The Effect of Carrier Phase Error on the Performance of a Duobinary Shaped QPSK Signal

An analysis is presented showing the effect of carrier phase error on the error-rate of a duobinary shaped, quaternary, phaseshift keying digital radio system. A simple upper bound on the probability of error as a function of phase error is derived and the results are compared to those obtained by computer simulation. The conclusion is reached that such a system exhibits approximately 1.0 dB degradation for a carrier phase error of 3° at an error-rate of 10^-5and a 10 dB degradation at a phase error of 15°.     

Analysis of equal-gain diversity with partially coherent fadingsignals

An analytical technique based on Gram-Charlier series expansion is presented for the computation of the error probability of equal-gain combiner (EGC) with partially coherent fading signals. Imperfect carrier recovery is attributed to the random noise present in the carrier recovery loops. The resulting noisy phase references are assumed to satisfy Tikhonov distribution. The fades on the diversity branches are assumed to be slowly varying and statistically independent with Rayleigh-distributed envelopes. The error-rate performance of coherent and differentially coherent phase-shift keying (PSK) systems are compared and the phase precision requirement for a reliable coherent detection is computed. Detection loss caused by carrier phase errors is computed for several signal-to-noise ratio (SNR) reliability and bit error probability levels. It is demonstrated that the effect of carrier phase errors on the mean SNR is negligible compared to their effect on deep fades or small bit error probabilities. It is also shown that the carrier phase precision requirement can be reduced through signal combination     

Decision-Aided Tracking Loops for Channels with Phase Jitter and Intersymbol Interference

The theory of decision-aided carrier tracking loops as developed by Lindsey and Simon is extended to include the effects of intersymbol interference. A major theoretical result is the solution of the Fokker-Planck equation for the probability density function (pdf) of the phase error for a first-order tracking loop. This function is used to average upper and lower bounds on the demodulator error rate so that an estimate of the overall system error rate may be obtained. The modulation technique analyzed is double-sideband-pulse-amplitude pulse-amplitude modulation. Curves are presented which display the threshold performance of the system error rate at low modulation index.     

Effects of Jitter and Cycle Slipping of Phase Reference Upon Unique Word Missed Detection in QPSK Systems

The effects of phase jitter and cycle slipping of the recovered carrier upon unique word (UW) missed detection in QPSK systems are investigated. Schrempp et al. have already presented the relationship between the UW missed detection probability (UWMP) and the bit error probability, which is simple and useful as long as the phase reference is noiseless. However, when the authors recently made some theoretical and experimental assessments of UW missed detection, they found that the above disturbances of the recovered carrier significantly affected the UW missed detection performance. Specifically, the actual UWMP was often worse than that predicted hy Schrempp et al. In fact, a bottoming effect takes place in the UWMP versus UW length characteristic. In this paper, after obtaining the conditional symbol and bit error probabilities for the recovered carrier with some phase error, we discuss the nature of phase fluctuation and cycle slipping for the recovered carrier. Consequently, we derive general expressions for the UWMP in both CPSK and DCPSK transmissions. The UWMP's are numerically calculated, and are then compared to our experimental data.     

Encoded 16-PSK: a study for the receiver design

The authors present the results of a design study of the receiver in a digital transmission system using the combined coding and modulation schemes known as Ungerboeck codes. Specifically, they examine the design of the receiver for encoded 16-PSK (phase shift keying) modulation, presenting first the traditional structure for the optimum receiver and then a simpler structure. The decoding depth of the Viterbi algorithm, the quantization of the metrics inside the Viterbi processor, and the phase jitter in the recovered carrier are considered. The impact of branch and path metric quantization inside the receiver is discussed, showing that a reasonable number of bits (8) is sufficient to obtain nearly optimum performance when the code complexity is limited. The effect of imperfect carrier recovery inside the receiver is studied, providing accurate analytical estimates of the error event probability as well as an upper bound to the symbol error probability. Results of a detailed simulation, including carrier and bit timing recovery blocks, show that the effects of imperfections on the bit error probability are very small, even at low signal-to-noise ratios. On the whole, results show the robustness of the Viterbi algorithm with respect to fairly rough quantizations of the metrics and indicate that carrier recovery is not as critical as expected     

Simplified noisy reference loss evaluation for digitalcommunication in the presence of slow fading and carrier phaseerror

Using a Maclaurin series expansion of the conditional (on the carrier phase error) bit error probability of binary and quaternary phase-shift keying (BPSK and QPSK, respectively) and then averaging this result over both the statistics of the carrier phase error and the channel fading, closed-form expressions for the average bit error probability are derived in a form that lend themselves toward obtaining simple formulas for the associated noisy reference loss. Numerical evaluation of this loss based on the use of these formulas is shown to provide excellent accuracy when compared with the exact evaluation, which requires two-fold numerical integration. Although the method is specifically applied to BPSK and QPSK, it is easily extended to other forms of modulation whose conditional bit error probability is known in a closed form     

Discrete Time Analyses of Nonuniform Sampling First- and Second-Order Digital Phase Lock Loops

The present paper considers discrete time analyses of firstand second-order digital phase lock loops. These loops are characterized by the fact that they track the zero crossings of the incoming signal; consequently, the sampling intervals are nonuniform. The firstorder loop is analyzed for phase step and frequency step inputs; mean time to skip cycle is also considered. For phase step input, approximate expressions are obtained for the steady-state phase error probability density and phase error variance, the second of which leads directly to a theoretical prediction of threshold. The second-order loop is analyzed for frequency step input. Approximate expressions for the steady-state phase error probability density, phase error variance, and a theoretical prediction of threshold are obtained. The analyses are confirmed by numerical results and simulation.     

Efficient estimation of continuous phase modulation with unknowncarrier phase

An efficient algorithm is presented for the estimation of continuous phase modulation (CPM) sequences over the Gaussian channel with unknown carrier phase. It operates on the excess phase trellis like the Viterbi algorithm, except that it is not a maximum-likelihood (ML) estimator. Its decision metric for survivor selection at each node is chosen so that it achieves the node error event probability of coherent ML estimation in the limit as the carrier phase remains constant over a long interval, so that the observation interval for forming the metric can be made large. It is shown for the case of minimum-shift-keying (MSK) that the bit-error probability (BEP) of perfectly coherent ML estimation is attained     

Optimal detection of FM clicks (Corresp.)

For the Case of an unmodulated carrier, the detection of an FM click is formulated as the detection of a non-Gaussian random signal embedded in colored Gaussian noise. This correspondence presents an approximation to the optimum detector of FM clicks along with its theoretical performance in terms of probability of false alarm and probability of error. Numerical results are presented in graphical form. The corresponding exact results for detection problems of this type are currently not available. The theoretical results help to explain the known practical result that FM threshold extenders are limited to threshold improvements of only a few dB. For the case of a modulated carrier, some comments concerning detector performance are presented. For comparison purposes, detector performance of a detector based on the heights of local maxima is also presented.     

Effect of noisy carrier reference signal and interference on performance of MSK receiver

This paper considers the coherent detection of minimum shift keying signal and a degradation in error rate performance from ideal due to an interference and a phase discrepancy between the carrier of the received signal and the carrier of the receiver. The error rate is calculated for the simple receiver model with integrate‐and‐dump circuits. The reference carrier signal unsteadiness is presented by the probability density function of the first order non‐linear PLL phase error, while the uncertainty due to an interference is involved in the system model with a random phase of cosine signal that accompanied the useful signal. Copyright © 2004 John Wiley & Sons, Ltd.     

认知无线网络中动态双门限协作频谱感知性能的优化方案

频谱感知作为认知无线电的关键技术,得到广泛深入的研究。其中衡量协作频谱感知性能的主要参数为全局虚警概率和全局漏检概率,它们之和被定义为全局错误概率。本文研究基于双门限能量检测的协作频谱感知性能的优化方案,首先,固定双门限能量检测的检测门限值,对表决融合准则的投票门限进行优化,使得在该能量检测门限值条件下,协作频谱感知的全局错误概率最小;然后在表决融合准则的投票门限取最优值的前提下,对双门限能量检测的检测门限值进行了优化,在不同接收信噪比条件下,最优的检测门限值是动态的,所以要根据信噪比确定最优的检测门限值,使得协作频谱感知的全局错误概率在各信噪比条件下都达到最小值,从而提高了协作频谱感知的性能。仿真结果表明,表决融合准则的投票门限和双门限能量检测的检测门限值取得各自的最优值时,全局错误概率最低,检测性能最好。      

Phase-lock-loop statistics without recourse to Fokker-Planck techniques

To obtain the steady-state probability distribution of the phase error for a phase-lock loop driven by the sum of modulated carrier and narrowband stationary noise, a familiarity with Fokker-Planck techniques is usually a prerequisite to formulate a differential equation that has the required distribution as its solution. Here a simpler treatment is offered, which uses the more standard tools of probability theory. The distribution of the frequency error is also considered.     

Near-far effects in land mobile random access networks withnarrow-band Rayleigh fading channels

The near-far effect of random access protocols in mobile radio channels with receiver capture is investigated. To this end, the probability of successful reception of a packet from a terminal at a known distance from the central receiver is obtained taking into account Rayleigh fading, UHF propagation attenuation, and the statistics of contending packet traffic in radio nets employing slotted ALOHA, carrier sense multiple access (CSMA) or inhibit sense multiple access (ISMA) protocols. Various models of receiver capture are compared, namely packet error rates for synchronous detection in slow- and fast-fading channels, and the probability that the signal-to-interference ratio is above a required threshold     

多天线认知系统中最优协作用户数的选择研究

针对非理想控制信道传输错误对认知系统中多天线多用户协作频谱感知性能影响的问题,提出一种使得认知系统误检概率最小的最优协作用户数选择方案,并推导给出其闭式表达式。该方案首先根据单根天线错误检测概率最小的原则推导出认知用户单根天线最优的判决门限。然后利用“K秩”准则对多天线进行合并,根据认知用户错误检测概率最小的原则推导出最优的“K”值。最后根据认知系统误检概率最小的原则推导出最优的协作感知用户数。通过仿真验证了该方案理论的正确性,并分析给出了控制信道错误概率对认知系统检测性能的影响。相比于传统的协作检测算法,本方案具有更好的检测性能。      

On the effects of a spacecraft subcarrier unbalanced modulator

This paper presents mathematical models with associated analysis of the deleterious effects which a spacecraft's subcarrier unbalanced modulator has on the performance of a phase-modulated residual carrier communications link. The undesired spectral components produced by the phase and amplitude imbalances in the subcarrier modulator can cause (1) potential interference to the carrier tracking and (2) degradation in the telemetry bit signal-to-noise ratio (SNR). A suitable model for the unbalanced modulator is developed and the threshold levels of undesired components that fall into the carrier tracking loop are determined. The distribution of the carrier phase error caused by the additive White Gaussian noise (AWGN) and undesired component at the residual RF carrier is derived for the limiting cases. Further, this paper analyses the telemetry bit signal-to-noise ratio degradations due to undesirable spectral components as well as the carrier tracking phase error induced by phase and amplitude imbalances. Numerical results which indicate the sensitivity of the carrier tracking loop and the telemetry symbol-error rate (SER) to various parameters of the models are also provided as a tool in the design of the subcarrier balanced modulator.     

Optimization of offset for OQPSK with time limited pulses

The optimum offset for offset quaternary phase shift keying (OQPSK) in the presence of carrier phase error is determined for some time limited pulse shapes. It is shown that, for certain pulse shapes, T/2 is optimum in a minimum probability of error sense. In the case of bipolar pulse shaping it is seen that T/2 is not the optimum. It is shown that OQPSK with shaped pulses may be much more robust with respect to carrier phase errors than OQPSK with non-return-to-zero pulses     

Approximate symbol error probability evaluation of M-ary pulse amplitude modulation with imperfect carrier recovery

In this letter, we propose an approximate symbol error probability (SEP) of M-ary pulse amplitude modulation (PAM) under a noisy carrier phase in a closed form when the carrier phase is governed by Tikhonov probability density function. The approximate results are desirable to evaluate the behavior of the system. The accuracy of the approximation is verified with respect to the numerical integration.     

Influence of imperfect carrier recovery on satellite QPSK communication system performance

The purpose of this paper is to provide the theoretical approach for determining the bit error probability in detecting a coherent quaternary phase-shift-keyed signal transmitted over a soft-limited channel in the presence of the uplink and downlink noise, as well as the noisy carrier reference signal. The uplink noise is considered in the specific way through the envelope variations and the frequency offset of the signal remitted by the satellite station having influence on the variations of the phase-locked loop parameters in the receiving ground station, consequently on the probability density function of the phase error, i.e. the average bit error probability. The downlink noise is also taken into consideration. The determined results are based on the non-linear phase-locked loop model with primary emphasis on the degradations in the system performance produced by the imperfect carrier signal extraction. Copyright © 1999 John Wiley & Sons, Ltd.     

Trellis-Coded MPSK with Reference Phase Errors

With trellis-coded MPSK schemes, reference phase errors have a major impact on the system performance. This paper analyzes the interrelation among the coded-modulation format, the reference phase tracker, and the carrier phase noise. A tight upper bound to the error probability of a maximum likelihood decoder is introduced. This bound reveals eight new distance-type functions which, along with the wellknown minimum Euclidean distance, characterize the coded-modulation scheme. Relationships between the new distance-type functions and the various system parameters as well as the irreducible probability of error are pointed out. Numerical results for uncoded QPSK and three Ungerboeck encoded 8-PSK schemes showy that excessive smoothing of the reference phase in presence of carder phase noise can degrade the performance of coded 8-PSK modulation considerably.     

Carrier Reference Error Sensitivity of a Viterbi Detector for PAM Data Transmission

In this paper we extend the probability of error analysis for Viterbi detectors for PAM data transmission to include the effects of steady-state carrier reference errors. It has earlier been found that the Viterbi detector is sensitive to the effects of constant carrier phase errors. However, for two reasonably complicated voiceband pulses taken from the literature, we find that the Viterbi detector is no more sensitive to random carrier phase errors than is a standard quantizing detector.