Space-time coding using estimated channel information Number:7,522,673 from the United States Patent and Trademark Office (PTO) owispatent The invention is directed to techniques for space-time coding in a wireless communication system in which the transmitter makes use of multiple transmit antennas. The transmitter uses channel information estimated by a receiving device and returned to the transmitter, e.g., as feedback. In one exemplary embodiment, the transmitter receives a mean feedback information that defines a mean channel value associated with the different channels of the different antennas. In another exemplary embodiment, the transmitter receives covariance feedback, e.g., statistical values associated with each of the different channels.<H information, estimated, Space, time, codi, 7522673.html, Patent, pto, 7522673

Title: Space-time coding using estimated channel information

Abstract: The invention is directed to techniques for space-time coding in a wireless communication system in which the transmitter makes use of multiple transmit antennas. The transmitter uses channel information estimated by a receiving device and returned to the transmitter, e.g., as feedback. In one exemplary embodiment, the transmitter receives a mean feedback information that defines a mean channel value associated with the different channels of the different antennas. In another exemplary embodiment, the transmitter receives covariance feedback, e.g., statistical values associated with each of the different channels.

Patent Number: 7,522,673 Issued on 04/21/2009 to Giannakis, et al.

Inventors: Giannakis; Georgios B. (Minnetonka, MN), Zhou; Shengli (St. Paul, MN)
Assignee: Regents of the University of Minnesota (Minneapolis, MN)

Appl. No.: 10/420,351

Filed: April 21, 2003

Related U.S. Patent Documents


Application Number	Filing Date	Patent Number	Issue Date
60374886	Apr., 2002
60374935	Apr., 2002
60374934	Apr., 2002
60374981	Apr., 2002
60374933	Apr., 2002

Current U.S. Class: 375/267

Current International Class: H04B 7/02 (20060101)

Field of Search: 375/260,267 370/208,210

References Cited [Referenced By]

U.S. Patent Documents


6188717	February 2001	Kaiser et al.
6891897	May 2005	Bevan et al.
6898248	May 2005	Elgamal et al.
2001/0033622	October 2001	Jongren et al.
2002/0122381	September 2002	Wu et al.
2002/0167962	November 2002	Kowalski
2002/0196842	December 2002	Onggosanusi et al.
2003/0035491	February 2003	Walton et al.
2004/0146014	July 2004	Hammons, Jr. et al.

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Primary Examiner: Vo; Don N
Attorney, Agent or Firm: Shumaker & Sieffert, P.A.

Government Interests

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

This invention was made with Government support under Contract Nos. ECS-9979443 and CCR-0105612, awarded by the National Science Foundation, and Contract No. DAAD19 01-2-0011 (University of Delaware Subcontract No. 497420) awarded by the U.S. Army. The Government may have certain rights in this invention.

Parent Case Text

This application claims priority from U.S. Provisional Application Ser. No. 60/374,886, filed Apr. 22, 2002, U.S. Provisional Application Ser. No. 60/374,935, filed Apr. 22, 2002, U.S. Provisional Application Ser. No. 60/374,934, filed Apr. 22, 2002, U.S. Provisional Application Ser. No. 60/374,981, filed Apr. 22, 2002, U.S. Provisional Application Ser. No. 60/374,933, filed Apr. 22, 2002, the entire contents of which are incorporated herein by reference.

Claims

The invention claimed is:

1. A method comprising: receiving estimated channel information for a space-time wireless communication system; coding signals for transmission by a multiple antenna transmitter based on the estimated channel information, wherein coding the signals comprises selecting symbols based on the estimated channel information; forming Eigen-beams, with a two-dimensional Eigen-beam-forming unit, based on the selected symbols and the estimated channel information, wherein forming the Eigen-beams comprises applying the following: .times..times..times..times..times..times..times..times..DELTA..times..ti- mes. ##EQU00048## sending the selected symbols via multiple antennas, wherein sending the selected symbols comprises sending the Eigen-beams via the multiple antennas.

2. The method of claim 1, wherein receiving estimated channel information comprises receiving information defining a mean estimate of multiple channels associated with the multiple antennas.

3. The method of claim 2, further comprising identifying that the channels are substantially slow time-varying channels.

4. The method of claim 1, wherein receiving estimated channel information comprises receiving a perturbation vector defining uncertainties of the channels relative to a nominal vector that nominally defines the channels.

5. The method of claim 1, wherein receiving estimated channel information comprises receiving information defining a covariance estimate of multiple channels associated with the multiple antennas.

6. The method of claim 5, further comprising identifying that the channels are substantially rapid time-varying channels.

7. The method of claim 1, wherein receiving estimated channel information comprises receiving information defining a mean estimate of multiple channels associated with the multiple antennas and receiving information defining a covariance estimate of the multiple channels.

8. The method of claim 7, further comprising: identifying that the channels are substantially slow time-varying channels; and coding signals for transmission by the multiple antenna transmitter using the mean estimate.

9. The method of claim 7, further comprising: identifying that the channels are substantially rapid time-varying channels; and coding signals for transmission by the multiple antenna transmitter using the covariance estimate.

10. The method of claim 1, wherein the method is performed by one of a wireless mobile device and a wireless base station.

11. A wireless device comprising: a coding unit to select symbols based on received channel information estimated for a space-time wireless communication system; multiple transmit antennas to send the symbols; and a two-dimensional Eigen-beam-forming unit to form Eigen-beams based on the selected symbols and the received channel information, wherein the multiple transmit antennas send the symbols by sending the Eigen-beams. and wherein the two-dimensional Eigen-beam-forming unit forms Eigen-beams by applying the following: .times..times..times..times..times..times..DELTA..times. ##EQU00049##

12. The wireless device of claim 11, wherein the coding unit applies a block coding matrix: .times..times..PHI..times..times..times..PSI..times. ##EQU00050## where s.sub.k.sup.R and s.sub.k.sup.I denote the real and imaginary parts of symbol s.sub.k, N.sub.t denotes the number of antennas, and for complex symbols {s.sub.k=s.sub.k.sup.R+js.sub.k.sup.l}.sub.k=1.sup.K, the matrices {.PHI..sub.k, .PSI..sub.k}.sub.k=1.sup.K each have entries drawn from {1, 0, -1}.

13. The wireless device of claim 12, wherein the following condition holds true: .times. .times..times. ##EQU00051## where the superscript H denotes Hermitian transpose, N.sub.t denotes the number of transmit antennas, and .sup.sk denotes a symbol.

14. The wireless device of claim 11 wherein the two-dimensional Eigen-beam-forming unit forms the Eigen-beams by applying the following: .times..times..delta..delta. .DELTA..times..times..times..times. ##EQU00052## where s denotes symbols, .delta..sub.1 and .delta..sub.2 denote power loading on two Eigen-beams, the superscript H denotes Hermitian transpose and u1 and u2 denote the two Eigen-beams.

15. The wireless device of claim 14, wherein: .delta..delta..delta..delta.>.gamma..ltoreq..gamma. ##EQU00053## where E.sub.s denotes the symbol energy, N.sub.0 denotes the noise variance and .gamma..sub.th denotes the threshold on E.sub.s/ N.sub.0 above which two beams are used and below which only one beam is used.

16. The wireless device of claim 11, wherein the received channel information estimated for the space-time wireless communication system includes a mean estimate of multiple channels associated with the multiple transmit antennas.

17. The wireless device of claim 11, wherein the received channel information estimated for the space-time wireless communication system includes a perturbation vector defining uncertainties of the channels relative to a nominal vector that nominally defines the channels.

18. The wireless device of claim 11, wherein the received channel information estimated for the space-time wireless communication system includes a covariance estimate of multiple channels associated with the multiple transmit antennas.

19. The wireless device of claim 11, wherein the device comprises one of a wireless mobile device and a wireless base station.

20. A computer readable medium comprising computer readable instructions that when executed in a wireless device cause the device to: code signals for transmission by a multiple antenna transmitter in a space-time wireless communication system based on received channel information estimated by a receiving device, wherein the instructions that cause the device to code the signals comprise instructions that cause the device to select symbols based on the received channel information; form Eigen-beams, with a two-dimensional Eigen-beam-forming unit, based on the selected symbols and the received channel information, wherein the instructions that cause the device to form the Eigen-beams comprise instructions that cause the device to apply the following: .times..times..times..times..times..times..times..times..DELTA..times..ti- mes. ##EQU00054## send the selected symbols via multiple antennas, wherein the instructions that cause the device to send the selected symbols comprise instructions that cause the device to send the Eigen-beams via the multiple antennas.

21. The computer readable medium of claim 20, wherein the channel information includes a mean estimate of multiple channels associated with the multiple antennas.

22. The computer readable medium of claim 20, wherein the channel information includes a perturbation vector defining uncertainties of the channels relative to a nominal vector that nominally defines the channels.

23. The computer readable medium of claim 20, wherein the channel information includes a covariance estimate of multiple channels associated with the multiple antennas.

24. A wireless device comprising: means for receiving estimated channel information for a space-time wireless communication system; and means for coding signals for transmission by a multiple antenna transmitter based on the estimated channel information, wherein the means for coding the signals comprises means for selecting symbols based on the estimated channel information; means for forming Eigen-beams, with a two-dimensional Eigen-beam-forming unit, based on the selected symbols and the estimated channel information, wherein the means for forming the Eigen-beams comprises means for applying the following: .times..times..times..times..times..times..times..times..DELTA..times..ti- mes. ##EQU00055## means for sending the selected symbols via multiple antennas, wherein the means for sending the selected symbols comprises means for sending the Eigen-beams via the multiple antennas.

25. The wireless device of claim 24, wherein the estimated channel information includes a mean estimate of the multiple channels associated with the multiple antennas.

26. The wireless device of claim 24, wherein the estimated channel information includes a perturbation vector defining uncertainties of the channels relative to a nominal vector that nominally defines the channels.

27. The wireless device of claim 24, wherein the estimated channel information includes a covariance estimate of multiple channels associated with the multiple antennas.

28. A space-time wireless communication system comprising: a first wireless device that estimates channel information based on a received signal and transmits the channel information; a second wireless device that receives the estimated channel information from the first wireless device and codes signals for subsequent transmission via multiple transmit antennas based on the estimated channel information, wherein the second wireless device codes the signals by selecting symbols based on the estimated channel information; and a two-dimensional Eigen-beam-forming unit that forms Eigen-beams based on the selected symbols and the estimated channel information, wherein the multiple transmit antennas send the symbols by sending the Eigen-beams, and wherein the two-dimensional Eigen-beam-forming unit forms Eigen-beams by applying the following: .times..times..times..times..times..times..DELTA..times. ##EQU00056##

29. The space-time wireless communication system 28, wherein the estimated channel information includes a mean estimate of multiple channels associated with the multiple transmit antennas.

30. The space-time wireless communication system 28, wherein the estimated channel information includes a perturbation vector defining uncertainties of channels relative to a nominal vector that nominally defines the channels.

31. The space-time wireless communication system 28, wherein the estimated channel information includes a covariance estimate of multiple channels associated with the multiple transmit antennas.

32. A method comprising: receiving communications from a transmitting device via multiple communication channels associated with multiple transmit antennas of the transmitting device; computing estimated channel information for the multiple channels; and communicating the estimated channel information to the transmitting device to control coding of signals for transmission by the multiple transmit antennas, wherein the transmitting device selects symbols based on the estimated channel information, and forms Eigen-beams, with a two-dimensional Eigen-beam-forming unit, based on the selected symbols and the estimated channel information, wherein the multiple transmit antennas send the selected symbols by sending the Eigen-beams, and wherein the transmitting device forms the Eigen-beams by applying the following: .times..times..times..times..times..times..DELTA..times. ##EQU00057##

33. The method of claim 32, wherein the estimated channel information includes a mean estimate of multiple channels associated with the multiple transmit antennas.

34. The method of claim 32, wherein the estimated channel information includes a perturbation vector defining uncertainties of the channels relative to a nominal vector that nominally defines the channels.

35. The method of claim 32, wherein the estimated channel information includes a covariance estimate of multiple channels associated with the multiple transmit antennas.

36. A wireless device comprising: means for estimating channel information for a space-time wireless communication system; and means for communicating the estimated channel information to a transmitter for use in transmitting subsequent signals by multiple antennas, wherein the transmitter selects symbols based on the estimated channel information, and forms Eigen-beams, with a two-dimensional Eigen-beam-forming unit, based on the selected symbols and the estimated channel information, wherein the multiple antennas send the selected symbols by sending the Eigen-beams, and wherein the transmitter forms the Eigen-beams by applying the following: .times..times..times..times..times..times..DELTA..times. ##EQU00058##

37. The wireless device of claim 36, wherein the estimated channel information includes a mean estimate of the multiple channels associated with the multiple antennas.

38. The wireless device of claim 36, wherein the estimated channel information includes a perturbation vector defining uncertainties of the channels relative to a nominal vector that nominally defines the channels.

39. The wireless device of claim 36, wherein the estimated channel information includes a covariance estimate of multiple channels associated with the multiple antennas.

40. A method comprising: receiving estimated channel information associated with multiple channels of a wireless communication signal; and coding subsequent signals for transmission based on the estimated channel information, wherein coding the subsequent signals comprises selecting symbols based on the estimated channel information; forming Eigen-beams, with a two-dimensional Eigen-beam-forming unit, based on the selected symbols and the estimated channel information, wherein forming the Eigen-beams comprises applying the following: .times..times..times..times..times..times..times..times..DELTA..times..ti- mes. ##EQU00059## sending the selected symbols via multiple transmit antennas, wherein sending the selected symbols comprises sending the Eigen-beams via the multiple transmit antennas.

41. The method of claim 40, wherein receiving estimated channel information comprises receiving information defining a mean estimate of the multiple channels.

42. The method of claim 40, wherein receiving estimated channel information comprises receiving information defining a covariance estimate of multiple channels.

43. The method of claim 40, wherein the multiple channels include channels associated with multiple transmit antennas.

44. The method of claim 40, wherein the multiple channels include channels of a multi-path signal associated with a transmit antenna.

Description

TECHNICAL FIELD

The invention relates to wireless communication and, more particularly, to coding techniques for multi-antenna transmitters.

BACKGROUND

Space-time coding using multiple transmit-antennas has been recognized as an attractive way of achieving high data rate transmissions with diversity and coding gains in wireless applications. For example, multi-antenna transmitters can offer significant diversity and coding advantages over single antenna transmitters. A number of space-time coding transmitter designs have been developed.

Most conventional space-time coding transmitters are designed for the scenario where the propagation channels are deterministically known. In practical wireless systems, however, propagation channels are typically not known at the transmitter. Moreover, in practical wireless systems, propagation channels can change over time, with changes in settings of the wireless devices or movement of one wireless device relative to the other wireless device, e.g., movement of a mobile unit relative to a base station.

SUMMARY

In general, the invention is directed to space-time coding techniques for wireless communication systems in which the transmitter makes use of multiple transmit antennas. As described in greater detail below, the transmitter uses channel information estimated by a receiving device and returned to the transmitter, e.g., as feedback. In other words, the channel information is estimated at the receiver and returned to the transmitter for use in subsequent transmissions to that the signals can be coded in an improved manner.

In one exemplary embodiment, the transmitter makes use of a mean feedback information that defines a mean channel value associated with the different channels of the different antennas or different multi-paths from one or more antennas. In another exemplary embodiment, the transmitter makes use of covariance feedback, e.g., statistical values associated with the different channels. The mean feedback may be particularly useful when the channels are slow time-varying channels, and the covariance feedback may be particularly useful when the channels are rapid time-varying channels. In other words, if the channels change slowly, the mean feedback can be very useful, but if the channels change rapidly the covariance feedback may be more useful.

In one embodiment, the invention provides a method comprising receiving estimated channel information for a space-time wireless communication system, and coding signals for transmission by a multiple antenna transmitter based on the estimated channel information.

In another embodiment, the invention provides a wireless device comprising a coding unit to select symbols based on received channel information estimated for a space-time wireless communication system, and multiple transmit antennas to send the symbols.

In some embodiments, the invention can be implemented in software. In that case, the invention may be directed to a computer readable medium comprising computer readable instructions that when executed in a wireless device cause the device to code signals for transmission by a multiple antenna transmitter in a space-time wireless communication system based on received channel information estimated by a receiving device.

In another embodiment, the invention provides a wireless device comprising means for receiving estimated channel information for a space-time wireless communication system, and means for coding signals for transmission by a multiple antenna transmitter based on the estimated channel information.

In another embodiment, the invention provides a space-time wireless communication system comprising a first wireless device that estimates channel information based on a received signal and transmits the channel information, and a second wireless device that receives the estimated channel information from the first wireless device and codes signals for subsequent transmission via multiple transmit antennas based on the estimated channel information.

In another embodiment, the invention provides a method comprising receiving communications from a transmitting device via multiple communication channels associated with multiple transmit antennas of the transmitting device, computing estimated channel information for the multiple channels, and communicating the estimated channel information to the transmitting device to control coding of signals for transmission by the multiple antennas.

In another embodiment, the invention provides a wireless device comprising means for estimating channel information for a space-time wireless communication system, and means for communicating the estimated channel information to a transmitter for use in transmitting subsequent signals by multiple antennas.

In another embodiment, the invention provides a method comprising receiving estimated channel information associated with multiple channels of a wireless communication signal, and coding subsequent signals for transmission based on the estimated channel information.

The invention may be capable of providing certain advantages. Specifically, the invention can improve the performance of wireless communication. Numerous embodiments and mathematical techniques are outlined in greater detail below, which can achieve varying levels of performance. In some cases, trade-offs between performance and complexity can be made to meet a specific level of performance and a specific level of complexity.

The details of one or more embodiments of the invention are set forth in the accompanying drawings and the description below. Other features, objects, and advantages of the invention will be apparent from the description and drawings, and from the claims.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a block diagram of a space-time wireless communication system according to an embodiment of the invention.

FIG. 2 is another block diagram of a space-time wireless communication system according to an embodiment of the invention.

FIG. 3 is a block diagram illustrating multiple antennas of a transmitter in accordance with an embodiment of the invention.

FIG. 4 is another block diagram of a space-time wireless communication system according to an embodiment of the invention.

FIG. 5 is a block diagram of a transmitting device which includes a space-time block coding unit, a set of power loaders, a beam-forming unit, and a set of antennas in accordance with an embodiment of the invention.

FIGS. 6-16 are graphs illustrating results of simulations of various embodiments of the invention.

DETAILED DESCRIPTION

The invention is directed to transmitter designs for space-time coding in which the transmitter makes use of multiple transmit antennas. The transmitter uses channel information estimated by a receiving device and returned to the transmitter, e.g., as feedback. In some embodiments outlined in greater detail below, the transmitter makes use of mean feedback information that defines a mean channel value associated with the channels of the different antennas or different multi-paths from one or more antennas. In other embodiments outlined in greater detail below, the transmitter makes use of covariance feedback, e.g., statistical values associated with the different channels. The mean feedback may be particularly useful when the channels are slow time-varying channels, and the covariance feedback may be particularly useful when the channels are rapid time-varying channels. In other words, if the channels change slowly the mean feedback can be very useful, but if the channels change rapidly the covariance feedback may be more useful.

FIG. 1 is a simplified block diagram of a space-time wireless communication system 10 including a transmitting device 12 (also referred to as transmitter 12) and a receiving device 14 (also referred to as receiver 14). In accordance with space time coding, transmitting device 12 codes signals and transmits the signals via multiple antennas 15A, 15B, 15C. Receiving device 14 includes antenna 16 for receiving signals from device 12. In some cases, receiving device 14 may also include multiple antennas, but the invention is not limited in that respect.

Transmitting device 12 and receiving device 14 may comprise any of a wide variety of wireless devices that communicate with one another. For example, one of devices 12, 14 may comprise a mobile device and the other of devices 12, 14 may comprise a base station, e.g., in a digital cellular communication system. Alternatively, one of devices 12, 14 may comprise a wireless computer and the other may comprise a wireless network access point, e.g., in a wireless networking setting. In addition, in other applications, each of devices 12, 14 may comprise direct two-way communication devices. In general, system 10 may comprise any of a wide variety of wireless communication systems which could benefit from the feedback techniques described herein.

In accordance with the invention, receiving device 14 measures channel information, such as the fading amplitudes of the various channels associated with transmission antennas 15A, 15B, 15C. Receiving device 14 sends this measured channel information back to transmitting device 12 so that subsequent signals can be coded based on the measured channel information. In other words, the invention provides a feedback technique in which channel information for multiple space-time channels collected at receiving device 14 is returned to transmitting device 12 for use in subsequent transmissions. In some examples, the channel information includes a mean channel value of the channels associated with the different transmit antennas 15A, 15B, 15C. In other examples covariance feedback is used in which the channel information includes statistical values associated with the different channels.

The signals transmitted between devices 12, 14 may comprise single carrier signals, or multi-carrier signals. Any of a wide variety of modulation techniques can be used, including, for example, code division multiple access (CDMA), time division multiple access (TDMA), frequency division multiple access (FDMA), orthogonal frequency division multiplexing (OFDM), various other modulation techniques, or even two or more modulation techniques.

In a space-time wireless system (such as system 10) with N.sub.t transmit antennas and N.sub.r receive antennas, the antenna coefficients can be collected into channel matrix H, with the (.mu., .nu.)th entry as h.sub..mu..nu.. For each receive antenna .nu., the vector: h.sub..nu.:=[h.sub.1.nu., . . . , h.sub.N.sub.t.sub..nu.].sup.T can be defined. The columns of H can be concatenated into one channel vector as:

.function. ##EQU00001##

With perfect channel state information, transmitter 12 knows each realization of h. However, with partial channel state information (CSI), transmitter 12 has some uncertainties on the channel realization h. The uncertainties can be modeled as unknown perturbations around the nominal channel. Specifically, conditioned on channel feedback, transmitter 12 perceives a "nominal-plus-perturbation" channel model as: {hacek over (h)}= h+.epsilon., (1.2) where h is deterministic known per feedback realization, and .epsilon. is a random vector capturing all uncertainties about h. The partial channel knowledge about the channel will then include the nominal channel h, and the statistical description on the perturbation error .epsilon.. We here use {hacek over (h)} to differentiate the channel perceived at the transmitter from the true channel h; however they have quite different statistical properties. The perception at the transmitter will be updated every time new feedback information becomes available.

The matrix corresponding to EQUATION 1.2 is: {hacek over (H)}= H+.XI., (1.3) where H and .XI. contain the nominal values and unknown perturbations to describe the N.sub.t.times.N.sub.r channel matrix H.

In practice, the perturbation errors may not be Gaussian distributed. But a Gaussian assumption will greatly simplify the transmitter design. The resulting closed-form solutions provide much insight on transmitter optimization based on partial channel knowledge. Hence, for convenience and simplicity, we model {hacek over (h)} as a Gaussian random vector. The statistical property is then described by the mean and covariance matrix of {hacek over (h)}. Specifically, based on channel feedback, the transmitter perceives a random channel distribution as: {hacek over (h)}.about.CN( h, .SIGMA..sub.h). (1.4)

EQUATION 1.4 provides the general model with Gaussian assumption on the uncertain perturbation errors. We next specify two simplified models, termed as mean feedback and covariance feedback, respectively.

In mean feedback, all entries of .epsilon. are assumed to be independent from each other, but having the same covariance .sigma..sub..epsilon..sup.2. Specifically, {hacek over (h)}.about.CN( h, .sigma..sub..epsilon..sup.2I.sub.N.sub.t.sub.N.sub.r). (1.5) Channel mean feedback is suitable to slowly time-varying channels, where instantaneous channel values are fed back. The same uncertainty on all channel coefficients is assumed for simplicity.

We next highlight several possibilities where channel mean feedback can be realized in practice. We illustrate how to obtain ( h, .sigma..sub..epsilon..sup.2) based on feedback information.

Case 1 (Ricean fading channels): In this case, there exist a line-of-sight (LOS) path and diffusing non-LOS paths between transmitter 12 and receiver 14. Hence, the true channel itself is Ricean distributed. We further assume that the diffusing components of all channel coefficients are uncorrelated but with identical variance .sigma..sub.h.sup.2. Hence, h.about.CN(.mu..sub.h, .sigma..sub.h.sup.2I.sub.N.sub.t.sub.N.sub.r), (1.6) where .mu..sub.h contains the channel coefficients corresponding to the LOS paths. In this scenario, we assume that receiver 12 feeds back to transmitter 14 the instantaneous values for the LOS paths and the variance of the diffusing components, without errors. We thus have h=.mu..sub.h, .sigma..sub..epsilon..sup.2=.sigma..sub.h.sup.2, (1.7A and 1.7B) in the channel mean feedback model.

Case 2 (delayed feedback): Here we assume that: i) the channel coefficients are slowly time varying according to Jakes' model with Doppler frequency f.sub.d: ii) antennas 15 are well separated. The channel coefficients are i.i.d. Gaussian distributed as h.about.CN(0, .sigma..sub.h.sup.2I.sub.N.sub.t); and, iii) the channel is acquired perfectly at receiver 14 and is fed back to transmitter 12 via a noiseless channel with delay .tau.. Let h.sub.f denote the channel feedback. Notice that both h and h.sub.f are complex Gaussian vectors, drawn from the same distribution CN(0, .sigma..sub.h.sup.2I.sub.N.sub.t).

It can be shown that E{hh.sub.f.sup.H}=.rho..sigma..sub.h.sup.2I.sub.N.sub.t, where the correlation coefficient .rho.:=J.sub.0(2.pi.f.sub.d.tau.) determines the feedback quality. The minimum mean-square error (MMSE) estimator of h based on h.sub.f is given by E{h|h.sub.f}=.rho.h.sub.f, with estimation error having covariance matrix .sigma..sub.h.sup.2(1-|.rho.|.sup.2)I.sub.N.sub.t.sub.N.sub.r. Thus, for each realization of h.sub.f=h.sub.f,0, the transmitter obtains: h=.rho.h.sub.f,0, .sigma..sub..epsilon..sup.2=.sigma..sub.h.sup.2(1-|.rho.|.sup.2). (1.8A and 1.8B) The deterministic values of h are updated when the next feedback becomes available.

Case 3 (quantized feedback): In this case, we assume that the channel is acquired at receiver 14, and is quantized to 2.sup.b code words {a(j)}.sub.j=1.sup.2.sup.b. The quantizer output is then encoded by b information bits, which are fed back to transmitter 12 with a negligible delay over a noiseless low-speed feedback channel. We assume that transmitter 12 has the same code book, and reconstructs the channel as a(j), if the index j is suggested by the received b bits. Although the quantization error is non-Gaussian and non-white in general, we assume that the quantization errors can be approximated by zero-mean and white Gaussian noise samples, in order to simplify the transmitter design. With .epsilon..sub.Q.sup.2 denoting the approximate variance of the quantization error, the parameters in (1.5) are: h=a(j), if index j is received, .sigma..sub..epsilon..sup.2=.epsilon..sub.Q.sup.2. (1.9A and 1.9B)

In addition to Cases 1-3, channel prediction based on pilots inserted at transmitter 12 is also another realization of the general notion of "mean feedback". Notice that channel predictors take both the feedback delay and the estimation errors into account.

In covariance feedback, we assume that the channel h varies too rapidly for transmitter 12 to track its instantaneous value. In this case, the channel mean is set to zero, and the relative geometry of the propagation paths manifests itself in a nonwhite covariance matrix .SIGMA..sub.h. Specifically, we simplify (1.4) to {hacek over (h)}.about.CN(0.sub.N.sub.t.sub.N.sub.r.times.1, .SIGMA..sub.h). (1.10) The statistical information .SIGMA..sub.h needs to be updated infrequently.

Through field measurements, ray-tracing simulations, or using physical channel models, transmitter 12 can acquire such statistical CSI a priori. For certain applications such as fixed wireless, the spatial fading correlations can be determined from such physical parameters as antenna spacing, antenna arrangement, angle of arrival, and angle spread. Likewise, for systems employing polarization diversity, second-order channel statistics will involve the correlation between differently polarized transmissions. Alternatively, receiver 14 can estimate the channel correlations by long-term averaging of the channel realizations, and feed them back reliably to transmitter 12 through a low data rate feedback channel. In applications involving Time Division Duplex (TDD) protocols, transmitter 14 can also obtain channel statistics directly since the forward and backward channels share the same physical (and statistically invariant) channel characteristics even when the time separation between the forward and the backward link is long enough to render the deterministic instantaneous channel estimates outdated. In Frequency Division Duplex (FDD) systems with small angle spread, the downlink channel covariance estimates can be also obtained accurately from the uplink channel covariance through proper frequency calibration processing.

EQUATION 1.10 specifies a general correlation model for Rayleigh fading channels. However other simplifications can be implemented based on particular propagation environments. EQUATION 1.10 can be further simplified by considering an application scenario where the base station (BS) is unobstructed, and the subscriber unit (SU) is surrounded by rich local scatterers. In this case, the receive antennas are uncorrelated, and the transmit correlation for each receive antenna .nu. are identical with .SIGMA..sub.0=E{h.sub..nu.h.sub..nu..sup.H}, .A-inverted..nu., (1.11) Again, in FIG. 1, either of transmitting device 12 or receiving device 14 can comprise the base station or the mobile unit.

.SIGMA..sub.0 is an arbitrary Hermitian matrix. It turns out, that the antenna spacing at the SU is much smaller (one or two orders of magnitude) than that at the BS, to yield uncorrelated channels among different antennas. In this simplified scenario, we have .SIGMA..sub.h=I.sub.N.sub.r{circle around (.times.)}.SIGMA..sub.0. (1.12) Albeit restrictive for the case with multiple receive antennas, the considered model in (1.12) is the most general for the single receive-antenna case, with .SIGMA..sub.h=.SIGMA..sub.0.

FIG. 2 illustrates a relatively simple design of transmitter 20, which may correspond to transmitter device 12 (FIG. 1). Also depicted in FIG. 2 is a receiver 24. Transmitter 20 includes a set of preorders 21A-21B and a set of antennas 22A-22B.

Transmitter 20 spreads the information symbol over both space and time. On each antenna (22) .mu., a length P spreading code c.sub..mu.:=[c.sub..mu.(0), . . . , c.sub..mu.(P-1].sup.T is used. Different antennas 22 use different spreading codes. This is inherently a low rate system, since only one information symbol is transmitted in P time slots. We will first look at this simple system.

Define the P.times.N.sub.t space time matrix C:=[c.sub.1, . . . , c.sub.N.sub.t], and collect the received samples corresponding to each information symbol into a P.times.N.sub.r matrix Y. The channel input-output relationship is Y=sCH+W.sub.1 (1.13) where W contains additive white Gaussian noise (AWGN) with each entry having variance N.sub.0.

The receiver weights the contribution from each entry of Y to form a decision variable as: s=tr{G.sup.HY} (1.14) Based on (1.13), a desirable maximum ratio combiner (MRC) can be found as: G.sub.opt=CH (1.15) The signal to noise ratio (SNR) at the MRC output is

.gamma..times..function..times..times..times..times..function..times..time- s..function..times..times..times. ##EQU00002## where E.sub.8:=E{|s|.sup.2} is the average energy of the underlying signal constellation.

For each realization of .gamma., the instantaneous symbol error rate (SER) is

.function..gamma..pi..times..intg..times..pi..times..function..gamma..time- s..times..theta..times..times.d.theta..function..gamma..times..intg..pi..t- imes..function..gamma..times..times..theta..times..times.d.theta..times..t- imes..times..intg..pi..pi..times..function..gamma..times..times..theta..ti- mes..times.d.theta..times. ##EQU00003## where b.sub.QAM:=4(1-1/ {square root over (M)})/.pi., and the constellation-specific constant g is defined as:

.function..pi..times..times..times..times..times..times..times..times..tim- es..times..times..times..times..times..times..times..times. ##EQU00004## Hence, if the channel is perfect known at transmitter 20, the SER performance can be easily determined from (1.17) and (1.18).

However, transmitter 20 has only partial knowledge {hacek over (h)}. Transmitter 20 views that the real channel h will be just one realization of {hacek over (h)} during this