GB2394131A

GB2394131A - Frequency offset estimator

Info

Publication number: GB2394131A
Application number: GB0223604A
Authority: GB
Inventors: Laolu Lijofi
Original assignee: Matsushita Electric Industrial Co Ltd
Current assignee: Panasonic Holdings Corp
Priority date: 2002-10-10
Filing date: 2002-10-10
Publication date: 2004-04-14
Anticipated expiration: 2022-10-10
Also published as: GB2394131B; GB0223604D0

Abstract

A radio receiver has a frequency offset predictor, which predicts the offset between a carrier frequency of a transmitter and a local reference frequency, and is capable of operation even in noisy conditions. As the carrier frequency is not known by the receiver, it is predicted from a calculation involving convolution of an estimate of the transmitted signal and an estimate of the channel impulse response. The frequency offset is estimated by calculating the phase difference between the received signal and the predicted received signal over a sampling period which may be determined by the amount of noise in the received signal. The relationship between successive phase difference is approximated, and the frequency offset is estimated from this relationship. The relationship may be linear in the sample number, and the frequency offset may be determined from the gradient of this linear relationship by linear regression, weighted averaging or a cross correlation process.

Description

Frequency Offset Estimator The present invention relates to a frequency

offset estimator (FOE) for estimating a frequency offset between a carrier frequency of a transmitter and a local reference frequency of the receiver in a communication system.

An offset or frequency difference usually exists between the receiver and transmitter frequencies in a communication system. This difference is caused by non-

idealities/instabilities in the receiver frequency oscillator and/or transmitter oscillator and Doppler offset due to relative motion between the transmitter and the receiver. It is necessary to compensate or correct for this offset, otherwise decoding errors may occur at the receiver. Thus, to improve receiver operation, this frequency offset should be estimated and corrected. Frequency offset estimation is particularly important in mobile communications systems but has applications in other areas.

US patent 4447910 discloses a phase tracking correction scheme for a high frequency modem using the differences in phase between actually received and predicted samples to correct the phase of the received samples. Each received sample is phase corrected by a constant plus an additional correction which increases linearly with time and is in effect a "frequency ofl'set" correction.

International patent application WO 01/86904 A discloses a method of estimating frequency offset. In this method, a phase difference is computed between successively collected samples of a frequency synchronization signal. Phase differences of successively collected samples are computed and added to produce the estimated frequency offset. The addition may be performed using linear regression or by computing a weighted average. These and other known methods of frequency offset estimation are useful in low noise/high signal environments but do not perform satisfactorily in noisy conditions. There is therefore a need for a method which is snore effective in noisy conditions.

The present invention provides a method of estimating a frequency offset in a radio receiver between a carrier frequency of a transmitter and a local reference frequency of the receiver, the method comprising the steps of a) calculating phase differences between respective samples of a received signal and a predicted received signal; b) approximating a relationship between successive calculated phase differences; and c) estimating the frequency offset from one or more parameters of said relationship. The invention also provides a frequency offset estimator employing the above method.

In an ideal situation, the relationship between successive phase differences is linear in k where k is the sample number. Therefore, it is this relationship that is approximated in the preferred embodiment of the invention. The frequency offset may be determined from the gradient of the linear relationship.

Linear regression techniques may be used to determine the gradient.

The sampling period may be determined in dependence on the amount of noise in the received signal. Because of this adjustability, the method is more accommodating of noise in the received signal.

The expected signal is the convolution of the transmitted signal and the channel impulse response. However, the receiver will not have knowledge of these functions. Therefore, in the preferred embodiment of the invention, an estimate of the transmitted signal is convolved with an estimate of channel impulse response to produce the predicted received signal.

An embodiment of the invention will now be described by way of example only and with reference to the accompanying drawing which is an illustration of the "reconstruction" of the transmitted signal burst.

Fundamentals An estimate of the frequency offset is obtained by computing the phase differential between successive samples of the received burst and the expected received burst.

Assume it(k) = kth sample of the actual received burst = Akei2n(f +^f) kTsOji ( I) R E (k) = k ah sample of the expected burst = Bke j2nfckTs e jA3 (2) fc = nominal carrier frequency.

Af = frequency offset in received burst.

Ts = sampling time.

Ak = amplitude of the kth sample of the actual received burst.

Bk = amplitude of the kth sample of the expected burst.

L = length of received burst (i.e. number of samples).

= received burst phase.

XE = expected burst phase.

The objective of the FOE is thus to obtain an estimation of of from R and RE (i.e. from equations (1) and (2)).

The phase of the actual and expected burst can be expressed, from (1) and (2), by calculating the arctangent of the ratio of the imaginary part (Q-) and real part (I-), as OR (k) = phase of the kth sample of the actual burst = 2n(fC + Af)kTs + (3) PRr (k) = phase of the kth sample of the expected burst = 211fCkTs + HE (4) From (3) and (4) it can be shown that the phase difference, A(k), between the kth sample of the actual and expected burst is: (ok) = IR (k)- FIRE (k) = 2rlfkTs + (A - XE) (5)

Equation (5) is a linear equation (in k), comparing (5) with the general equation of a straight line, y(x)=mx+c, it can be shown that m = gradient = 2IlAfTs (6) c = y_intercept = (\ - kE) From (6), the estimated frequency offset is given by of = m (= gradient) 2nTS Hence to obtain the estimated offset, the gradient (or first derivative with respect to each sample of the burst) of the phase difference (between the actual and predicted burst) must be obtained.

Linear regression methods may be applied to obtain the 'line of best fit' for the phase difference values obtained per sample. The frequency offset is calculated by substituting the gradient of the 'best fit' line into (7) .

Linear Regression Suppose M measurements Of Y= [Y! YM] at sample instances X= [X,XM] are taken.

Let y(x) = me + c be the equation of the 'line of best fit' that approximates the relationship between the dependent variable Y and the independent variable X. What values of 'm' and 'c' are appropriate such that the mean square error between the actualmeasurements Y=[y,...yM]and y(X)=mX+c isminimised? The mean square error, E, is given by M E= [Yi (mx; +C)]2 (8) i=l Taking and equating the is' partial derivatives of (8) with respect to 'm' and 'c', to zero simplifies to am x i [Yi - (mx; + c)] = 0 (9 ]=1

M aC =[Yi -(mad +c)]=0 (10) I=1 M M M M M M

Let Sx=xi; Sy=yj; Sxx=xixi; Sxy=xjyi;s3iy=yiyi; S=1 (11) i=l i=1 i=1 i=1 i=1 i=1 It can be shown that solving (9) and (10), gives the gradient, m, of the line of best fit m = SSXY -sxsY (12) SSXx -sxsx The foregoing represents a second order linear regression process.

Thus substituting (12) into (7) gives 2nTe (ss,, -SxSx) ( 13) Recall from (5) that A(k) = 2nAfkTs + (A - HE) SO replacing 'y' with (ok) and 'x' with 'k', the equivalence of (13) is SSk,-Sk So ( 14) 2nT5 (SSkk-SkSk) is the required estimated frequency offset.

To reduce computational complexity, the computation required to achieve frequency offset estimation may be simplified by using either or both of the following: À The number of phase differences computations, M, can be varied per burst, i.e. number of samples needed to perform linear regression (LR) can be changed from burst to burst depending on channel conditions (usually evident from the amount of noise in the received signal).

À The gradient, m of equation (12) can be simplified to m=Sxy (12b) Sxx M if the variable 'x' is chosen such that SX =x; =o i=l This implies from equation ( 14) that Af= nSk6S = estimated offset (14b)This is in effect a weighted averaging or cross correlation technique for determining the gradient, m. Constructing the predicted burst

As shown in the preceding sections, obtaining the frequency offset involves constructing' the predicted received burst. Ideally, the expected (predicted) burst is the convolution of the transmitted burst and the channel impulse response. However, the receiver has no prior knowledge of both. Hence an estimate of the transmitted burst is convolved with the estimate of channel impulse response (i.e. provided by the channel estimator) to produce the predicted burst.

In other words, the predicted received burst, as the name connotes, represents the predicted burst at the receiver given knowledge of the transmitted burst and the propagation channel conditions. It is obtained by convolving the estimated channel impulse response (CIR) with an estimate of the transmitted burst - an estimate of the transmitted burst is used because it may not be possible to accurately determine, at the receiver, the actual transmitted burst due to channel-induced errors.

Figure I illustrates how the transmitted burst is reconstructed for a normal burst (NB) or a synchronization burst (SB) in a GSM signal to produce the aforementioned estimate of the transmitted burst. This particular example uses equalised SOVAs (soft output Viterbi algorithm) which are then hard coded (i.e. subject to hard decisions). In general any soft decision output can be handled in the same way. The output values will typically be in the form of percentages or probability values. The method illustrated in Figure 1 is summarised below: À The data bits of the NB or SB are replaced by performing threshold detection (or hard coding or hard decision making) on the corresponding equalised soft- output (obtained from the equaliser).

Two schemes are proposed, the choice of which will depend on the equalization technique used by the receiver equaliser.

Scheme 1: if ith equalised Soft-output (Si) < Threshold (T) predicted data bit = logical 'O' else predicted data bit = logical '1' Scheme 2: if it'' equalised Solt-output (Si) > Threshold (T) predicted data bit = logical 'O'

else predicted data bit = logical '1' OR the data bits are replaced by the corresponding output of an equaliser (producing hard bits).

À The tail bits and training sequence codes are inserted in the bursts appropriately.

The estimate of the transmitted burst thus obtained is then convolved with an estimate of the channel impulse response in order to obtain the predicted received signal. In the case of the NB or SB this is conveniently derived from the training sequence contained in the signal burst using known CIR estimation techniques.

Claims

Claims:

1. A method of estimating a frequency offset in a radio receiver between a carrier frequency of a transmitter and a local reference frequency of the receiver, the method comprising the steps of: a) calculating phase differences between respective samples of received signal and a predicted received signal, b) approximating a relationship between successive calculated phase differences; and c) estimating the frequency offset from one or more parameters of said relationship.

2. A method as claimed in claim 1 in which the relationship is linear in k, where k is the sample number.

3. A method as claimed in claim 2 in which the frequency offset is determined from the gradient of the linear relationship.

4. A method as claimed in claim 3 in which the gradient is determined using linear regression.

5. A method as claimed in claim 3 in which the gradient is determined from a weightd averaging or cross correlation process.

6. A method as claimed in claim 3,4 or 5 in which the frequency offset is determined from the equation Af = Kcm where Af = frequency offset in received signal burst m = gradient of relationship between phase difference and sample number and Kc = a constant.

7. A method as claimed in claim 3,4 or 5 in which the frequency offset is determined from the equation Of= m 2nTs where Af = frequency offset in received signal burst m = gradient of relationship between phase difference and sample number (k) Is = sampling period.

8. A method as claimed in any preceding claim in which the sampling period is determined in dependence on the amount of noise in the received signal.

9. A method as clamed in any preceding claim in which the number of phase difference computations carried out per transmitted burst is varied from burst to burst depending on channel conditions.

10. A method as claimed in any preceding claim in which an estimate of the transmitted signal is convolved with an estimate of channel impulse response to produce the predicted received signal.

11. A method as claimed in claim 10 in which the estimate of the transmitted signal is obtained by hard-coding the soft output of the receiver equaliser.

12. A method as claimed in claim l l in which the soft output values are subject to a thresholding process to generate a binary digit for each soft output value.

13. A method as claimed in claim 11 or 12 in which the transmitted signal contains fixed data and variable data and in which the hard-coding process is carried out on the variable data only.

14. A method as claimed in claim 13 in which the fixed data is inserted into the hard coded data to construct the predicted received signal.

15 A method as claimed in claim 13 or 14 when dependent on claim 10 in which the fixed data contains training data which is used to estimate the channel impulse response.