Differential phase shift keying (DPSK) in the presence of both additive white Gaussian noise and a phase impairment, modeled by a Brownian motion is considered. A time-diversity scheme is used for mitigating the effects of phase noise. This scheme renders a repetition coding approach where the transmitter sends multiple replicas of each data bit. An upper bound on the bit error probability, relying on a bivariate moment-generating function admitted by certain real functionals of the phase sample-path, is derived. The approach taken yields a trackable analysis, which rigorously adheres the phase noise effects. The impact of an incomplete statistical characterization on the tightness of the resultant bound is addressed. The theory, which is applicable to assess the design and performance of general heterodyned lightwave systems using (delay) differential demodulation (as DPSK and CP-FSK, or continuous phase frequency-shift keying), is exemplified and explicit results for the considered time-diversity DPSK scheme are provided. The optimum design of the diversity level is discussed and it is concluded that power efficient transmission is feasible even at bit rates comparable with the signal linewidth. >

Time diversity in DPSK noisy phase channels

A rigorous method to find the upper bound of the error probability of noncoherent quadratically detected signals in the presence of both additive white Gaussian noise and Brownian carrier phase noise is presented. An analytical upper bound on the bit error probability is derived, relying on a bivariate moment-generating function of two bounded exponential functionals of the Brownian phase path. These functionals, whose exact statistics are unknown, yield the two basic impairments arising due to phase noise: in-band signal suppression and intersymbol crosstalk . The classical theory of Chebyshev systems is applied to obtain the limiting values of the involved generating function, utilizing a multidimensional moment characterization of the involved functionals. The impact of the incomplete-statistical characterization used on the resultant upper-bound tightness is addressed. Assessing the design and performance of lightwave heterodyned systems using this method is discussed. The method enables the analysis of interchannel crosstalk effects in frequency-division multiplexing systems. >

An upper bound on the error probability of quadratic-detection in noisy phase channels

The performance of noncoherent detection of orthogonal phase-noise impaired signals in the presence of additive white Gaussian noise is considered. The authors present a novel class of upper and lower bounds on the error probability of a binary hypothesis test, comprising quadratic forms of the additive noise and of the filtered noisy-phase signal plus noise. Filtering the noisy-phase signal gives rise to bounded nonlinear functionals of the Brownian motion sample-path, the exact statistics of which are unknown. The classical theory of Chebyshev systems is utilized to solve the limiting values of the required stochastic expectations, based on the availability of the corresponding generalized moments. The resulting multidimensional moment bounds constitute the tightest possible error bounds for the given set of generalized moments, and require only modest computational efforts. The theory is applicable to assess the design and performance of optical heterodyne systems and is most suitable for coded systems employing hard-decisions, for which the obtained bounds are remarkably tight. >

Performance bounds for noncoherent detection under Brownian phase noise

Low to moderate complexity coding schemes are suggested and examined for binary DPSK modulation. The model of the communication channel consists of both a Brownian motion phase noise and an additive white Gaussian noise. Decoding utilizes a mismatched soft-decision metric, which comprises the prefiltering of the phase noise impaired signals followed by differential demodulation. The resulting equivalent, binary-input, output-symmetric, discrete-time, coding channel is stationary and memoryless. It accounts as well for an underlying time-diversity, thus providing an effective simple, means of boosting the capabilities of less powerful codes to cope with the existing phase noise levels. An analytical upper bound on the coded error probability is derived, which strictly addresses the Brownian motion phase model. It features a convenient decoupling of the code structure from the coding channel. The latter is completely specified via a single, scalar, generic parameter which relies on the univariate moments admitted by certain exponential functionals of the Brownian motion sample path, the exact statistics of which is intractable. The theory is illustrated while studying the performance of low constraint length, rate 1/n, binary convolutional codes, which are optimally combined with time-diversity. The advantages obtained by less trivial forms of code concatenation are examined. The approach treated is to use a two level concatenation scheme for which the binary inner code dimension matches the alphabet size of an outer non-binary code. >

Coding for DPSK noisy phase channels

This paper describes the design and performance of an M ary frequency shift keyed (FSK) signaling and demodulation scheme for an optical communication system using semiconductor lasers and heterodyne detection. Frequency or phase noise in semiconductor lasers causes spectral spreading, producing a nonzero linewidth laser signal. This degrades communication performance when compared to a system using an ideal laser with zero linewidth. We present estimates of the bit error rate (BER) performance of M -ary frequency shift keying (FSK) with noncoherent demodulation in the presence of white Gaussian frequency noise and additive channel noise. This is typical of an optical system using semiconductor lasers and heterodyne detection. Estimates use the union-Chernoff bound with a simplified channel model to predict the effects of frequency noise. Two effects of frequency noise are identified: signal attenuation or suppression, and crosstalk. These cause an offset in the BER curve from the BER in the absence of frequency noise, and an error rate floor, respectively. The error rate floor is lower than previously predicted. When performance is not crosstalk limited, M -ary FSK is found to perform better than binary FSK with the same system bandwidth constraints, as would be predicted if ideal lasers are used. Theoretical results are compared with Monte Carlo simulations of the system.

M-ary FSK performance for coherent optical communication systems using semiconductor lasers

http://ieeexplore.ieee.org/iel4/5787/15446/00720027.pdf

On the Error Probability of Noisy Phase Channels Using Mfsk

Concatenated Coding For Heterodyne Optical FSK And OOK Signals Impaired By Phase Noise

The authors consider a stationary discrete-time memoryless communication channel with a binary input alphabet and real-valued output. An orthogonal codebook with M words is constructed, for which the nonzero components of distinct codewords do not overlap. The block length of this code is M*N, where N is the number of degrees of freedom used per codeword. A class of asymptotically robust detectors is constructed among which is the quadratic functional. The reception of general stochastic signals in additive white Gaussian noise is considered. The optimum kernel of the quadratic functional is shown to be the resolvent kernel for the covariance function of the stochastic signal. The authors specialize to the coherent lightwave channel which presents both AWGN and Brownian phase noise. It is concluded that the (suboptimal) correlation kernel features the same functional dependency on the SNR (defined at the Brownian-phase linewidth) as does the optimal detector. For large SNR and long correlation time, the optimum kernel reduces to a time-invariant singly-resonant realizable filer, and thus facilitates a simple implementation. >

Asymptotically robust communication using an orthogonal codebook over energy-limited channels

https://ieeexplore.ieee.org/iel4/557/4025/00695117.pdf

Y.E. Dallal

Papers

On the Error Probability of Noisy Phase Channels Using Mfsk

Concatenated Coding For Heterodyne Optical FSK And OOK Signals Impaired By Phase Noise

Asymptotically robust communication using an orthogonal codebook over energy-limited channels

Asymptotically Robust Communication Using An Orthogonal Codebook Over Energy-limited Channels