An upper bound on the error probability of quadratic-detection in 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. >

[1]  Larry J. Greenstein,et al.  Envelope statistics for filtered optical signals corrupted by phase noise , 1989, IEEE Trans. Commun..

[2]  Katsumi Emura,et al.  An optical FSK heterodyne dual filter detection system for taking advantage of DFB LD applications , 1990 .

[3]  R.A. Linke,et al.  Optical heterodyne communications systems , 1989, IEEE Communications Magazine.

[4]  J. Pierce.  Theoretical Diversity Improvement in Frequency-Shift Keying , 1958, Proceedings of the IRE.

[5]  Giovanni Vannucci,et al.  Characterizing filtered light waves corrupted by phase noise , 1988, IEEE Trans. Inf. Theory.

[6]  Larry J. Greenstein,et al.  Optical power requirements for detecting OOK and FSK signals corrupted by phase noise , 1989, IEEE Trans. Commun..

[7]  Israel Bar-David,et al.  On dual optical detection: homodyne and transmitted-reference heterodyne reception , 1988, IEEE Trans. Commun..

[8]  Shlomo Shamai,et al.  Asymptotically robust communication using an orthogonal codebook over energy-limited channels , 1991, 17th Convention of Electrical and Electronics Engineers in Israel.

[9]  J. C. Mairhuber.  ON HAAR'S THEOREM CONCERNING CHEBYCHEV APPROXIMATION PROBLEMS HAVING UNIQUE SOLUTIONS' , 1956 .

[10]  G. Jacobsen,et al.  Theoretical analysis of heterodyne optical receivers for transmission systems using (semiconductor) lasers with nonnegligible linewidth , 1986 .

[11]  Robert N. McDonough,et al.  Detection of signals in noise , 1971 .

[12]  D. Zaccarin,et al.  Performance analysis of optical heterodyne PSK receivers in the presence of phase noise and adjacent channel interference , 1990 .

[13]  J. Salz,et al.  Modulation and detection for coherent lightwave communications , 1986, IEEE Communications Magazine.

[14]  C. Henry.  Phase noise in semiconductor lasers , 1986 .

[15]  G. Jacobsen,et al.  Phase noise in weakly coherent systems , 1989 .

[16]  Hideo Kuwahara,et al.  Channel allocation and crosstalk penalty in coherent optical frequency division multiplexing systems , 1988 .

[17]  Kung Yao,et al.  Moment space upper and lower error bounds for digital systems with intersymbol interference , 1976, IEEE Trans. Inf. Theory.

[18]  S. Shamai,et al.  On the Error Probability of Noisy Phase Channels Using Mfsk , 1989, The Sixteenth Conference of Electrical and Electronics Engineers in Israel,.

[19]  Kung Yao,et al.  Multidimensional moment error bounds for digital communication systems , 1980, IEEE Trans. Inf. Theory.

[20]  E. Wong,et al.  Stochastic Processes in Engineering Systems , 1984 .

[21]  Leonid G. Kazovsky,et al.  Impact of Laser Phase Noise on Optical Heterodyne Communication Systems , 1986 .

[22]  Niloy K. Dutta,et al.  Crosstalk penalty in a two-channel ASK heterodyne detection system with non-negligible laser line width , 1987 .

[23]  Andrew J. Viterbi,et al.  Advances in coding and modulation for noncoherent channels affected by fading, partial band, and multiple-access interference , 1975 .

[24]  Ja-Ling Wu,et al.  Performance analysis of polarization-insensitive phase diversity optical FSK receivers , 1990 .

[25]  Michel Loève,et al.  Probability Theory I , 1977 .

[26]  M. Kreĭn,et al.  The Markov Moment Problem and Extremal Problems , 1977 .

[27]  Larry J. Greenstein,et al.  Noncoherent detection of coherent lightwave signals corrupted by phase noise , 1988, IEEE Trans. Commun..

[28]  L. Kazovsky,et al.  ASK and FSK coherent lightwave systems: a simplified approximate analysis , 1990 .

[29]  G. Turin.  The characteristic function of Hermitian quadratic forms in complex normal variables , 1960 .

[30]  Gunnar Jacobsen,et al.  Impact of phase noise in weakly coherent systems: a new and accurate approach , 1990 .

[31]  R. Pedersen,et al.  Weakly coherent optical systems using lasers with significant phase noise , 1988 .

[32]  J. E. Mazo,et al.  Probability of error for quadratic detectors , 1965 .

[33]  R. Gallager.  Information Theory and Reliable Communication , 1968 .

[34]  Vincent W. S. Chan,et al.  M-ary FSK Performance for Coherent Optical Communication Systems Using Semiconductor Lasers , 1986, IEEE Trans. Commun..

[35]  L. Kazovsky.  Multichannel coherent optical communications systems , 1987 .

[36]  L. Miller,et al.  Probability of Error Analyses of a BFSK Frequency-Hopping System with Diversity Under Partial-Band Jamming Interference - Part I: Performance of Square-Law Linear Combining Soft Decision Receiver , 1984, IEEE Transactions on Communications.