Distortion and crosstalk of linearly filtered, angle-modulated signals

An important problem in the theory and practice of receiving angle-modulated signals is the design of the filtering elements which must be employed. It has long been known that filtering introduces distortion and crosstalk into the signal. However, the computation of these effects is difficult. The methods customarily used employ approximations of one kind or another, and the equations used do not apply to all cases of practical interest. Here formulas are presented which enlarge somewhat the domain of cases amenable to calculation. In this analysis, an angle-modulated signal having an arbitrary phase function is applied to a general linear filter, and the phase of the output is expanded in a series having the linearly filtered input as the leading term. The expansion is then specialized to the case of a narrowband signal applied to a narrow, symmetrical, bandpass filter. A spectral analysis is performed by assuming a Gaussian input phase and examining terms through fifth order in the output phase expansion. This leads to the main results of the paper, namely expressions for the leading terms in the output spectrum. It is argued that these terms represent the principal contribution in the case where the distortion is small. To demonstrate their application to a practical problem, the formulas are used to calculate the distortion and crosstalk produced when an FM signal, having a flat baseband spectrum, is passed through a single-pole filter. This example is of some current interest because such a filter has been employed in the forward path of a feedback FM receiver used for satellite communication. A number of cases are considered, and the results of the computations are plotted.     

Blind detection of CPM signals transmitted over frequency-flatfading channels

We propose a novel detection scheme for continuous-phase modulation (CPM) signals transmitted over frequency-flat fading channels. Its most significant feature is that it operates without statistical information on the fading channel, and for this reason it is nicknamed “blind detector.” Its error-rate performance is assessed with minimum shift keying (MSK) and Gaussian MSK (GMSK) schemes and compared with the performance of other decoders     

Soft-decision phase detection with Viterbi decoding for CPM signals

It is known that continuous phase modulation (CPM) signals can be optimally detected by using coherent demodulation followed by Viterbi decoding. However, such a receiver is generally complicated, particularly at higher numbers of states, as it requires many correlators and many reference signals in the demodulator. In this study, a much simpler receiver, which employs a soft-decision phase detector followed by a Viterbi decoder, is proposed for the detection of CPM signals. The phase detector makes a decision in favor of one of the preselected phase subregions at the end of every interval, which is then used to calculate metrics for decoding. As in optimal detection, the Viterbi decoder decodes according to the trellis structure of CPM signals. The proposed receiver is analyzed in a narrow-band Gaussian channel with 2REC, 2-h, and trellis-coded continuous-phase frequency-shift keying signals. Numerical results show that the proposed receiver performs close to optimal detection with all types of signals considered in this study. The effect of the number of subregions in the phase detector is examined     

On Walsh filtering method for decoding of CPM signals

Walsh filtering has been used as a method to reduce receiver complexity in several coding and modulation systems, especially in continuous phase modulation systems. In this paper, we show that its lowpass filtering ability is poor and alias components arising from an adjacent channel can significantly degrade the maximum-likelihood decoding. Instead, a lowpass filtering method is more robust against adjacent channel interference and thus gives less decoding errors than the Walsh filtering method.     

Advanced intermediate frequency zero-crossing detection of bandpass filtered MSK signals

Short range communication systems such as Bluetooth deploy Gaussian frequency shift keying modulation which has been derived from minimum shift keying (MSK). The authors present and analyze an improved zero-crossing detector for MSK signals called a zero-crossing decorrelation detector. The impact of bandlimitation is taken into account.     

Soft-output detection of CPM signals in frequency flat, Rayleighfading channels

Symbol-by-symbol detection algorithms are useful in systems in which soft-decision metrics are important, e.g., systems with interleaved coded modulation. A soft-output algorithm for the detection of continuous phase modulated (CPM) signals transmitted over frequency flat, Rayleigh fading channels is developed. Since the optimum detector is computationally too complex for any practical implementation, some suboptimal detectors which give near optimal performance are proposed. Some theoretical approximations for the performance of the interleaved coded system are given. The performance of the soft-output algorithms is also extensively characterized by means of Monte-Carlo simulations     

Double-filter differential detection of PSK signals transmittedover linearly time-selective Rayleigh fading channels

Linearly time-varying fading models are used to investigate differential detection of PSK signals transmitted over frequency-flat fading channels. The structure of the optimal differential PSK detector is derived and an analytical technique is developed to compute its error performance. Results obtained by computer simulation are in excellent agreement with the analytical predictions     

Locally optimum rank detection of correlated random signals inadditive noise

Nonparametric detection of a zero-mean random signal in additive noise is considered. The locally optimum detector based on signs and ranks of observations is derived, for good weak-signal detection performance under any specified noise probability density function. This detector is shown to have interesting similarities to the locally optimum detector for random signals. It may also be viewed as a generalization of the locally optimum rank detector for known signals. Examples of the test statistic of the detector are given for some specific noise probability density functions. Asymptotic and finite sample-size performance of the locally optimum rank detector is also considered     

Approximating filtered scale-variant signals.

We develop theorems that place limits on the point-wise approximation of the responses of filters, both linear shift invariant (LSI) and linear shift variant (LSV), to input signals and images that are LSV in the following sense: they can be expressed as the outputs of systems with LSV impulse responses, where the shift variance is with respect to the filter scale of a single-prototype fillter. The approximations take the form of LSI approximations to the responses. We develop tight bounds on the approximation errors expressed in terms of filter durations and derivative (Sobolev) norms. Finally, we find application of the developed theory to defoveation of images, deblurring of shift-variant blurs, and shift-variant edge detection.     

On optimum aperture usage for randomly propagated signals

We consider a random communication channel that models, among other things, optical communication through turbulent atmosphere. We estimate signal amplitude with large apertures and show that as large an aperture as possible is best and that there exists a practically best finite transmitted amplitude.     

Approximately optimum detection of deterministic signals inGaussian and compound Poisson noise

An approximate but explicit likelihood ratio is derived for detecting deterministic signals in Gaussian and compound Poisson noise. The approximation in the derivation is based on the assumption that the localized noise elements rarely overlap each other. The derived log-likelihood ratio consists of two distinct parts. One is the conventional correlation detector for detecting deterministic signals in Gaussian noise. The other is a nonlinear processor which compensates for the degradation of the correlation detector caused by the localized noise, and is activated only by the presence of the localized noise. As such, it involves covariance operators of both the Gaussian and the localized noise, and is obtained by using the simultaneous diagonalization and orthogonalization of quadratic forms in function space involving eigenfunctions of certain composite operators     

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     

一种新颖的CPM信号接收技术

以8CPFSK为例对连续相位调制（CPM）信号的同步技术和解调技术进行研究，并提出一种新颖的解调和同步联合的接收方案。该方案利用了“多符号差分检测”和CPM信号特有的相位特性，反馈地修正同步误差。仿真结果表明使用该方案不但能简便准确地同步信号接收。而且能大幅度提高连续相位调制信号的误码性能。     

On the error probability of linearly modulated signals on Rayleighfrequency-flat fading channels

Consideration is given to optimal detection of linearly modulated signals subject to multiplicative Rayleigh-distributed distortion and additive white Gaussian noise. For coherent detection, regenerated amplitude and phase references are employed at the receiver to compensate for amplitude and phase deviations from the correct values. A system model is formulated under the assumption of perfect symbol timing and in the absence of intersymbol interference, producing a final additive noise term, applied just before the detection, which contains the effects of the original additive and multiplicative distortions and of the errors in the phase and amplitude references. By determining the probability density function of this final noise term for arbitrary types of linear modulation, it is possible to perform exact calculations of error probabilities     

A series technique for the optimum detection of stochastic signals in noise

A procedure for the optimum detection of stochastic signals in noise is discussed. The optimum test function is expanded in a point-wise convergent series for which a bound on the convergence properties can be obtained. Knowledge of this bound permits the substitution of a truncated version of the series for the optimum test function. This leads to a test procedure that uses a variable number of terms of the series for each decision and also gives the same decision as the optimum detector. For detection of stochastic signals in Gaussian noise, an expansion is obtained in terms of the eigenfunctions associated with the Gaussian probability density function, which leads to optimum decisions with a moderate number of terms of the series. It is also well suited for adaptive detection in which the distribution function of the stochastic signal is unknown--the coefficients of the expansion factor into two terms, one dependent only on the noise distribution and the other dependent on the distribution of the stochastic signal. Computer results for Gaussian noise are given. For this case, the test procedure can be viewed as a sequence of linear, quadratic, etc., detectors that, when a basic inequality is met, terminates with an optimum decision.     

Decomposition of M-ary CPM signals into PAM waveforms

It is widely known that minimum shift keying (MSK) may be seen as a PAM signaling scheme and that the same is true, albeit approximately, with MSK-like modulations. It is also known (perhaps not so widely) that any binary continuous phase-modulated (CPM) signal may be exactly decomposed into the sum of a few PAM waveforms. In this paper we show that this property extends to multilevel CPM signaling. Features of a PAM decomposition are discussed as a function of the alphabet size, the modulation index, and the frequency response of the system. It is found that, especially with signaling schemes with a long memory, the decomposition has so many terms that it becomes unmanageable. For these cases an approximation is proposed with a limited number of terms     

On the representation of CPM signals by linear superposition ofimpulses in the bandpass domain

A novel signal generation concept for continuous phase modulations (CPMs) with modulation index 1/2 based on real impulses is presented. With this concept, bandpass CPM signals can be generated directly in one step instead of the two consecutive steps, namely, the generation of the complex envelope and the modulation of the carrier by the complex envelope, which are necessary in conventional signal generators. Mathematical expressions for both the real impulses and the bandpass CPM signals are derived and a simple modulator structure is discussed. Examples for the real impulses are given. Among these are the well-known CPM schemes of minimum shift keying (MSK), sinusoidal frequency shift keying (SFSK), and Gaussian minimum shift keying (GMSK). As an example, the validity of the novel signal generation concept is shown for the latter CPM scheme     

Joint phase and timing recovery with CPM signals

We describe joint carrier phase and timing recovery algorithms for CPM signaling. They may be employed with any CPM format, and with either full or reduced state detectors. Their implementation is fully digital, and involves a limited computational complexity. Simulation results show that these algorithms have excellent tracking performance. When operated in their simplest form, however, they may exhibit false locks. In particular, this occurs with multilevel and partial response formats. A simple solution to the false lock problem is proposed