Capacity-achieving transmitter and receiver pairs for dispersive MISO channels

We focus on data transmission over continuous-time, dispersive M-input/single-output (MISO) channels where the transmitter knows all M channels. The biorthogonal Karhunen-Loeve (KL) expansion in the continuous-time domain is proposed as a unifying analytical framework for studying dispersive MISO channels. Using this KL expansion, we rigorously derive an expression for the capacity of the continuous-time dispersive MISO channel and show that a dispersive MISO channel is equivalent, in terms of channel capacity, to a dispersive single-input/multiple-output (SIMO) channel. Our derivations based on the KL expansion avoid the well-known problems associated with the "frequency splitting" approach. We show that the capacity-achieving transmitter for a dispersive MISO channel can be broken into two parts: (1) an optimal encoder for a dispersive single-input/single-output (SISO) channel and (2) an M-dimensional (M-D) matched filter (or a broadband beamformer). The M-D matched filter turns the original dispersive MISO channel into an equivalent SISO channel with exactly the same capacity as the capacity of the original MISO channel, and the one-dimensional encoder is just the well-known optimal encoder of Gallager for this equivalent SISO channel created by the M-D matched filter. As the number of transmit antennas increases, we show that the channel seen by the receiver approaches a flat-fading SISO channel (even when the individual forward channels are dispersive); hence, water filling in the transmitter can be dropped without much degradation. Second, this shows that with a large number of transmit antennas, the achievable data rate using a pre-RAKE at the transmitter and a very simple symbol-by-symbol detector at the receiver is quite close to the actual capacity of the dispersive MISO channel. With a large number of transmit antennas, this implies that the receiver for a capacity-achieving dispersive MISO system can be considerably less complex than the receiver for a dispersive SISO channel.

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

[2]  L. H. Brandenburg,et al.  Capacity of the Gaussian channel with memory: The multivariate case , 1974 .

[3]  Upamanyu Madhow,et al.  Space-Time transmit precoding with imperfect feedback , 2001, IEEE Trans. Inf. Theory.

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

[5]  E. Visotsky,et al.  Space-time precoding with imperfect feedback , 2000, 2000 IEEE International Symposium on Information Theory (Cat. No.00CH37060).

[6]  Khaled Ben Letaief,et al.  MISO CDMA transmission with simplified receiver for wireless communication handsets , 2001, IEEE Trans. Commun..

[7]  Erik Dahlman,et al.  WCDMA-the radio interface for future mobile multimedia communications , 1998 .

[8]  A. Goldsmith,et al.  On optimality of beamforming for multiple antenna systems with imperfect feedback , 2001, Proceedings. 2001 IEEE International Symposium on Information Theory (IEEE Cat. No.01CH37252).

[9]  John M. Cioffi,et al.  Spatio-temporal coding for wireless communication , 1998, IEEE Trans. Commun..

[10]  A. Robert Calderbank,et al.  Space-Time Codes for High Data Rate Wireless Communications : Performance criterion and Code Construction , 1998, IEEE Trans. Inf. Theory.

[11]  J. Salz,et al.  Digital transmission over cross-coupled linear channels , 1985, AT&T Technical Journal.

[12]  Jack H. Winters,et al.  Smart antennas for wireless systems , 1998, IEEE Wirel. Commun..

[13]  Gerard J. Foschini,et al.  Layered space-time architecture for wireless communication in a fading environment when using multi-element antennas , 1996, Bell Labs Technical Journal.

[14]  Siavash M. Alamouti,et al.  A simple transmit diversity technique for wireless communications , 1998, IEEE J. Sel. Areas Commun..

[15]  R. Courant,et al.  Methods of Mathematical Physics , 1962 .

[16]  Emre Telatar,et al.  Capacity of Multi-antenna Gaussian Channels , 1999, Eur. Trans. Telecommun..

[17]  Gregory W. Wornell,et al.  Efficient use of side information in multiple-antenna data transmission over fading channels , 1998, IEEE J. Sel. Areas Commun..

[18]  I. M. Glazman,et al.  Theory of linear operators in Hilbert space , 1961 .

[19]  R. Gray Entropy and Information Theory , 1990, Springer New York.