimal. With the latter scheme, in most situations, the optimal training length equals the number of the transmit antennas and the corresponding optimal power allocation can be easily computed with the proposed formula.

The quadrature component unbalance generated by a non-ideal component such as an imperfect 90-degree phase shifter is an inevitable physical phenomenon and leads to performance degradation in a practical coherent M-ary phase shift keying (MPSK) transceiver. In this letter, we present an exact and general expression involving the one- and two-dimensional Gaussian Q-functions for the symbol error rate (SER) of MPSK with I/Q phase unbalance over an additive white Gaussian noise (AWGN) channel. The SER expression provided here offers a convenient way to evaluate the performance of MPSK systems for various cases of practical interest.

The enormous capacity potential of multiple-input multiple-output (MIMO) is based on some unrealistic assumptions, such as the complete channel state information (CCSI) at the receiver and Gaussian distributed data. In this paper, in frequency-flat Rayleigh fading environment, we investigate the ergodic capacity of MIMO systems with M-ary phase-shift keying (MPSK) modulation and superimposed pilots for channel estimation. With linear minimum mean square error (LMMSE) channel estimation, the optimal pilots design is presented. For the mathematical tractability, we also derive an easy-computing closed-form lower bound of the channel capacity. Furthermore, the optimal power allocation between the data and pilots is investigated by numerical optimization. It is shown that more power should be devoted to the data in low SNR environments and to the pilots in high SNR environments.

Two rotational transformations are used to derive a new expression for the symbol error probability (SEP) of an M-ary phase shift keying (MPSK) with an I-Q unbalance over additive white Gaussian noise (AWGN) and Rician fading channels. We used the new expression to investigate the effect of the I-Q unbalance on the MPSK SEP performance. Our investigation confirms that this approach is a convenient way to evaluate the average SEP of an MPSK for various cases of the Rician factor.

This letter derives a new exact and general closed-form expression involving a two-dimensional joint Gaussian Q-function for the symbol error rate (SER) of M-ary Phase Shift Keying (MPSK) under an additive white Gaussian noise (AWGN) channel. By using two rotations of coordinates the correlation coefficient between two Gaussian random vectors is provided, then with the derived correlation coefficient that characterizes the two-dimensional joint Gaussian Q-function, a new expression for the SER of MPSK is presented. The derived new SER expression offers a convenient method to evaluate the performances of MPSK for various cases of practical interest.

This paper presents the approximate error rates of M-ary phase shift keying (MPSK) for optimum combining (OC) with multiple interferers in a flat Rayleigh fading channel. The approximations, which have been used to evaluate the performance of binary PSK for OC, are extended to the performance analysis of MPSK for OC in the presence of arbitrary numbers of antennas and interferers. The mean eigenvalues of interference-plus-noise covariance matrix are analyzed to compare the approximation techniques, i.e., first-order approximation and the orthongal approximation. Using the moment generating function (MGF)-based method, the approximate error rates of MPSK for OC are derived as the closed-form expressions in terms of the exact error rates of MPSK for MRC. The approximate analytical results show the simple and accurate way to assess the average symbol error rate of MPSK for OC with arbitrary numbers of antennas and interferers.

Multi-Code CDMA (MC-CDMA) can not only be integrated easily with a conventional CDMA system, but also achieve good spectral efficiency and high processing gain. MC-CDMA requires a linear amplifier due to the increasing value of its peak-to-average power ratio (PAPR) as the number of codes increases. As such, a multi-phased MC-CDMA (MP-CDMA) system is proposed to provide a variable rate service that is not susceptible to the nonlinear characteristics of an amplifier. A clipping technique is used between the output of a multi-code modulator and the input of an MPSK modulator to improve the performance of the MPSK chip demodulator and reduce the system's complexity. System performance is analyzed and compared with the number of codes and clipping levels. The optimum clipping level is also evaluated for the number of codes on both AWGN and flat fading channels.

The performances of M-ary PSK (MPSK) and QAM (MQAM) systems using L-branch selection combining (SC) diversity reception in frequency-nonselective slow Nakagami fading channels are derived theoretically. For integer values of the Nakagami fading parameter m, the general formula for evaluating symbol error rate (SER) of MPSK signals in the independent branch diversity system comprises numerical analyses with the integral-form expressions. An exact closed-form SER performance of MQAM signals under the effect of SC diversity via numerical integration is presented.

The performances of M-ary DPSK (MDPSK) and PSK (MPSK) systems using L-branch selection combining (SC) diversity reception in frequency-nonselective slow Nakagami fading channels are derived theoretically. For integer values of the Nakagami fading parameter m, the general formula for evaluating symbol error rate (SER) of MDPSK signals in the independent branch diversity system comprises numerical analyses with the integral-form expressions. An exact closed-form SER performance of MPSK signals under the effect of SC diversity via numerical integration is presented.

In modems for burst transmission of digital data, rapid carrier and clock synchronization are essential. Typically, frequency correction occurs prior to phase recovery since estimators are sensitive to frequency offsets. In this paper, we derive the bit error rate (BER) performance of a M-ary phase shift keying (MPSK) receiver in a closed form when there is no frequency offset estimator. Then we derive a relationship of the required burst length for certain BER with frequency offset estimator. To obtain the BER=10-4, approximately we need the burst length of 101 at Eb/N0=10 dB and 69 at Eb/N0=15 dB.

Approximate maximum likelihood (ML) detection implemented by a reduced state Viterbi algorithm (VA), called the reduced state Viterbi coherent detection (RSVCD) algorithm in this paper, is described for the reception of uncoded M-ary PSK (MPSK) signals transmitted over additive white Gaussian noise (AWGN) channels. An M-state trellis, each state representing one of M signal constellation points, is used. The RSVCD algorithm performs parallel channel estimation based on the per-survivor processing principle (PSPP). Simple decision feedback CD (DFCD) is deduced as a special case of RSVCD. Unified BER expressions are derived for RSVCD, DFCD, and approximate ML detection implemented as an ML-state Viterbi algorithm (referred to as VACD) [6] as well as ideal CD and differential detection (DD). Computer simulation results are also presented and compared with theoretical results.

We have investigated the BER performance of TC 8PSK with 2 branch SC and MRC diversities on spatially correlated Rayleigh fading channel. The upper bounds using the transfer function bounding technique are derived several numerical results are shown. Although the correlation between branches causes signal-to-noise (SNR) loss (relative to uncorrelated fading case) for SC and MRC diversities, the diversity can lead to achieve the diversity gain compared to the system without diversity. It is found that the diversity gain of 4-state TC 8PSK is larger than 8-state TC 8PSK. It is also shown that the BER performance of TC 8PSK is decreased as the antenna separation is decreased.