# A canonical space-time characterization of mobile wireless channels

TL;DR: A canonical space-time characterization of mobile wireless channels is introduced in terms of a fixed basis that is independent of the true channel parameters that provides a robust representation of the propagation dynamics and dramatically reduces the number of channel parameters to be estimated.

Abstract: A canonical space-time characterization of mobile wireless channels is introduced in terms of a fixed basis that is independent of the true channel parameters. The basis captures the essential degrees of freedom in the received signal using discrete multipath delays, Doppler shifts, and directions of arrival. This provides a robust representation of the propagation dynamics and dramatically reduces the number of channel parameters to be estimated. The resulting canonical space-time receivers deliver optimal performance at substantially reduced complexity compared to existing designs.

## Summary (1 min read)

### I. INTRODUCTION

- T HE USE OF antenna arrays for enhancing the capacity and quality of multiuser wireless communication systems has spurred significant interest in space-time signal processing techniques [1] .
- In addition to eliminating the need for estimating arbitrary delays, Doppler shifts and DOA's of dominant scatterers, the canonical space-time receivers dictated by their signal model deliver optimal performance at substantially lower complexity compared to existing "idealized" receivers, especially in dense multipath environments.

### II. CANONICAL CHANNEL CHARACTERIZATION

- The authors develop the signal model using continuous aperture, as illustrated in Fig. 1 . denotes the angular spread of the scatterers associated with the desired signal.
- The complex baseband signal received at location in the aperture is (1) where denotes the signal arriving from direction and denotes the carrier wavelength.
- The signal is related to the transmitted symbol waveform via the angledependent time-varying channel impulse response or, equivalently, the multipath-Doppler spreading function [2] , [3].
- Similarly, the finite aperture dictates that possesses only a finite number of spatial degrees of freedom that are 1.
- The following canonical space-time characterization of identifies the essential spatio-temporal degrees of freedom in the channel that are observable at the receiver.

### Canonical Channel Representation

- The signal admits the equivalent representation (3) in terms of the space-time basis waveforms (4) The coefficients are uniformly spaced samples of the smoothed spreading function (5) where and The number of terms in (3) are determined by and where Proof [5] :.
- The canonical representation (12) provides an new equivalent characterization of the ideal statistic (13) that eliminates the need for DOA and delay estimates (14) Note that the canonical receiver only requires estimates of the fading coefficients and the number of canonical coordinates, can be substantially smaller than the number of physical coordinates, especially in dense multipath environments.
- Even if joint angle-delay estimation frameworks [1] are employed, a large number of observations and relatively complex algorithms are necessary to obtain accurate parameter estimates for the "idealized" conventional receivers.

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2,331 citations

### "A canonical space-time characteriza..." refers background in this paper

...The signal is related to the transmitted symbol waveform via the angledependent time-varying channel impulse response or, equivalently, the multipath-Doppler spreading function [2], [3]...

[...]

1,059 citations

### "A canonical space-time characteriza..." refers background in this paper

...Conventional coherent space–time receivers, such as those proposed in [1], are based on the “ideal” test statistic...

[...]

...Even if joint angle-delay estimation frameworks [1] are employed, a large number of observations and relatively complex algorithms are necessary to obtain accurate parameter estimates for the “idealized” conventional receivers....

[...]

...T HE USE OF antenna arrays for enhancing the capacity and quality of multiuser wireless communication systems has spurred significant interest in space–time signal processing techniques [1]....

[...]

686 citations

372 citations

### "A canonical space-time characteriza..." refers background in this paper

...In particular, the dimensional canonical coordinates defined by the basis (10) characterize the inherent diversity afforded by a wide-sense stationary uncorrelated scatterer (WSSUS) channel [5], [4]....

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...The accuracy of (12) can be improved by increasing although at the expense of losing orthogonality [4], [5]....

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...3The special case of canonical multipath-Doppler coordinates in time-only processing is discussed in [4] and [6]....

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...Due to the finite duration and essentially finite bandwidth of the signal exhibits only a finite number of temporal degrees of freedom that are captured by a set of uniformly spaced discrete multipath delays and Doppler shifts [4]....

[...]

35 citations

### "A canonical space-time characteriza..." refers background or methods in this paper

...In particular, the dimensional canonical coordinates defined by the basis (10) characterize the inherent diversity afforded by a wide-sense stationary uncorrelated scatterer (WSSUS) channel [5], [4]....

[...]

...Furthermore, the canonical matched filter outputs can be efficiently computed via a space–time RAKE receiver structure [5]....

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...While the canonical representation (12) is quite general, it is particularly advantageous in the context of spread spectrum signaling [5], [6]....

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...The number of terms in (3) are determined by and where Proof (sketch) [5]: Via a change of variables in (1), can be written as...

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...The choice can generate an approximately orthonormal basis, albeit at the expense of a loss of accuracy in (12) [5], [7]....

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