Multi-h CPM信号的减少状态多符号差分非相干检测

针对多指数连续相位调制(Multi-h CPM)载波恢复困难且实现复杂度高的难题,提出了一种适用于Multi-h CPM信号的减少状态多符号差分非相干检测算法。该算法利用多符号差分信息进行分支度量计算的同时引入参考相位信号,实现了具有残留载波频偏校正的非相干序列检测,并且结合逐幸存处理技术,利用幸存路径上的假设判决信息减少了网格状态数。通过计算和搜索接收信号所有可能调制指数序列所对应的分支度量信息实现了调制指数的估计与同步。计算机仿真结果表明,与相干最大似然序列检测相比,该算法能够以较小的性能损失获得其实现复杂度的降低,而且当存在残留载波频偏时,该算法的检测性能也较为稳健。     

Simplified Soft-Output Detection of CPM Signals Over Coherent and Phase Noise Channels

We consider continuous phase modulations (CPMs) in iteratively decoded serially concatenated schemes. Although the overall receiver complexity mainly depends on that of the CPM detector, almost all papers in the literature consider the optimal maximum a posteriori (MAP) symbol detection algorithm and only a few attempts have been made to design low-complexity suboptimal schemes. This problem is faced in this paper by first considering the case of an ideal coherent detection, then extending it to the more interesting case of a transmission over a typical satellite channel affected by phase noise. In both cases, we adopt a simplified representation of an M-ary CPM signal based on the principal pulses of its Laurent decomposition. Since it is not possible to derive the exact detection rule by means of a probabilistic reasoning, the framework of factor graphs (FGs) and the sum-product algorithm (SPA) is used. In the case of channels affected by phase noise, continuous random variables representing the phase samples are explicitly introduced in the FG. By pursuing the principal approach to manage continuous random variables in a FG, i.e., the canonical distribution approach, two algorithms are derived which do not require the presence of known (pilot) symbols, thanks to the intrinsic differential encoder embedded in the CPM modulator.     

Continuous Phase Modulation of F-QPSK-B Signals

A continuous phase modulation (CPM) implementation alternative of a recently standardized class of Feher-patented quadrature phase-shift keying (F-QPSK-B) modulation is proposed. Based on the fact that the F-QPSK-B signal has a quasi-constant envelope and continuous phase characteristics, it is shown that it can indeed be generated by the CPM scheme. For example, an F-QPSK-B signal can be fully generated using an existing FM-based transmitter with a modulation index of 0.5. Furthermore, a premodulation filter and an alternating change monitor differential encoder for the continuous-phase-modulated F-QPSK-B signal to be fully compatible with the I/Q modulated F-QPSK-B signal are proposed, allowing direct symbol-by-symbol coherent detection without the use of any special decoding schemes inherent in all CPM schemes. It is shown that the power spectral density and eye diagram of the continuous-phase-modulated F-QPSK-B signal are practically the same as those of the I/Q modulated F-QPSK-B signal. By utilizing CPM characteristics, an optimum maximum-likelihood (ML) coherent receiver for the F-QPSK-B signal is proposed. It is shown that the bit-error-rate performances of the optimum ML coherent detection, symbol-by-symbol coherent detection, and noncoherent detection of the continuous-phase-modulated F-QPSK-B signal are almost the same as those of the I/Q modulated F-QPSK-B signal     

连续相位调制的非相干减少状态差分序列检测算法

该文提出了连续相位调制的一种非相干减少状态的差分序列检测(RSDSD)算法.该算法基于减少状态序列检测(RSSD)的思想,利用简化状态格状图进行一码元差分Viterbi检测.分析了全响应连续相位调制(CPM)信号和部分响应CPM信号简化状态格状图的最小平方欧氏距离.在AWGN信道下以八进制h=1/8的2RC信号为例给出RSSD和RSDSD算法的性能.对不同的简化方案以及存在多普勒频移时相干RSSD和非相干RSDSD的性能进行了比较.仿真结果表明:所提出的算法比相干最大似然序列检测在10-3误比特率时信噪比损失约为2dB,但它对于载波恢复困难的情形更为合适和稳健.     

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     

Performance evaluation of differential and discriminator detection of continuous phase modulation

Recently, bandwidth efficient constant-amplitude digital modulation schemes have also been shown to be power efficient when coherent detection is used. Partial-response continuous phase modulation (CPM) schemes are within this class. In some applications noncoherent detection is preferred. The performance of CPM systems is analyzed for differential and discriminator detection. An additive white Gaussian channel is assumed. The detectors make symbol-by-symbol decisions. The considered schemes are M-ary with an arbitrary modulation index and pulse shaping over several symbol intervals. The performance is analyzed by means of error probability expressions. The IF filter for the detectors is optimized within a special class of filters to give good performance. The differential detector is also analyzed on a Rayleigh fading channel. The fading is assumed to be slow. The IF filter is also optimized on this channel. Simulated error probabilities for discriminator detection with a Viterbi detector are also presented both for the Gaussian and the Rayleigh fading channel. The discriminator detector making symbol-by-symbol decisions is simulated on the Rayleigh fading channel. It is shown that partial-response CPM schemes with good performance can also be obtained with noncoherent detectors.     

Reduced-complexity detection and phase synchronization of CPMsignals

Based on an extension of Laurent (1986) decomposition of continuous phase modulation (CPM) signals into a sum of linearly modulated components, we derive a class of reduced-complexity maximum-likelihood (ML) coherent detection and closed-loop phase synchronization schemes. The complexity of the resulting detection schemes, expressed in terms of the number of matched filters and states of a Viterbi algorithm, is significantly reduced with respect to that of optimal coherent receivers with negligible performance loss. This result extends a known one valid for the binary case to multilevel CPM. The proposed synchronization schemes do not require an increased number of matched filters, and are perfectly suitable to be used in conjunction with these receivers. Based on the phase-locked loop (PLL) equivalent linear model, a method for optimizing the parameters of digital second-order PLL's is presented. Numerical examples, based on theoretical analysis and computer simulation, are provided for two specific formats in the CPM class: tamed frequency modulation (TFM) and a quaternary raised-cosine (RC) modulation     

Noncoherent detection of convolutionally encoded continuous phasemodulation

The authors consider the error probability at large signal-to-noise ratios of rate-1/2 convolutionally encoded CPFSK (continuous-phase frequency-shift keying) with an optimum noncoherent detector on an additive white Gaussian noise channel. The performance is given in terms of a parameter called the minimum squared normalized equivalent Euclidean distance which plays the same role mathematically as the minimum squared normalized Euclidean distance used for coherent detectors. It is shown that by introducing convolutional coding the error performance is significantly improved. The authors propose a decoding algorithm for these convolutionally encoded CPM schemes which is based on a limited tree search algorithm and uses the maximum-likelihood decision rule for noncoherent detection. Computer simulations show that the degradation in error performance compared to the performance of the optimum coherent Viterbi detector is less than 1 dB with a relatively simple noncoherent detector on an additive white Gaussian noise channel for most of the schemes considered     

CPM—the effect of filtering and hard limiting

The attractive properties of the digital constant amplitude modulation scheme CPM (continuous phase modulation) have been demonstrated in a previous paper in this journal.¹ This concerned both the power and spectral efficiency of the large family of CPM schemes over the Gaussian channel. In this paper the considered channel can be both bandlimited or band- and amplitude-limited at the same time. Analytical results as well as simulations are presented for a number of selected CPM schemes. In today's increasing demand for bandwidth, CPM is an attractive candidate for future satellite applications because of its spectral efficiency. In addition to this comes the fact that the transmitted signal has a constant amplitude and good detection performance when optimal coherent detection is performed.     

Joint synchronization and demodulation of trellis codes

This paper examines the joint synchronization and detection of Ungerboeck coded modulation. Estimation theory is used to derive a synchronization structure that is efficient in estimating carrier phase and symbol timing. The maximum likelihood receiver generates estimates of carrier phase and timing that are free of data-dependent jitter for any continuous pulse shape. Various feedback schemes to be used with Ungerboeck codes are presented and simulated. Simulations show that efficient estimates of carrier and clock can be found when joint data and parameter estimation of an Ungerboeck coded signal is performed     

Differential detection via the Viterbi algorithm for offsetmodulation and MSK-type signals

The differentially coherent reception of two families of constant-envelope signals, the linear offset quaternary phase shift keying and the binary partial response continuous phase modulation with index 0.5, is addressed. When the conventional (PSK-type) differentially coherent detector is used, a large performance degradation, compared with that of coherent receiver, is observed. The reason for this is the presence of an inherent intersymbol interference (ISI) in the signal and also noise enhancement and correlation introduced by the receiver filter. A differential detection strategy which compensates for ISI and avoids noise enhancement is presented. A phase estimate that takes into account the presence of the inherent ISI is derived. This phase estimate is then used in the decision metric of a coherent receiver. The resulting decision rule can be implemented using the Viterbi algorithm. Simple Viterbi receivers with good performance are obtained. Simulation results are given     

Pilot symbol-assisted detection of CPM schemes operating in fastfading channels

We present a coherent detection technique for continuous phase modulation (CPM) operating in the Rayleigh flat fading channel. The technique is based on the idea of inserting periodically data dependent pilot symbols that force the CPM signal to pass through known phase states. This transmission format enables the receiver to extract from the received signal the channel fading gains at regularly spaced instants. When coupled with proper channel estimation filters, very accurate channel state information (CSI) can be estimated at the receiver for fading compensation. Moreover, the accuracy of the CSI can be further refined by adopting a multiple-pass decoding approach. The paper discusses (a) the pilot symbol encoding technique required to force a M-level CPM scheme with a modulation index of p/M, p is an integer, to return periodically to a set of known phase states, (b) the optimal channel estimation filters, (c) a trellis-based precoding technique that can reduce the bit error rate in M-level CPM systems by close to 50%, and (d) a multiple-pass channel estimator/demodulator. Analytical and simulation results are presented for minimum shift keying (MSK), Gaussian MSK, and four-level continuous phase frequency shift keying with a modulation index of 1/4. It is observed that our pilot symbol-assisted CPM schemes exhibit no irreducible error floor even at a channel fade rate of three percent the symbol rate. The implicit phase coding in CPM and the accurate CSI provided by the pilot symbols lead to a diversity effect in the bit error rate curves of these modulation schemes     

Multiple differential detection of continuous phase modulationsignals

A sequence estimation algorithm for the differential detection of the continuous phase modulation (CPM) signals, yielding significant gains in BER performance and with considerable resistivity to fading, is introduced. These advantages, along with the reduced hardware complexity, low cost, and fast synchronization which characterize the differential detector, make the proposed receiver useful for land mobile radio and mobile-satellite communications. The new receiver is based on multiple differential detection. The multiple differential detection strategy provides the decoder with more information regarding the transmitted data and applies a noise decorrelation process on the received signal, useful to the sequence estimation. The algorithm is derived in a general form, and can be applied on any CPM scheme, with any degree of complexity. The authors have evaluated the receiver for two of the most popular CPM schemes, the tamed frequency modulation (TFM) and Gaussian minimum-shift keying (GMSK) (with B₁ T=0.25), in the presence of additive white Gaussian noise (AWGN) and Rician fading. The BER performance evaluation results indicated significant gains and considerable reduction of error floors. In AWGN improvements close to 9 dB have been verified     

微波通信中连续相位调制的非相干检测算法

提出了一种适合微波通信传输使用的多进制连续相位信号的频偏校正2码元差分检测算法.该算法利用2码元差分信息提取分支度量,进行维特比检测.同时利用判决反馈对微波通信中的载波频偏进行校正.通过对接收信号的复指数分解,分支度量的计算量得到了很大的简化.仿真结果表明,该算法的性能优于1码元差分检测.当接收信号存在载波频偏时,该算法仍然具有较好的检测性能.     

Noncoherent sequence detection of CPM

Schemes in which noncoherent sequence detection based on the Viterbi algorithm are proposed for linearly modulated signals transmitted over additive white Gaussian noise channels, have recently been proposed by the authors. These schemes are attractive because their performance closely approaches that of coherent receivers with acceptable complexity, and they avoid the drawbacks of phase-locked loops. The authors extend these results to M-ary continuous phase modulation (CPM) signals     

Minimum Mean-Square Error Timing Recovery Schemes for Digital Equalizers

Two algorithms are presented for optimum timing recovery in digitally implemented equalizers. The first one is a polarity-type algorithm based on the conventional minimum mean-square error criterion. A theoretical analysis is made to characterize the algorithm phase detector and evaluate its steady-state phase jitter variance. Influence of various channel and system design parameters on the algorithm performance is illustrated using phase jitter probability densities obtained by means of computer simulations. Interaction of the algorithm with decision-directed carrier recovery is also examined. It is shown that interaction with carrier recovery may considerably degrade the timing acquisition performance, and a second algorithm is then presented which eliminates this interaction. The second algorithm is based on the minimization of a modified mean-square error criterion which provides a measure of the intersymbol interference, independently of the carrier phase. Decision-directed timing and carrier recoveries are thus decoupled and the system startup period is considerably reduced. Phase detector characteristic and steady-state jitter performance of the second algorithm are evaluated by analytical means and computer simulations, as in the first algorithm.     

连续相位调制的非相干复合网格解调算法

该文提出了一种基于复合网格处理的CPM信号非相干解调算法。该算法将CPM信号的基本网格图和相位旋转网格图合并组成复合网格图,并在复合网格图的单元网格之间引入状态耦合转移,实现了对CPM信号初始相位和频偏的有效跟踪。仿真表明,当单元网格数达到4个以上时,该文提出的非相干解调算法性能非常接近相干解调,且具有较好的频偏跟踪性能,对于载波恢复困难的盲解调情况具有实用意义。     

On Optimum and Suboptimum Coherent Detection of Continuous Phase Modulation on a Two-Ray Multipath Fading Channel

In this paper, the performance of continuous phase modulation (CPM) transmitted on a two-ray fading channel and received in white Gaussian noise is studied. The optimum coherent maximum likelihood (ML) detector and approximations thereof and their performance are studied by means of minimum Euclidean distance and simulated symbol error probability. A linear detector optimum at large signal-to-noise ratios is also studied and the performance is given by means of error probability. It is assumed that measurements on the channel provide information about the channel parameters. It is found that the loss in signal power due to the channel is small when an ML detector or an approximation thereof is used for binary schemes with modulation indexh =1/2. The loss for these schemes with a linear detector becomes significantly larger, especially when MSK is transmitted. The performance for this linear detector can, however, be improved significantly by using decision feedback, but still, the performance of the ML detector is superior.     

Suboptimum detection of trellis-coded CPM for transmission onbandwidth- and power-limited channels

The authors consider a communication scheme based on continuous phase modulated (CPM) signals used in conjunction with trellis-coded modulation (TCM) for transmission over a channel affected by Gaussian noise and fading. This scheme provides a power saving due to the coding gain of TCM and a reduced bandwidth occupancy due to the features of CPM signals. Moreover, CPM provides constant-envelope signals. To keep the complexity of the receiver manageable and to be able to use interleaving/deinterleaving techniques to spread the fade bursts, suboptimal detection schemes must be used. Two such schemes, based on coherent and noncoherent detection of CPM, are considered. Their performance is evaluated by computing the computational cutoff rate of the discrete channel generated by CPM     

Reduced phase-state detection based on virtual modulation indexes for Multi-h CPM

.Simplified detection with reduced phase-state based on virtual modulation indexes was designed for Multi-h CPM.Multiple sets of modulation indexes different from the transmitter were constructed in the receiver,and the per-survivor processing was used to solve the mismatch caused by the inconsistency of the modulation indexes between the receiver and the transmitter.When the denominator of virtual modulation index was much smaller than the original denominator of actual transmitted signal,the phase states of coherent sequence detection could be effectively simplified,thus the complexity of coherent detection for Multi-h CPM could be reduced.The trellis could be simplified further via combining with the frequency pulse truncation(FPT) used for simplifying correlation states.The simulation results show that for advanced range telemetry (ARTM) CPM signal,various simplified receiving schemes based on virtual modulation indexes can be designed.When the virtual modulation indexes are set to $\left[\frac{\text{3}}{\text{4}}\text{,}\frac{\text{2}}{\text{4}}\right]$,the number of trellis states can be reduced from 512 (in optimal detection) to 64,but the performance loss is less than 0.05 dB.Further combined with FPT algorithm,the number of trellis states can be reduced to 16,while the performance loss is only 0.75 dB.