The effect upon channel capacity in wireless communications of perfect and imperfect knowledge of the channel

We present a model for time-varying communication single-access and multiple-access channels without feedback. We consider the difference between mutual information when the receiver knows the channel perfectly and mutual information when the receiver only has an estimate of the channel. We relate the variance of the channel measurement error at the receiver to upper and lower bounds for this difference in mutual information. We illustrate the use of our bounds on a channel modeled by a Gauss-Markov process, measured by a pilot tone. We relate the rate of time variation of the channel to the loss in mutual information due to imperfect knowledge of the measured channel.

[1]  B. Nelin,et al.  Corrections to "The Effect of Frequency Selective Fading on the Binary Error Probabilities of Incoherent and Differentially Coherent Matched Filter Receivers" , 1963 .

[2]  Pravin Varaiya,et al.  Capacity of fading channels with channel side information , 1997, IEEE Trans. Inf. Theory.

[3]  P. Bello Characterization of Randomly Time-Variant Linear Channels , 1963 .

[4]  Sergio Verdú,et al.  A general formula for channel capacity , 1994, IEEE Trans. Inf. Theory.

[5]  B. Rimoldi Rate-Splitting Multiple Access and Cellular Communication , 1996 .

[6]  Edward C. van der Meulen,et al.  A survey of multi-way channels in information theory: 1961-1976 , 1977, IEEE Trans. Inf. Theory.

[7]  Axthonv G. Oettinger,et al.  IEEE Transactions on Information Theory , 1998 .

[8]  W. C. Jakes,et al.  Microwave Mobile Communications , 1974 .

[9]  Michael B. Pursley,et al.  Multipath Diversity Reception of Spread-Spectrum Multiple-Access Communications , 1987, IEEE Trans. Commun..

[10]  Robert G. Gallager,et al.  An Inequality on the Capacity Region of Multiaccess Multipath Channels , 1994 .

[11]  William C. Y. Lee,et al.  Mobile Communications Engineering , 1982 .

[12]  S. Verdu,et al.  Multiple-access channels with memory with and without frame synchronism , 1989, IEEE Trans. Inf. Theory.

[13]  Bixio Rimoldi,et al.  Potential impact of rate-splitting multiple access on cellular communications , 1996, Proceedings of GLOBECOM'96. 1996 IEEE Global Telecommunications Conference.

[14]  Jacob Wolfowitz,et al.  Multiple Access Channels , 1978 .

[15]  H. A. Leinhos Capacity calculations for rapidly fading communications channels , 1995, 'Challenges of Our Changing Global Environment'. Conference Proceedings. OCEANS '95 MTS/IEEE.

[16]  Multiaccess Multipath Channels An Inequality on the Capacity Region of , 1994 .

[17]  James L. Massey,et al.  Capacity of the discrete-time Gaussian channel with intersymbol interference , 1988, IEEE Trans. Inf. Theory.

[18]  Shlomo Shamai,et al.  Information-theoretic considerations for symmetric, cellular, multiple-access fading channels - Part II , 1997, IEEE Trans. Inf. Theory.

[19]  Andrew J. Viterbi,et al.  Two different philosophies in CDMA-a comparison , 1996, Proceedings of Vehicular Technology Conference - VTC.

[20]  Hu Kuo Ting On the Information Stability of a Sequence of Channels , 1962 .

[21]  Rudiger Urbanke,et al.  Single user coding for the discrete memoryless multiple access channel , 1995, Proceedings of 1995 IEEE International Symposium on Information Theory.

[22]  A. El Gamal,et al.  Multiple user information theory , 1980, Proceedings of the IEEE.

[23]  J. Massey,et al.  Communications and Cryptography: Two Sides of One Tapestry , 1994 .

[24]  Venceslav Kafedziski Capacity of frequency selective fading channels , 1997, Proceedings of IEEE International Symposium on Information Theory.

[25]  Muriel Médard The capacity of time varying multiple user channels in wireless communications , 1995 .

[26]  H. Viswanathan,et al.  Simultaneous communication and detection over compound channels , 1998, Proceedings. 1998 IEEE International Symposium on Information Theory (Cat. No.98CH36252).

[27]  R. Knopp,et al.  Multiple-accessing over frequency-selective fading channels , 1995, Proceedings of 6th International Symposium on Personal, Indoor and Mobile Radio Communications.

[28]  Israel Bar-David,et al.  Capacity and coding for the Gilbert-Elliot channels , 1989, IEEE Trans. Inf. Theory.

[29]  van der MeulenE. A Survey of Multi-Way Channels in Information Theory: , 1977 .

[30]  Shlomo Shamai,et al.  Information theoretic considerations for cellular mobile radio , 1994 .

[31]  B. Anderson,et al.  Optimal Filtering , 1979, IEEE Transactions on Systems, Man, and Cybernetics.

[32]  Gordon L. Stüber Principles of mobile communication , 1996 .

[33]  A. Goldsmith,et al.  Capacity definitions and coding strategies for general channels with receiver side information , 1998, Proceedings. 1998 IEEE International Symposium on Information Theory (Cat. No.98CH36252).

[34]  Masoud Salehi,et al.  Multiple access channels with arbitrarily correlated sources , 1980, IEEE Trans. Inf. Theory.

[35]  John H. Park Two-user dispersive communication channels , 1981, IEEE Trans. Inf. Theory.

[36]  Anna Scaglione,et al.  On the capacity of linear time-varying channels , 1999, 1999 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings. ICASSP99 (Cat. No.99CH36258).

[37]  S. Qureshi,et al.  Adaptive equalization , 1982, Proceedings of the IEEE.

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

[39]  Sergio Verdú,et al.  The capacity region of the symbol-asynchronous Gaussian multiple-access channel , 1989, IEEE Trans. Inf. Theory.

[40]  Shlomo Shamai,et al.  Fading channels: How perfect need "Perfect side information" be? , 2002, IEEE Trans. Inf. Theory.

[41]  A. Wyner,et al.  Coding Theorem for Stationary, Asymptotically Memoryless, Continuous-time Channels , 1972 .

[42]  D. A. Bell,et al.  Information Theory and Reliable Communication , 1969 .

[43]  Shlomo Shamai,et al.  Fading Channels: Information-Theoretic and Communication Aspects , 1998, IEEE Trans. Inf. Theory.

[44]  Sergio Verdú,et al.  Gaussian multiaccess channels with ISI: Capacity region and multiuser water-filling , 1993, IEEE Trans. Inf. Theory.

[45]  Audra E. Kosh,et al.  Linear Algebra and its Applications , 1992 .

[46]  A. Wyner A note on the capacity of the band-limited Gaussian channel , 1966, The Bell System Technical Journal.

[47]  Robert G. Gallager,et al.  RESIDUAL NOISE AFTER INTERFERENCE CANCELLATION ON FADING MULTIPATH CHANNELS , 1997 .

[48]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .

[49]  P. E. Green,et al.  A Communication Technique for Multipath Channels , 1958, Proceedings of the IRE.

[50]  BORIS S. TSYBAKOV Survey of USSR contributions to random multiple-access communications , 1985, IEEE Trans. Inf. Theory.

[51]  Suhas N. Diggavi Analysis of multicarrier transmission in time-varying channels , 1997, Proceedings of ICC'97 - International Conference on Communications.

[52]  Robert M. Gray,et al.  On the asymptotic eigenvalue distribution of Toeplitz matrices , 1972, IEEE Trans. Inf. Theory.

[53]  David R. Cox,et al.  Correlation Bandwidth and Delay Spread Multipath Propagation Statistics for 910-MHz Urban Mobile Radio Channels , 1975, IEEE Trans. Commun..

[54]  Robert J. McEliece,et al.  Asynchronous multiple-access channel capacity , 1981, IEEE Trans. Inf. Theory.

[55]  James L. Massey,et al.  User-separating demodulation for code-division multiple-access systems , 1994, IEEE J. Sel. Areas Commun..

[56]  Thomas Kailath,et al.  Sampling models for linear time-variant filters , 1959 .

[57]  Michael L. Ulrey,et al.  The Capacity Region of a Channel with s Senders and r Receivers , 1975, Inf. Control..

[58]  Jr. J. Spilker On the Characterization and Measurement of Randomly Varying Filters , 1965 .

[59]  Ernst Pfaffelhuber,et al.  Channels with asymptotically decreasing memory and anticipation , 1971, IEEE Trans. Inf. Theory.

[60]  J. Wolfowitz Coding Theorems of Information Theory , 1962, Ergebnisse der Mathematik und Ihrer Grenzgebiete.

[61]  Imre Csiszár,et al.  Capacity of the Gaussian arbitrarily varying channel , 1991, IEEE Trans. Inf. Theory.

[62]  Rüdiger L. Urbanke,et al.  A rate-splitting approach to the Gaussian multiple-access channel , 1996, IEEE Trans. Inf. Theory.

[63]  R. Morgan Mobile radio communications. , 1982, Hospital engineering.

[64]  Robert G. Gallager,et al.  A perspective on multiaccess channels , 1984, IEEE Trans. Inf. Theory.

[65]  Shlomo Shamai,et al.  Systematic Lossy Source/Channel Coding , 1998, IEEE Trans. Inf. Theory.

[66]  Rudiger Urbanke,et al.  On single-user decodable codes for the Gaussian multiple access channel , 1994, Proceedings of 1994 IEEE International Symposium on Information Theory.

[67]  Andrew J. Viterbi,et al.  Very Low Rate Convolutional Codes for Maximum Theoretical Performance of Spread-Spectrum Multiple-Access Channels , 1990, IEEE J. Sel. Areas Commun..

[68]  Moshe Zakai,et al.  Band-Limited Functions and the Sampling Theorem , 1965, Inf. Control..

[69]  Amiel Feinstein,et al.  Information and information stability of random variables and processes , 1964 .

[70]  Te Sun Han,et al.  An Information-Spectrum Approach to Capacity Theorems for the General Multiple-Access Channel , 1998, IEEE Trans. Inf. Theory.

[71]  Jacob Wolfowitz Coding Theorems of Information Theory , 1962 .

[72]  Wayne E. Stark,et al.  Channels with block interference , 1984, IEEE Trans. Inf. Theory.

[73]  Rudolf Ahlswede,et al.  Multi-way communication channels , 1973 .