WO2004109949A1

WO2004109949A1 - Method for estimation of maximum doppler frequency

Info

Publication number: WO2004109949A1
Application number: PCT/CN2003/000438
Authority: WO
Inventors: Oskar Mauritz
Original assignee: Huawei Technologies Co., Ltd.
Priority date: 2003-06-05
Filing date: 2003-06-05
Publication date: 2004-12-16
Also published as: CN100373801C; AU2003245806A1; CN1788427A

Abstract

The invention is a method for estimating the maximum Doppler frequency, comprising: calculating autocorrelation functions of complex channel estimates from a received signal; detecting whether the values of the real part of the autocorrelation function become negative or 0 within a predefined lag threshold; if it is, estimating the maximum Doppler frequency with a method appropriate for high Doppler spreads otherwise with a method appropriate for low Doppler spreads. The invention solves the problem of the estimation of maximum Doppler frequency not only for high Doppler spreads but also for low Doppler spreads. The maximum Doppler frequency can be estimated more accurately over a wider range of Doppler spreads than prior art.

Description

METHOD FOR ESTIMATION OF MAXIMUM DOPPLER

FREQUENCY

Field of the Technology

The present invention relates generally to digital radio communications and mobile communications, and in particular to estimation of maximum Doppler frequency.

Background of the Invention

The knowledge of the maximum Doppler frequency has many applications in digital radio communications systems such as adaptive coding, power control, modulation, antenna diversity and so on. The mobile velocity v being proportional to the maximum f Doppler frequency fd through v = —c , where f_c is the carrier frequency of the radio

J c wave, c is the speed of light, the estimation of the mobile velocity v is equivalent to the estimation of the maximum Doppler frequency f_d. The speed of the mobile unit is an important parameter for Radio Resource Management (RRM). It is one of the parameters that give the optimal window length for signal strength averaging in handoff algorithms. In a hierarchical cell structure (HCS), according to the velocity of a mobile, a mobile with low speed should be assigned to a microcell and a mobile with high speed should be assigned to a macrocell in order to reduce the number of handoffs and the interference.

The radio channel in a mobile communications system induces an additional modulation of the transmitted signal. Every single path in the radio channel is characterized by a time- varying complex channel coefficient h(f). The spectrum S(f) of the channel coefficient h(f) for a non line-of-sight path is usually modeled by the so-called Jakes' spectrum, given by c

S(f) = \f\ < U flf_d)²

0 otherwise

(1) wherein/is the frequency, C is a constant, and i is the maximum Doppler frequency, also called the Doppler spread. Corresponding to expression (1), the autocorrelation function of h(f) which is noted as r_/,(τ), is r_h(τ) = CJ₀(ω_dτ), (2)

wherein J_n is the wth-order Bessel function of the first kind defined as

J_n (x) = — ^e^{j(χs[n φ}-^nφ)dφ . (3)

2π

The time-varying channel requires the channel coefficients to be adaptively estimated. The estimation is improved by filtering pilot symbols through a low-pass filter with the same bandwidth as the maximum Doppler frequency and implies lower required transmit power. The same filtering of pilot symbols lowers the noise floor in a multipath searcher, which implies improved dynamics of the searcher and/or larger detection probability and/or lower probability of false alarm for the multipath components.

There are several methods for maximum Doppler frequency estimation at present. There are two methods that represent the closest prior art.

One is described in C. TepedelenliogTu and G. B. Giannakis, "A Spectral Moment

Approach to Velocity Estimation in Mobile Communications", Proc. Of Wireless Communications and Networking Conf., Chicago, IL, Sept. 23-28 2000, and "On Velocity Estimation and Correlation Properties of Narrow-Band Mobile Communication Channels", IEEE Trans. Veh. Technol., vol 50, 1039-1051, July 2001 (in the following contexts named as document [1]), and is here named curve-fitting method. In this document, a covariance-based method, which has a rapid convergence and is robust to non-uniform scattering object distributions, is presented. The maximum Doppler frequency is calculated from the parameters of a curve fitting to the covariance function of the channel. Note that since h(t) is zero-mean, the auto-covariance and the autocorrelation are equivalent. The method is shown below:

l.Make N complex-valued channel estimates,

, from the received signal, with sampling period T_s.

2. Calculate L values of the autocorrelation function of the real or imaginary part of the complex channel estimates. For instance, if the real part of the channel estimates is used: N-l-L r_Λ(/ = — ^l— ∑Rfi{Λ(« + /)}Re{/.(»)}, 1 = 1,2,...L.

3. Find the curve fitting parameters ά_k = argmin_fl, ^ r_A (/ _s ) - _ a_kl^k

4. Obtain r_ll (0) = ά₀; r;_ι'(0) = 2ά₂/T wherein r*(0) is the real part of the autocorrelation function value at zero, and r,"(0) is the second derivative of f_h(lTs) at zero .

5. Estimate the maximum Doppler frequency as f_d

The expression for f_d in the last step can be derived from expressions (2) and (3).

The autocorrelation value for =0 is omitted since its expectation value includes additive noise. The method in document [1] was designed for narrow-band mobile communication channels where

LT_s«\lf_d. (4)

The test case is shown in table 1. In the narrow-band mobile communication systems, 2 =41.6μs with a carrier frequency f_c of 900 MHz and a mobile velocity v=T00 km/h, giving/^ 83 Hz and l/(ftT_s) 290. In the third generation communications systems, velocities may be as high as 500 km/h df_c is of the order of 2GHz, giving a maximum f_d 900 Hz. A natural choice for T_s in WCDMA is the slot period 667μs. The resulting l/(/r_fTy is about 1.6. As a consequence, expression (4) is obviously not fulfilled.

Table 1

Furthermore, simulation results show that the method in document [1] has a good performance only for a small range off_d. So the method in document [1] is not fit for the third generation communications systems. Therefore there is a need for a method that can estimate the Doppler frequency over a wide range of frequencies.

Another method is disclosed in US patent 0172307 (in the following contexts named as document [2]), and is here named first zero detection. The first zero detection is based on finding the first zero, τ₀, of the autocorrelation function. Since r/_z(τ) is proportional to

Jo(2π/r_fτ) , the first zero of r/,(τ), τ₀, is given by

2.40 , . , . .. , 0.382 τ₀ « — — , which implies f_d « .

A linear interpolation is made between the first two adjacent samples of the real part of the autocorrelation function that have positive and non-positive sign, respectively. The first zero detection can give accurate estimates of fd up to about 400 Hz and reasonable results in the whole range of interest. As fd decreases τ₀ increases and more values of the autocorrelation function need to be calculated. This leads to higher complexity.

Furthermore the first zero detection is more sensitive to noise than the curve fitting method since it relies on two values only of r/,(τ) ,whereas as the curve fitting talces L values into account. When autocorrelation values for τ up to LT_S are calculated, first zero detection is not applicable if f_d < 0.382/ LT_S .

To sum up, the curve-fitting method is useful for lower Doppler spreads. As τ₀ increases, the first zero detection method becomes more and more complex. Neither the curve-fitting method nor the first zero detection method can be used for estimating Doppler spreads in all kinds of situations.

Summary of the invention

The purpose of the present invention is to provide a maximum Doppler frequency estimation method that is useful for all kinds of situations.

The technical scheme for implementing the purpose of the invention is that of a hybrid method for estimating maximum Doppler frequency. The method at least comprises: calculating autocorrelation functions of complex channel estimates from a received signal; detecting whether the autocorrelation function values become negative or 0 within a predefined lag threshold; if it is, estimate the maximum Doppler frequency with a method appropriate for high Doppler spreads, otherwise estimate the maximum Doppler frequency with a method appropriate for low Doppler spreads. Said autocorrelation functions are composite autocorrelation functions referring as:

P-\ N-l-L .

∑ ∑ h_j (n + I)h ' (n), wherein j labels the path and 1=0,1,..., L; {*,(«) j"^"1 is N j=ύ Λ=0 samples estimates of the complex channel for every path of P paths and * is the conjugate operator.

Said step of calculating composite autocorrelation functions further comprising: making N estimates [h_j («)/ _^"' of the complex channel for every path of P paths with sampling period T_s respectively, wherein/ labels the path andj-0,1,..., P-l; calculating the real part R_h(lT_s) of the composite autocorrelation function using both real and imaginary parts of the complex channel estimates (A .

as :

R_h (IT, ) = a

where / goes from 0 to L, L+l is the number of the autocorrelation function values to be calculated ; a is a constant .

Said method appropriate for high Doppler spreads is the first zero detection method, comprising: making an interpolation between the samples in the first set of adjacent samples of the real part of me composite autocorrelation function , R_h(lT_s), that have positive and non-positive sign to estimate τo which is the lag of the first zero of the composite autocorrelation function;

0.382 estimating the maximum Doppler frequency^ as f_d = ^■ ^T

Said interpolation is a linear interpolation.

Said method appropriate for low Doppler spreads is the curve fitting method, comprising: finding the curve fitting parameters ά_k as

ά_k = argmin_ni ζ R_h (lT_s ) -~Υ_Jk a_kl^k , where K is even and equal or greater than 0, the second sum is only over even values of k, and R/,f?7y is the real part of the composite autocorrelation function; obtaining the real part R^(0) of the composite autocorrelation function value at zero as R_Λ (0) = ₀ , and the second derivative R (0) of R_h(IT_s) at zero as R_k"(0) = 2ά₂/T_s ² ;

1 — 27?" (( estimating the maximum Doppler frequency f_d as f^ = — /

2π R_h (0)

Said predefined lag threshold, T, is less than or equal to L.

Furthermore, any Doppler spread should be considered as either low or high. Preferably, regarding the maximum Doppler frequency f_d which is greater than 0.382/(7T_s) as high Doppler spread, and, regarding the maximum Doppler frequency f_d which is less than 0.382/(7Ty) as low Doppler spread.

The invention solves the problem of estimating the maximum Doppler frequency not only for high Doppler spreads but also for low Doppler spreads. Through the method provided in the invention, the maximum Doppler frequency can be estimated more accurately over a wider range of Doppler spreads than prior art. Compared with prior art, the invention avoids the complexity of the estimation of maximum Doppler frequency only with first zero detection method. Furthermore, by calculating the real part of the composite autocorrelation function of the complex channel estimates for every path of P paths respectively, and by modifying the curve fitting method, the accuracy of the estimation of maximum Doppler frequency is greatly improved.

Brief Description of the Drawings Fig.l shows the difference between 2^nd order polynomial fit and 4^th order polynomial fit as Doppler spread increases.

Embodiments of the Invention The present invention now will be described more fully hereinafter with reference to the accompanying drawings, in which preferred embodiments of the invention are shown. This invention may, however, be embodied in many different forms and should not be construed as limited to the embodiments set forth herein; rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the invention to those skilled in the art. The invention estimates the maximum Doppler frequency according to the situations of whether the values of the real part of the autocorrelation function become negative or 0 within a predefined lag threshold. The proposed method is a hybrid method that utilizes two algorithms: a method suitable for low Doppler spreads, e.g. a modified version of the curve fitting method described in the previous section and a method suitable for high Doppler spreads, e.g. the first zero detection method. Furthermore, the autocorrelation function is replaced by a composite autocorrelation function, i.e., the sum of the autocorrelation functions of the channel estimates for different resolved multipaths. If only one multipath is resolved, the composite autocorrelation function reduces to the autocorrelation function.

The curve fitting method is modified to fit polynomials of higher degree than two to the calculated curve fitting parameters so that the accuracy of the estimation can be greatly improved. For example, using a 4^th degree polynomial, the range of f_d for which the curve fitting method is adequate is more than doubled. This, in itself, is however not enough to cover the range of interest.

The detailed steps of the hybrid method are shown below: 1. Make N complex channel estimates of every path,

, j=0,\,..., PA, from the received signal, with sampling period T_s, wherein j labels the path, and P paths are considered.

2. Calculate the real part of the composite autocorrelation function using both real and imaginary parts of the complex channel estimates of step (1):

R_h (lT_s) = a / = 0,1,...J,

where α can be any constant, e.g., α =1, P paths are taken into account. Here, because Rι,(lT_s) might be used for high Doppler spread, / also takes the value 0, in contrast to the method in document [1]. For example, in the first zero detection method, if Rj,(lT_s) is negative (/=T), then a linear interpolation between 1=0 and 1=1 can for instance be made to get an estimate of the maximum Doppler spread. Note that the value of R_h(lT_s) at 1=0 is not used for low Doppler spread since that value includes noise and is of poorer quality than for other /. 3. Let 7/ be a threshold such that T L. If R_h(lT_s) O for any I such that

, then use an estimation for high Doppler spread, e.g., the first zero detection method else use an estimation for low Doppler spread, e.g., the curve fitting method. Here, T should be chosen so that the most accurate method of the first zero detection method and the curve fitting method is used.

In step (3), the first zero detection method is described below: a. For the smallest value of /, 0<l T with R_h(lT_s)^0 estimate the first zero, τ₀ of R_/, by interpolation, e.g., using linear interpolation of R_h((l-1)T_S) and R_h(lT_s), i.e. a linear interpolation is made between the first two adjacent samples of the real part of the composite autocorrelation function that have positive and non-positive sign, respectively.

Of course, the interpolations can be others such as quadratic interpolations, cubic interpolations etc, so the first set of adjacent samples of the real part of the composite autocorrelation function that have positive and non-positive sign are needed.

0 382 b. Estimate the maximum Doppler frequency as f_d = — . ^τo In step (3), the curve fitting method is described below:

a. Find the curve fitting parameters a_k = argmin_fli ^T R_h (lT_s ) - ^_k a_kl

where the second sum a,.l ^c is over all even numbers from 0 to K. K is not restricted to 2 as in document [1]. b. Obtain R_h (0) = ά₀; R '(0) = 2ά₂/T_s ² , wherein R_h(0) is the real part of the composite autocorrelation function value at zero, and R_/'(0) is the second derivative of Rι,(lTs) at zero .

c. Estimate the maximum Doppler frequency f_d as f_d =

f Of course, the velocity of the mobile can be estimated as v = — — c .

J c

Compared to the prior art of the curve fitting method, the parameters ά_k are modified to improve the accuracy of the estimation. The cause is shown as below:

When K=2 the estimation is good as long as the part of the autocorrelation function to fit to the polynomial to has a parabolic shape, which is indeed the case for the lowest maximum Doppler spreads. However, as the Doppler spread increases, the error of estimation with the curve fitting method will become larger. A higher order polynomial fit will increase the range of Doppler spreads for which the estimator has certain accuracy. See figure 1 that illustrates what happens as the Doppler spread increases (going from left to right). The dotted line is theoretical autocorrelation functions R/_;(t), the dashed line is the 2^nd order polynomial fit (K=2), and the solid line is the 4^th order polynomial fit (K-4 . In the left graph, there is no difference between the two fits, but with the Doppler spread increasing; there is already a big difference.

The invention can be applied to any receiver that receives a radio signal containing a sequence of pilot symbols. It can be applied in a mobile communications system regardless the multiple access scheme.

While the present invention has been described with respect to particular example embodiments, those skilled in the art will recognize that the present invention is not limited to those specific embodiments described and illustrated herein.

Claims

1 Ϊ A method for estimating maximum Doppler frequency, comprising: calculating autocorrelation functions of complex channel estimates from a received signal; detecting whether the values of the real part of the autocorrelation function become negative or 0 within a predefined lag threshold T; if it is, estimate the maximum Doppler frequency with a method appropriate for high Doppler spreads, otherwise estimate the maximum Doppler frequency with a method appropriate for low Doppler spreads.

2 The method of claim 1, wherein the autocorrelation functions are composite p-\ Ή-\-L autocorrelation functions referring as: T h_j (n + l)h^* (n), wherein j labels the 0 «=0 path and 1=0, 1, ..., L; ψ_j ri)j ^~ is N estimates of the complex channel for every path of P paths, and _* is the conjugate operator.

3 The method of claim 2, the step of calculating composite autocorrelation functions further comprising: making N estimates ψ (")/ _^"' of the complex channel for every path of P paths with sampling period T_s , respectively; calculating the real part R/,(/7 ) of the composite autocorrelation function using both real and imaginary parts of the complex channel estimates h_j

as :

where goes from 0 to L, L+l is the number of the autocorrelation function values to be calculated ; a is a constant .

4 The method of claim 2 or 3, wherein the method appropriate for high Doppler spreads is the first zero detection method, comprising: making an interpolation between the samples in the first set of adjacent samples of the real part of the composite autocorrelation function, R_h(lT_s) , that have positive and non-positive sign to estimate τo which is the lag of the first zero of the composite autocorrelation function;

0 382 estimating the maximum Doppler frequency^ as f_d = — . ^τo

5 -, The method of claim 4, wherein the interpolation is a linear interpolation.

6> The method of claim 2 or 3, wherein the method appropriate for low Doppler spreads is the curve fitting method, comprising:

2 finding the curve fitting parameters ά_k as ά_k = argmin_a/, R_h (lT_s) - a_kl^k ,

where the second sum _k a_kl^k is over all even numbers from 0 to K, K is an even number, and R_h(lT_s) is the real part of the composite autocorrelation function; obtaining the real part Rή(0) of the composite autocorrelation function value at zero as R_h (0) = ά₀ , and the second derivative R (0) of R_Λ( 7 at zero as R_h"(0) = 2a₂/T_s ² ;

estimating the maximum Doppler frequency f as f_d =

7> The method of claim 3, wherein the predefined lag threshold T, is less than or equal to L.

8 The method of claim 3, further comprising: regarding the maximum Doppler frequency f_t which is greater than 0.382/(TT_s) as high Doppler spread, and, regarding the maximum Doppler frequency f_t which is less than 0.382/( TT_S) as low Doppler spread.

π