Suboptimum coherent detection of orthogonal phase-modulated signals

A suboptimum scheme for coherent demodulation of orthogonal phase-modulated signals in the additive white Gaussian noise channel is proposed and analyzed in terms of bit error probability. It is analytically shown that the suboptimum scheme provides the bit error performance competitive to the conventional optimum scheme, while requiring much less implementation complexity.     

Noncoherent multistage multiuser detection of M-ary orthogonal signals

In recent years, a great deal of research has been performed on methods of alleviating the performance degradations suffered by code division multiple access (CDMA) systems due to multiple access interference. In this paper, we consider a multistage detector for noncoherent CDMA using M-ary orthogonal signals. Using a decorrelating detector as its first stage, the detector iteratively estimates the multiple access interference affecting the desired signal, subtracts the estimated interference, and forms symbol estimates for each of K users. Through numerical examples, the bit error performance of the proposed detector is demonstrated to be superior to that of previous detectors for the same signalling scheme. This revised version was published online in June 2006 with corrections to the Cover Date.     

Robust detection of signals in dependent noise

The robust detection of signals in additive dependent noise is considered. The solution to the finite-sample problem is obtained when the Bayes risk is used as the performance measure. For the multivariate densities involved we assume that they belong to an e-contamination model. The robust detection structure is shown to be optimum for the least-favorable density and is a censored version of the nominal likelihood ratio.     

Adaptive detection of statistical signals in noise

This paper deals with the forms and properties of a detector operating in an environment in which little statistical information about either the signal or noise field is or can be available. An adaptive detector based on the theory of nonparametric statistics has been designed for this purpose. The detector uses amplitude samples taken from two distinct receivers, only one of which may contain signals from a target. The detector maintains a constant false alarm rate despite any nonstationarity of the noise. The theory of nonparametric statistics suggests that the data from the two sources be ranked in order of amplitude, that a linear weighting (a correlator) be applied to the ranking, and the result be applied to a threshold. In this study, we have considered an adaptive detector of this form. The adaptation mechanism selects the weight (correlating) function on the basis of the past observed data. This class of adaptive detectors is shown to have excellent performance in terms of signal detectability for signals of adequate strength. However, for a given detector design, signals weaker than a certain critical threshold cannot be detected regardless of the amount of data available. Thus, in contrast to the kind of signal suppression effect which characterizes conventional passive detection schemes, the adaptive detector has a sharp minimum detectable signal threshold.     

An analytical formulation of phase noise of signals with Gaussian-distributed jitter

The output of many oscillatory systems can be approximated by a stochastic square-wave signal with noise-free amplitude and Gaussian-distributed jitter. We present an analytical treatment of the phase noise of this signal with white and Lorentzian jitter spectra. With a white jitter spectrum, the phase noise is nearly Lorentzian around each harmonic. With a Lorentzian jitter spectrum, it is a sum of several Lorentzian spectra, a summation that has a 1/f/sup 4/ shape at far-out frequencies. With a combination of the two, it has 1/f/sup 4/ and 1/f/sup 2/ shapes at close-in and far-out frequencies, respectively. In all cases, the phase noise at the center frequency and the total signal power are both finite. These findings will improve our understanding of phase noise and will facilitate the calculation of phase noise using time- domain jitter analysis.     

Envelope detection of a unit-index amplitude-modulated cartier accompanied by noise

The facts concerning the relative merits of linear and square-law envelope detection of a sinusoidally modulated carrier accompanied by Gaussian noise are clarified in this paper. The comparison when the carrier is weakly modulated and has mean power substantially greater than that of the noise in the input circuit has been fully covered in prior technical literature. In this special case the signal-to-noise ratio (SNR) in the detected output is the same for the two methods, and the distortion of the signal is worse with square-law operation because of inherent second-harmonic production. Since noise in the detected output is typically measured in the absence of signal modulation, the fact that the relative performance changes when the index of modulation approaches 100 percent tends to be overlooked. It is shown in the present paper that the noise performance of the square-law detector suffers a penalty approaching 1.8 dB when the carrier is strongly modulated. Also, the distortion in the square-law case is characterized by a second harmonic only 12 dB down from the fundamental, while the second harmonic in the output of the linear detector is practically negligible. These results are important in the evaluation of techniques in diversity reception.     

Robust detection of known signals in asymmetric noise

The detection of signals in noise with possibly asymmetric probability density functions is considered. The noise density model allows a symmetric contaminated-nominal central part and an arbitrary tail behavior. For detection of known signals, the robust nonlinear-correlator (NC) detector is obtained based on detector efficacy as performance criterion. The robustM-detector structure for constant-signal detection is also explicitly obtained.     

Time domain phase noise correction for OFDM signals

We introduce an algorithm for compensating for carrier phase noise in an OFDM communication system. Through the creation of a linearized parametric model for phase noise, we generate a least squares (LS) estimate of the transmitted symbol. Using digitized DVB-T RF signals created in a laboratory and a DVB-T compliant receiver model, simulation results are presented to evaluate the effectiveness of the algorithm in practical environments.     

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     

Excess phase noise in self-heterodyne detection

The interpretation of self-heterodyne spectra is difficult if, apart from spontaneous emission, additional noise sources are presented. Measurements on an external-cavity semiconductor laser show how, for a relatively long delay, the high-frequency (Lorentzian) wings of the self-heterodyne spectrum are a sensitive measure for the quantum-limited (Schawlow-Townes) laser linewidth. The quantum-limited laser linewidth is shown to be inversely proportional to the output power. Values below 5 kHz are routinely measured. The full width at half maximum (FWHM) laser linewidth is larger than this due to excess low-frequency fluctuations, which are shown to result from the presence of side modes     

Sampling designs for the detection of signals in noise

Sampling designs for the detection of sure signals in Gaussian noise are considered. Both deterministic and random sampling schemes, using optimal and nonoptimal detectors, are presented and their performance is studied. The analytical results are supplemented by comparison of performance for small and large Sample size for some representative processes including the Gauss-Markov and Wiener processes.     

The output signals and noise from a nonlinearity with amplitude-dependent phase shift

On the assumption that each input signal represents only a small part of the total input power, the output signals and output noise spectrum are found by extending the Barrett-Lampard diagonal expansion to the case of the quadrivariate distribution of input amplitude and phase at two different times. This expansion yields a decomposition of the nonlinearity into a summation of generalized Laguerre polynomials with uncorrelated outputs, whose spectra are simply autoconvolutions of the input spectrum. A slight generalization of the notion of memoryless nonlinearity allows this result to he applied very simply to devices, such as limiters and TWT amplifiers, that cause AM-to-PM conversion.     

Noncoherent detection of coherent lightwave signals corrupted byphase noise

Waves are treated that modulate by either on-off keying (OOK) or binary frequency-shift keying (FSK) and are further impaired by additive Gaussian noise. Heterodyne detection of such a waveform produces an electronic bandpass signal, which, to ease demodulation in the presence of phase noise, is noncoherently demodulated to extract the baseband pulse stream. The treatment goes beyond previous bit error rate (BER) analyses of optical heterodyne receivers for OOK and FSK. First, there is full adherence to the standard (Brownian motion) model of phase noise. Also, the receiver structure is formulated in such a way that the probability density function of the receiver output samples can be accurately determined. This permits calculations of the additive noise and phase noise tolerable when achieving bit error rates as small as 10 ^-9. Finally, the study is comprehensive regarding the range of parameters explored. Filtering at an intermediate frequency (IF) alone, as well as IF filtering plus postdetection low-pass filtering, is considered. When the receiver parameters decision threshold (for OOK) and IF filter bandwidth are optimized, large amounts of phase noise can be accommodated with only minor increases in required signal-to-noise ratio. This is especially important when the bit rate is moderate compared to the laser linewidth     

Envelope detection of an amplitude-modulated carder accompanied by noise (Corresp.)

Some new results are presented on the harmonics and noise in the output of a linear envelope detector whose input is an amplitude-modulated carrier accompanied by noise. The transition region between the cases of weak and strong modulation is also studied. The signal-to-noise ratio is assumed throughout to be large and the index of modulation to be near unity.     

Generalized quadratic receivers for orthogonal signals over theGaussian channel with unknown phase/fading

The orthogonal signal structure has been shown to be the superposition of an antipodal signal set and an unmodulated (pilot tone) component which can be used for channel measurement. Starting from this point of view, the quadratic receiver for orthogonal signals over the Gaussian channel with unknown phase/fading has been shown to be equivalent to a detector-estimator receiver. The estimator makes an optimum estimate of the unknown complex channel gain based on the channel measurement provided by the unmodulated component of the received signal. This channel estimate then forms a (partially) coherent reference for the detector in detecting the data carried by the antipodal signaling component of the received signal. This paper exploits this detector-estimator structure of the quadratic receiver, and generalizes it to a receiver in which the estimator makes an estimate of the channel gain in each signaling interval based on the totality of signals received over all the signaling intervals or a subset of these intervals. The generalized quadratic receiver is just as simple to implement as the conventional quadratic receiver, and theoretical and simulation results show that it can achieve substantial performance gains over the conventional receiver. A theory is presented to show that the generalized quadratic receiver is an implementable approximation to the optimum symbol-by-symbol receiver for uncoded orthogonal signals over the Gaussian channel with unknown phase/fading. The theory shows that the structure provides a unified and systematic approach to the design of coherent symbol-by-symbol receivers, and shows that the conventional carrier-loop-type receivers are ad hoc     

Coding of optical on-off keying signals impaired by phase noise

The benefits of coding for an optical communication system that employs binary on-off keying and heterodyne detection are quantified. The system is impaired by laser phase noise as well as by additive white Gaussian noise (AWGN). A receiver structure especially designed to mitigate the effects of phase noise in the presence of AWGN is assumed. This special receiver structure requires a wider-band front-end IF filter than would be required for a phase-noise-free signal. The results, computed for several different coding schemes, indicate that the benefits of coding are large and the costs are small. For a linewidth-to-bit-rate ratio (βT) of 0.64 (for example, 45 Mb/s and 29 MHz linewidth), a half-rate binary code that can correct 3 bit errors provides a 50% reduction in the required IF filter bandwidth (and, therefore, the required IF) and about 5 dB of reduction in required laser power. The benefits of coding are greatest under high-βT conditions, corresponding to low bit rates where coders and decoders are most practical to implement     

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     

联合多脉冲检测的PSWF正交调制信号盲自适应均衡

卫星通信信道的复杂时变特性,使基于椭圆球面波函数(Prolate Spheroidal Wave Function,PSWF)的正交调制信号脉冲组的正交性受到破坏,已有均衡方法未能充分利用多脉冲干扰中的有用信息,效果有限。针对该问题,结合信道均衡与多脉冲检测各自的优势,提出一种联合多脉冲检测的PSWF时域正交调制信号自适应均衡方法,利用多脉冲检测消除脉冲间干扰的能力,降低均衡模块的阶数及算法难度;同时,利用均衡模块对信道的部分补偿作用,为多脉冲检测改善信道环境。在相同信道条件下,所提方法获得同等量级误比特率所需信噪比较自适应判决反馈均衡算法降低约2 dB。     

Coherent detection of optical quadrature phase-shift keying signals with carrier phase estimation

This paper describes a coherent optical receiver for demodulating optical quadrature phase-shift keying (QPSK) signals. At the receiver, a phase-diversity homodyne detection scheme is employed without locking the phase of the local oscillator (LO). To handle the carrier phase drift, the carrier phase is estimated with digital signal processing (DSP) on the homodyne-detected signal. Such a scheme presents the following major advantages over the conventional optical differential detection. First, its bit error rate (BER) performance is better than that of differential detection. This higher sensitivity can extend the reach of unrepeated transmission systems and reduce crosstalk between multiwavelength channels. Second, the optoelectronic conversion process is linear, so that the whole optical signal information can be postprocessed in the electrical domain. Third, this scheme is applicable to multilevel modulation formats such as M-array PSK and quadrature amplitude modulation (QAM). The performance of the receiver is evaluated through various simulations and experiments. As a result, an unrepeated transmission over 210 km with a 20-Gb/s optical QPSK signal is achieved. Moreover, in wavelength-division multiplexing (WDM) environment, coherent detection allows the filtering of a desired wavelength channel to reside entirely in the electrical domain, taking advantage of the sharp cutoff characteristics of electrical filters. The experiments show the feasibility to transmit polarization-multiplexed 40-Gb/s QPSK signals over 200 km with channel spacing of 16 GHz, leading to a spectral efficiency as high as 2.5 b/s/Hz.