A unified approach to the probability of error for noncoherent and differentially coherent modulations over generalized fading channels

We present a unified approach to determine the exact bit error rate (BER) of noncoherent and differentially coherent modulations with single and multichannel reception over additive white Gaussian noise and generalized fading channels. The multichannel reception results assume independent fading in the channels and are applicable to systems that employ post-detection equal gain combining. Our approach relies on an alternate form of the Marcum Q-function and leads to expressions of the BER involving a single finite-range integral which can be readily evaluated numerically. Aside from unifying the past results, the new approach also allows for a more general solution to the problem in that it includes many situations that in the past defied a simple solution. The best example of this occurs for multichannel reception where the fading on each channel need not be identically distributed nor even distributed according to the same family of distributions.

[1]  K. Sohrabi,et al.  Wideband channel measurements at 900 MHz , 1995, 1995 IEEE 45th Vehicular Technology Conference. Countdown to the Wireless Twenty-First Century.

[2]  H. Janes,et al.  Some Tropospheric Scatter Propagation Measurements near the Radio Horizon , 1955, Proceedings of the IRE.

[3]  Valentine A. Aalo,et al.  Performance analysis of noncoherent binary DS/CDMA systems in a Nakagami multipath channel with arbitrary parameters , 1996, Proceedings of GLOBECOM'96. 1996 IEEE Global Telecommunications Conference.

[4]  M. Tanda.  Bit error rate of DQPSK signals in slow Nakagami fading , 1993 .

[5]  Giovanni E. Corazza,et al.  A statistical model for land mobile satellite channels and its application to nongeostationary orbit systems , 1994 .

[6]  Keum-Chan Whang,et al.  A channel model for nongeostationary orbiting satellite system , 1997, 1997 IEEE 47th Vehicular Technology Conference. Technology in Motion.

[7]  B. M. Reddy,et al.  C and L band transionospheric scintillation experiment: Some results for applications to satellite radio systems , 1992 .

[8]  Gordon L. Stuber,et al.  Principles of Mobile Communication , 1996 .

[9]  R. C. North,et al.  Performance of coherent MPSK on frequency selective slowly fading channels , 1996, Proceedings of Vehicular Technology Conference - VTC.

[10]  William C. Lindsey.  Error probabilities for Rician fading multichannel reception of binary and n -ary signals , 1964, IEEE Trans. Inf. Theory.

[11]  George L. Turin,et al.  A statistical model of urban multipath propagation , 1972 .

[12]  R. M. Barts,et al.  Modeling and simulation of mobile satellite propagation , 1992 .

[13]  G.L. Stuber,et al.  Co-channel interference of microcellular systems on shadowed Nakagami fading channels , 1993, IEEE 43rd Vehicular Technology Conference.

[14]  H. Hashemi.  Simulation of the urban radio propagation channel , 1979, IEEE Transactions on Vehicular Technology.

[15]  Carl W. Helstrom,et al.  Elements of signal detection and estimation , 1994 .

[16]  T. Tjhung,et al.  BER performance of DQPSK in slow Rician fading , 1992 .

[17]  Clare D. McGillem,et al.  A statistical model for the factory radio channel , 1991, IEEE Trans. Commun..

[18]  Homayoun Hashemi,et al.  Impulse Response Modeling of Indoor Radio Propagation Channels , 1993, IEEE J. Sel. Areas Commun..

[19]  A. Goldsmith,et al.  A unified performance analysis of DS-CDMA systems over generalized frequency-selective fading channels , 1998, Proceedings. 1998 IEEE International Symposium on Information Theory (Cat. No.98CH36252).

[20]  Shu-Hung Leung,et al.  Analysis of DPSK with equal gain combining in Nakagami fading channels , 1997 .

[21]  Ramjee Prasad,et al.  Performance evaluation of direct-sequence spread spectrum multiple-access for indoor wireless communication in a Rician fading channel , 1995, IEEE Trans. Commun..

[22]  M. Nakagami.  The m-Distribution—A General Formula of Intensity Distribution of Rapid Fading , 1960 .

[23]  Ray S. Hoyt.  Probability functions for the modulus and angle of the normal complex variate , 1947 .

[24]  Seymour Stein,et al.  Unified analysis of certain coherent and noncoherent binary communications systems , 1964, IEEE Trans. Inf. Theory.

[25]  B. Chytil,et al.  The distribution of amplitude scintillation and the conversion of scintillation indices , 1967 .

[26]  S. O. Rice,et al.  Statistical properties of a sine wave plus random noise , 1948, Bell Syst. Tech. J..

[27]  G. H. Munro.  Scintillation of radio signals from satellites , 1963 .

[28]  F.I. Meno,et al.  Mobile fading—Rayleigh and lognormal superimposed , 1977, IEEE Transactions on Vehicular Technology.

[29]  Andrzej H. Wojnar,et al.  Unknown Bounds on Performance in Nakagami Channels , 1986, IEEE Trans. Commun..

[30]  Bruce Barton Barrow.  Error probabilities for data transmission over fading radio paths , 1962 .

[31]  G. R. Sugar.  Some Fading Characteristics of Regular VHF Ionospheric Propagation , 1955, Proceedings of the IRE.

[32]  Emanoel Costa,et al.  250 MHz/GHz Scintillation Parameters in the Equatorial, Polar, and Auroral Environments , 1986, IEEE J. Sel. Areas Commun..

[33]  Asrar U. H. Sheikh,et al.  Indoor mobile radio channel at 946 MHz: Measurements and modeling , 1993, IEEE 43rd Vehicular Technology Conference.

[34]  J.E. Mazo,et al.  Digital communications , 1985, Proceedings of the IEEE.

[35]  Paul J. Crepeau,et al.  Uncoded and coded performance of MFSK and DPSK in Nakagami fading channels , 1992, IEEE Trans. Commun..

[36]  D. Owen.  Handbook of Mathematical Functions with Formulas , 1965 .

[37]  Theodore S. Rappaport,et al.  UHF fading in factories , 1989, IEEE J. Sel. Areas Commun..

[38]  Samy A. Mahmoud,et al.  A comparison of indoor radio propagation characteristics at 910 MHz and 1.75 GHz , 1989, IEEE J. Sel. Areas Commun..

[39]  R. Pawula.  Relations between Rice Ie-function and Marcum Q-function with applications to error rate calculations , 1995 .

[40]  Laurence B. Milstein,et al.  Comparison of hybrid FDMA/CDMA systems in frequency selective Rayleigh fading , 1994, IEEE J. Sel. Areas Commun..

[41]  Michael Rice,et al.  Statistical models for the ACTS K-band land mobile satellite channel , 1997, 1997 IEEE 47th Vehicular Technology Conference. Technology in Motion.

[42]  Daniel Cygan,et al.  The land mobile satellite communication channel-recording, statistics, and channel model , 1991 .

[43]  Vijay K. Bhargava,et al.  Unified error analysis of DQPSK in fading channels , 1994 .

[44]  W. R. Braun,et al.  A physical mobile radio channel model , 1991 .

[45]  H. Suzuki,et al.  A Statistical Model for Urban Radio Propogation , 1977, IEEE Trans. Commun..

[46]  Jules Aarons,et al.  Estimation of the Cumulative Amplitude Probability Distribution Function of Ionospheric Scintillations , 1972 .

[47]  T. Aulin,et al.  Characteristics of a digital mobile radio channel , 1981, IEEE Transactions on Vehicular Technology.

[48]  Theodore S. Rappaport,et al.  Statistical channel impulse response models for factory and open plan building radio communicate system design , 1991, IEEE Trans. Commun..

[49]  E. Fremouw,et al.  Worldwide Behavior of Average VHF-UHF Scintillation , 1971 .

[50]  Milton Abramowitz,et al.  Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables , 1964 .

[51]  Chun Loo,et al.  A statistical model for a land mobile satellite link , 1985, IEEE Transactions on Vehicular Technology.

[52]  Mohamed-Slim Alouini,et al.  A unified approach to the performance analysis of digital communication over generalized fading channels , 1998, Proc. IEEE.

[53]  K. Bischoff,et al.  A note on scintillation indices , 1969 .

[54]  Marvin K. Simon,et al.  A new twist on the Marcum Q-function and its application , 1998, IEEE Communications Letters.

[55]  J. Chouinard,et al.  Error probability expressions for non-coherent diversity in Nakagami fading channels , 1997, 1997 IEEE 47th Vehicular Technology Conference. Technology in Motion.

[56]  U. Charash.  Reception Through Nakagami Fading Multipath Channels with Random Delays , 1979, IEEE Trans. Commun..

[57]  G. W. Swenson,et al.  The scintillation of radio signals from satellites , 1959 .

[58]  J. Proakis.  On the Probability of Error for Multichannel Reception of Binary Signals , 1968 .

[59]  P. Shaft.  On the Relationship Between Scintillation Index and Rician Fading , 1974, IEEE Trans. Commun..

[60]  George M. Dillard,et al.  Recursive Computation of the Generalized Q Function , 1973, IEEE Transactions on Aerospace and Electronic Systems.

[61]  E. Fremouw,et al.  On the statistics of scintillating signals , 1980 .