WO1993000741A1

WO1993000741A1 - A method for optimizing an adaptive filter update coefficient

Info

Publication number: WO1993000741A1
Application number: PCT/US1992/003767
Authority: WO
Inventors: Kevin L. Baum
Original assignee: Motorola, Inc.
Priority date: 1991-06-28
Filing date: 1992-05-08
Publication date: 1993-01-07
Also published as: CA2086548C; KR960011120B1; JPH06500913A; GB2264600A; DE4292034T1; US5276707A; KR930701866A; DE4292034C2; JP2960165B2; US5230007A; GB9303631D0; GB2264600B; MX9203306A; BR9205341A

Abstract

The method of the present invention generates an optimal adaptive filter update coefficient by first generating three error signals using a signal input and three update coefficients (301-303). Mean Square Error (MSE) values are estimated (307 and 308) for the first and third error signals. The first MSE value (307) is subtracted (309) from the third MSE value (308) to generate a difference signal. The difference signal is used to generate (310) an update signal that is used to modify the update coefficients. The process of the present invention is repeated until the difference signal is substantially zero, thus optimizing the second update coefficient. This process enables an update coefficient for an adaptive filter to quickly adapt to a changing environment.

Description

A METHOD FOR OPTIMIZING AN ADAPTIVE FILTER UPDATE COEFFICIENT

Field of the Invention

The present invention relates generally to the field of communications and particularly to digital cellular commu¬ nications.

Background of the Invention

U.S. digital cellular communications uses digitized voice and data signals for communication between a mobile telephone and a base station. When the mobile moves, it may encounter degraded communication channels due to noise and multipath distortion; both noise and distortion varying with time. The multipath distortion is due to a signal being received by the mobile at different times when it bounces off buildings and terrain. Multipath channels can cause inter- symbol interference (ISI) that can be removed with an adap¬ tive equalizer, a specific type of an adaptive filter.

A typical adaptive filter is illustrated in FIG. 1. The in¬ put signal (106) is processed by the adaptive filter (101), pro¬ ducing the adaptive filter output signal (102). The output of the filter is then subtracted (105) from a reference signal (103), to produce an error signal (104). This error signal (104) is used by an adaptive algorithm with an update coefficient, μ, in the adaptive filter to update the filter coefficients. The update coefficient is also referred to as a tracking coefficient or mem- ory coefficient. It is assumed that the memory of the adaptive algorithm increases as the value of μ increases.

The update coefficient controls the memory of the adap¬ tive algorithm and its determination is a trade-off between the rate that the filter can track the changing channel character- istics and the amount of noise averaging that will be accom¬ plished by the adaptive algorithm. As the adaptive algorithm memory is shortened, the algorithm is better able to track time variations in the communication channel but will become more sensitive to noise on the communication channel. If the coefficient is chosen to filter out more noise, then filter's channel tracking capability will be reduced.

The adaptive algorithm can be a Ealman, Recursive Least Square, or Least Mean Square (LMS) algorithm. The typical goal of the adaptive algorithm is to minimize the mean square value of the error signal (104). This value is typically designated mean square error (MSE).

FIGs. 2A, B, and C illustrate the three possible classes of adaptive filter operating environments. FIG. 2A is a time invariant system in a noisy environment. In this case, the to¬ tal MSE, designated ET, comes only from the noise, designated E_n, since the system is not time varying. The total MSE is pro¬ portional to μ.

FIG. 2B is a time varying but stationary system in a noisy environment; a stationary system having higher order signal statistics that do not change over time, hi this exam- pie, E (203) consists of the sum of two independent compo¬ nents, the lag error (201) and the noise (202). The lag error (201) is due to the filter attempting to track the time varying system. The lag error (201), designated EL, is inversely pro¬ portional to μ. The noise component (202) is due to the noisy environment as illustrated in FIG. 2A. It can be seen in FIG.

2B that the total MSE can be minimized by choosing the value of μ corresponding to the intersection of the curves (204).

The last environment is a time varying, non-stationary system in a noisy environment. The total MSE in this case consists of the same components as in FIG. 2B. The differ¬ ence between the two systems is that in this case, the curves are shifting or changing slope over time causing the mini¬ mu point on the curve to shift thus changing the optimal value of μ over time. This environment is illustrated by com- paring FIGs. 2B and 2C. FIG. 2B represents the MSE charac- teristic at some time ti while FIG. 2C represents the MSE characteristic at some later time t₂.

A fixed update coefficient in the last environment would not provide adequate filter performance due to the changing environment. There is a resulting need for automatically adapting the update coefficient according to the vehicle speed and channel conditions thereby improving filter performance.

Summary of the Invention

The method of the present invention produces an opti¬ mum adaptive filter update coefficient in an apparatus having a plurality of adaptive algorithms, each adaptive algorithm having an update coefficient. The method starts by comparing performances of each of the plurality of adaptive algorithms then modifying the update coefficients in response to a differ¬ ence in the performances.

Brief Description of the Drawings

FIG. 1 shows a block diagram of a typical adaptive fil¬ ter.

FIGs. 2A, B, and C show three different adaptive filter operating environments.

FIG. 3 shows a block diagram of the preferred embodi¬ ment of the process of the present invention.

FIG. 4 shows a block diagram of an alternate embodi¬ ment of the process of the present invention. FIG. 5 shows a graph of MSE versus μ in accordance with the process of the present invention.

FIG. 6 shows a plot of a fixed update coefficient and an optimized update coefficient in accordance with the process of the present invention. FIG. 7 shows a plot of an update coefficient, in accor¬ dance with the process of the present invention, in a delay spread environment.

The process of the present invention provides automatic adjustment and optimization of an adaptive filter update coef¬ ficient in a changing environment. The update coefficient is continuously updated by a feedback signal that is generated by the filtered difference between MSE estimates for two adaptive filters.

A block diagram of the preferred embodiment of the process of the present invention is illustrated in FIG. 3. The process is comprised ofthree adaptive filters (301 - 303). Each of the filters is identical except for having different update co¬ efficients, μi, μ₂, and μ₃- The second update coefficient, μ₂, is the coefficient that is optimized by the process. The optimal update coefficient is subsequently referred to as μ*. Since μ₂ is the optimized update coefficient, the second adaptive filter

(302) is the filter used to perform the actual desired adaptive filtering function.

The update coefficients have the following relationship:

μι < μ2 < μ3 μi = μ2 - μa μ3 = μ2 + μa,

where μ_<_ is a constant chosen for the particular system in which the communication device is to operate as well as the particular adaptive algorithm used. In an alternate embodi¬ ment, μa would vary with time as the update coefficients change. In the preferred embodiment, μ_<_ is 0.01 using an LMS adaptive algorithm. The process first generates error signals from the adap¬ tive filters (301 - 303). This is accomplished by the adaptive fil- ters (301 - 303) filtering the input signal in such a way that it forms a signal that matches the reference signal as close as possible. In the preferred embodiment, the input is the de¬ tected symbols in the communication receiver. These output signals are referred to as OUTPUT1, OUTPUT2, and

OUTPUT3 in FIG. 3. Each output signal from the filters is then subtracted (304 - 306) from a reference signal. In the pre¬ ferred embodiment, the reference signal is the received signal. The difference between these two signals is the error signal.

Mean square error estimates are performed (307 and 308) on the error signals from the first and third adaptive fil¬ ters (301 and 303). The MSE for each error signal is estimated as follows: lc + n

X lerrorlp

k + n

∑ |eιroτ3f

where k is the start value and n is the number of samples of the error signal. For example, if k = 1 and n ^■= 10 for the first estimation cycle, k will start at 12 for the next cycle.

The difference between the estimated MSE's (309), _d s E-π - E ₃ , provides an indication of which direction to move along the μ axis to get closer to μ*. In the preferred em¬ bodiment, E_d is input to a comparator (310) where it is com¬ pared to 0. If E_d < 0, then μi is closer to μ* than μ₃. The coeffi¬ cients, therefore, should be decremented in order to move μ₂ closer to μ*. In this case, the coefficient updates are illus- trated as follows:

if E < 0 then: μi = μi - Δ μ₂ = μ₂ - Δ μ3 - μ3 - Δ,

otherwise, if E > 0 then the coefficients should be incre- mented:

μi = μ_x + Δ μ2 = μ₂ + Δ μ3 = μ3 + Δ,

where Δ is the update coefficient step size. This value is appli¬ cation dependent. Δ can be chosen as a very small value for time invariant and stationary environments and slightly larger for non-stationary environments. This value deter- mines the resolution of the update coefficient estimate and the adaptation speed of the update coefficient. In the preferred embodiment, Δ is 0.005 using an LMS adaptive algorithm. As with μ_d, in an alternate embodiment, Δ could vary with time. In an alternate embodiment, illustrated in FIG. 4, E is input to a filter (410) instead of a comparator. The filter pro¬ vides a time varying step size (compared to the fixed step size Δ) that is responsive to the size of the error difference signal. For example, when the error difference signal becomes large, the step size automatically increases resulting in faster con- vergence of the algorithm. Using the filter, however, in¬ creases the complexity of the invention and may cause stabil¬ ity problems if a higher order filter is used. A first order digi¬ tal infinite impulse response (IIR) filter is preferred due to stability and simplicity considerations. In this case, the up- date coefficients are adapted by adding the value of the output of the filter to the coefficients.

After several adaptation iterations, μi is slightly smaller than μ*, μ₃ is slightly larger than μ*, μ₂ is approxi¬ mately equal to μ*, and the error difference signal is approx- innately zero. Adaptive filter 2 (302) is now optimized for the current environment. If the environment changes, the pro- cess of the present invention detects and tracks the change to maintain the optimality of adaptive filter 2 (302).

The above described process can be illustrated graphi¬ cally as seen in FIG. 5, a plot of MSE versus μ. In the case where E < 0, En and E ₃ (501) are on the right part of the curve and must move down the curve to the left in order to lo¬ cate μ₂ at the bottom of the curve which is the optimum point. This requires decrementing the update coefficients by Δ to move μ₂ closer to the μ* point. Similarly, if E_d > 0, Eτι and E ₃ (502) are on the left part of the curve and must move down the curve to the right to locate μ₂ at the optimum point. This re¬ quires incrementing update coefficients by Δ to move μ₂ closer to the μ* point (503).

The improvement using the process of the present in- vention over a fixed update coefficient is illustrated in FIGs. 6 and 7. In these graphs, the process is used with a least mean square (LMS) adaptive channel estimator in simulations of a Maximum Likelihood Sequence Estimation equalizer for the U.S. digital cellular system. The fixed update coefficient is set at μ = 0.38 to allow adequate performance when the mobile ra¬ diotelephone is traveling in vehicle at high speeds. By using the process of the present invention, the performance of the equalizer is improved at significantly lower vehicle speeds, as illustrated in FIG. 6. FIG. 6 shows the performance of the equalizer as a function of multipath delay and the vehicle speed is approximately 5 mph. FIG. 7 shows how the process operates in a channel with delay spread and co-channel inter¬ ference when the vehicle speed drops instantaneously from 63 mph to 5 mph. It can be seen that the update coefficient quickly decreases to a new lower level suitable for the lower vehicle speed.

In the preferred embodiment, the process of the present invention is implemented as an algorithm. Alternate embod¬ iments of the invention can be implemented in hardware or combinations of hardware and software; each block of the pro- cess being either an algorithm or a hardware circuit equiva¬ lent of that block.

In summary, a process of automatically optimizing an adaptive filter update coefficient in a changing environment has been described. By comparing the performance of each adaptive algorithm to determine how to change the update co¬ efficients, an optimal update coefficient for that particular en¬ vironment can be obtained. Communication devices using the process of the present invention can out-perform devices using a fixed update coefficient.

Claims

1. A method for generating an optimum adaptive filter update coefficient in an apparatus having a plurality of adaptive algo- rithms, each adaptive algorithm having an update coefficient, the method characterized by the steps of: comparing performances of each of the plurality of adaptive algorithms; and the method further characterized by modifying the update coefficients in response to a dififer- ence in the performances.

2. A method for generating an optimal adaptive filter update coefficient in an apparatus having an input signal, the method characterized by the steps of: generating a first error signal in response to the input signal and a first update coefficient; generating a second error signal in response to the in¬ put signal and a second update coefficient; generating a third error signal in response to the input signal and a third update coefficient; estimating a first mean square error in response to the first error signal; estimating a second mean square error in response to the third error signal; subtracting the second mean square error from the first mean square error to produce a mean square error difference; generating an adaptation signal in response to the mean square error difference; modifying the first, second, and third update coeffi- cients in response to the adaptation signal; and the method further characterized by repeating from the first step to make the mean square error difference substantially zero.

3. The method of daim 2 and fiirther characterized in that the first, second, and third error signals are generated by adaptive filters.

4. The method of daim 3 and further characterized in that the adaptive filters are adaptive equalizers.

5. The method of dai 2 and further characterized in that the adaptation signal is generated by comparing the mean square error difference to zero.

6. A method for generating an adaptive filter update coeffi- ent in an apparatus having an input signal, the method characterized by the steps of: filtering the input signal, in a first adaptive filter hav¬ ing a first update coeffident, to generate a first error signal; filtering the input signal, in a second adaptive filter having a second update coeffident, to generate a second error signal; filtering the input signal, in a third adaptive filter hav¬ ing a third update coeffident, to generate a third error signal; estimating a first mean square error in response to the first error signal; estimating a second mean square error in response to the third error signal; subtracting the second mean square error from the first mean square error to produce a mean square error difference; filtering the mean square error difference to produce an adaptation signal; modifying the first, second, and third update coeffi- dents in response to the adaptation signal; and the method further characterized by repeating from the first step to make the mean square error difference substantially zero.

7. The method of daim 6 and further characterized in that the first, second, and third adaptive filters are adaptive equalizers.

8. A method for generating an adaptive filter update coeffi¬ dent in an apparatus having an input signal, the method characterized by the steps of: filtering the input signal, in a first adaptive filter hav¬ ing a first update coeffident, to generate a first error signal; filtering the input signal, in a second adaptive filter having a second update coeffident, to generate a second error signal; filtering the input signal, in a third adaptive filter hav¬ ing a third update coeffident, to generate a third error signal; estimating a first mean square error in response to the first error signal; estimating a second mean square error in response to the third error signal; subtracting the second mean square error from the first mean square error to produce a mean square error difference; comparing the mean square error difference to a prede¬ termined value to produce an adaptation signal; modifying the first, second, and third update coeffi- dents in response to the adaptation signal; and the method further characterized by repeating from the first step to make the mean square error difference substantially zero.

9. The method of claim 8 and further characterized in that the first, second, and third adaptive filters are adaptive equalizers.

10. The method of claim 8 and further characterized in that the predetermined value is zero.