Study On Carrier Synchronization Technique For Continous Phase Modulation

High information rate and low amplifier power are effective measures to ensure the capacity and concealment of military communications.However,with the fast increase of data size and battle unit number,the accessible bandwidth and power resources are unable to fulfill the requirement with the classical linear modulation technique.Continuous phase modulation(CPM)has attracted much attention due to its high spectrum and high power efficiency.On one hand,CPM is of high spectrum efficiency due to its phase constancy,which leads to narrow-band main lobe and fast-attenuated side lobe.On the other hand,the constant envelope of CPM makes itself robust to the nonlinearity of amplifiers,and thus,allows such amplifiers to work at saturation state,which makes CPM be of high power efficiency.The characteristics of both high spectrum and high power efficiency make CPM be extensively used in satellite communications,telemetry communications and emergency communications,etc.However,the good performance,especially the bit-error-rate(BER)performance of CPM,must rely on coherent demodulation,which is on the foundation of carrier synchronization.Therefore,study on carrier synchronization technique for CPM is of significant importance.In order to provide theory and engineering foundation for further usage of CPM in the military communications,a study on the carrier synchronization for CPM is made in the manuscript.The knowledge of optimization theory,digital signal processing theory,communication theory and information theory are essential for this manuscript.The main contributions of this paper are listed below:Firstly,in order to solve the problem of high complexity of the existing algorithms when performing the data-aided(DA)frequency offset acquisition,a time-domain dichotomous search method is proposed.The proposed method provides a demonstration that for the three commonly used frequency pulse functions of CPM,the modulated all-one waveform forms a sinusoidal signal.By using the obtained sinusoidal signal,a time-domain target function is generated via the log-likelihood function(LLF).Compared to the classical frequency-domain target function,our proposed time-domain target function can eliminate the fast Fourier transform(FFT)operation,leading to low complexity implementation.Sequently,the dichotomous search method is used to find the maximum bin of the time-domain target function,and therefore,the accurate frequency offset is derived after several search iterations.Besides the elimination of FFT operation,the empirical results show that the mean square error(MSE)of the acquired frequency offset can achieve the Cramer-Rao bound(CRB)through less iterations.Moreover,our proposed time-domain dichotomous search method has low signal-to-noise ratio(SNR)threshold.Secondly,an analysis is made on the joint estimator of phase offset,frequency offset and timing offset for CPM proposed by Hosseini and Perrins(H&P algorithm).This joint estimator obtains the estimation of the parameters through closed-form expressions,which is of low complexity.However,the errors of the preceding-estimated parameters will have effect on the ones to be estimated inevitably.We make H&P algorithm for example and derive the variances of the three parameters through the closed-form expressions.By comparing the variances of these parameters with their corresponding CRBs,the concept of the conditional CRB(CCRB)is proposed.Furthermore,the CCRB of phase offset with the existence of frequency offset error is computed,together with the CCRB of timing offset with the existence of phase offset error and frequency offset error.Through the computation,the following two conclusions are obtained: 1).the acquisition of timing offset is independent of the acquisition of carrier parameters;2).the variance of phase offset will be influenced by the frequency offset error.Sequently,the second conclusion is extended to any format of phase modulation,i.e.,the second conclusion always holds true in the DA acquisition for any phase modulation format.Finally,the PLL structure is introduced to alleviate the influence in the open loop acquisition and a DA-PLL scheme is provided for CPM carrier synchronization.Thirdly,the tracking accuracy for multiple symbol trellis-coded continuous phase frequency shift keying(MSTC-CPFSK)is derived.CPFSK is a special kind of full response CPM with the frequency pulse function of rectangular(REC).By combining the convolutional encoder with CPFSK,the trellis-coded CPFSK(TC-CPFSK)system is obtained,and by combining one symbol output of the convolutional encoder with multiple CPFSK symbols,the MSTC-CPFSK is got.The preceding proposed DA-PLL structure is utilized to conduct carrier synchronization and demodulation of MSTC-CPFSK system.An all-zero sequence is used for DA acquisition,and then,the PLL structure is introduced for tracking.To measure the accuracy of the second-order PLL structure,the equivalent CRB(ECRB)is presented and computed in detail.The obtained ECRB is extended to any order PLL structures in the tracking processing.Moreover,the ECRB for MSTC-CPFSK is also derived to measure the accuracy of the system.It is demonstrated that for the given PLL structures,the tracking accuracy of the MSTC-CPFSK system depends not only on the SNR,but also on the number of multiple symbols combining with the convolutional encoder output.Finally,empirical results corroborate our theoretical analysis.Finally,the joint carrier tracking and demodulation of serially concatenated CPM(SCCPM)is researched.This algorithm deduces the a posteriori probabilities(APPs)of CPM parameters with the existence of residual carrier parameters.Sequently,the joint carrier tracking and BCJR demodulation are performed using the obtained APPs.By conducting the two steps iteratively,our proposed algorithm is got.Considering the large state number of CPM and high complexity of the algorithm,a reduced-complexity algorithm for MSK-type signals is proposed.In order to measure the tracking accuracy,the Cramer-Rao lower bound(CRLB)is derived.Empirical results show that our proposed algorithm is sensitive to the loop bandwidth of the PLL,and therefore,the tracking accuracy and the tracking range must be considered in practical design.However,under the condition of appropriate loop bandwidth,the MSE coincides with the CRLB,and the BER performance degradation can be neglected compared to that with ideal synchronization.Furthermore,the reduced-complexity algorithm for MSK-type signals can achieve low complexity with little BER degradation.