WO1993000747A1

WO1993000747A1 - Automatic frequency control by an adaptive filter

Info

Publication number: WO1993000747A1
Application number: PCT/US1992/003763
Authority: WO
Inventors: Kevin L. Baum; Bruce D. Mueller
Original assignee: Motorola, Inc.
Priority date: 1991-06-28
Filing date: 1992-05-08
Publication date: 1993-01-07
Also published as: JP2830471B2; DE4292274T1; CA2089154A1; GB9303663D0; JPH05508989A; GB2263829A; GB2263829B; DE4292274C2; KR960005386B1; MX9203307A; KR930701869A; CA2089154C

Abstract

The process of the present invention generates an optimum automatic frequence control signal in an apparatus that has a plurality of adaptive algorithms, each adaptive algorithm having a reference signal with an associated frequency dither. The process starts by comparing the performance of each of the plurality of adaptive algorithms. This difference is input to a comparator (6) where it is compared to zero. This delta signal then modifies the numerically controlled oscillator frequency (8). After several iterations, the frequency offset is reduced to substantially zero.

Description

AUTOMATIC FREQUENCY CONTROL BY AN ADAPTIVE

FILTER

Fi_=M of tl__e Invention

The present invention relates generally to the field of communications and particularly to automatic frequency con¬ trol.

Background of the Invention

U.S. digital cellular (USDC) communications uses digi¬ tized voice and data signals for communication between a mo¬ bile telephone and a base station. The mobiles and bases em- ploy time division multiple access (TDMA) modulation for the transmission of these signals. A typical format for the TDMA data bursts is illustrated in FIG. 5. This data burst, as well as USDC in general, is discussed in more detail in the USDC specification EIA/TIA IS-54 available from Electronic Industries Association, Engineering Department, 2001 Eye

Street, N.W., Washington, D.C. 20006.

When the mobile moves, it may encounter degraded communication channels due to noise and multipath distor¬ tion; both noise and distortion varying with time. The multi- path 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 adaptive channel equalizer, a specific type of adaptive filter. An adaptive channel estimator is another type of 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), typically the unfiltered input signal (106), to produce an error signal (104). This error signal (104) is used by an adaptive al- gorithm with an update coefficient, μ, in the adaptive filter to update the filter coefficients. The update coefficient is also re¬ ferred to as a tracking coefficient or memory coefficient. The memory of the adaptive algorithm increases as the value of μ increases.

The adaptive algorith may be a Kal an, 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), fixed update coefficient. This value is typically designated mean square error (MSE). A detrimental characteristic of adaptive channel equal¬ izers is that they can experience degraded performance in the presence of a frequency offset of more than approximately 10 Hz (in a system with a 24 kHz symbol rate). While the speάfi- cation for a transmission system requires a certain frequency variation limit, the adaptive channel equalizer may require a stricter limit. An example is the USDC system. USDC re¬ quires the receiver operating frequency to be locked within 200 Hz of the transmitter. The adaptive channel equalizer will not perform properly in this environment. A coarse automatic frequency control (AFC) is typically used to remove most of the offset. Any remaining offset, however, can detrimentally af¬ fect a detection algorithm and increase the detected bit error rate. There is a resulting need for an AFC that can reduce the frequency offset to an acceptably small level and track any variation of the offset as the environment changes when the mobile moves.

Summary of the Invention

The process of the present invention generates an opti¬ mum automatic frequency control signal in an apparatus that has a plurality of adaptive algorithms, each adaptive algo¬ rithm having a reference signal with an associated frequency dither. The process starts by comparing the performance of each of the plurality of adaptive algorithms then modifying the automatic frequency control signal in response to a difference in the performances.

Brief Description of the Drawings

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

FIG. 2 shows a block diagram of the process of the pre- sent invention.

FIG. 3 shows a graph of mean square error versus residual frequency offset in accordance with the process of the present invention.

FIG. 4 shows a graph of residual frequency offset ver- sus time in accordance with the process of the present inven¬ tion.

FIG. 5 shows the format of a TDMA data burst used in the U.S. digital cellular communication system.

FIG. 6 shows an alternate embodiment of the process of the present invention.

Detailed Description of the Preferred Embodiment

The process of the present invention provides fine au- tomatic frequency control in a device using adaptive filters.

The difference in performance of the adaptive filters is used to modify the AFC signal, thereby reducing the frequency offset.

A linear coherent digital radio receiver typically de¬ modulates the incoming signal by mixing the signal to base- band using a local oscillator. The frequency of the local oscil¬ lator must be kept reasonably close to the frequency of the transmitter. After the signal has been mixed down to base¬ band, further analog or digital signal processing is performed to recover an estimate of the transmitted data. In the follow- ing description of the process of the present invention, it is as¬ sumed that the baseband signal has been converted by an ana- log to digital converter to a form suitable for further digital signal processing.

The preferred embodiment of the process of the present invention, as illustrated in FIG. 2, is comprised of three adap- tive filters (1 - 3) configured as adaptive channel estimators (ACE). The three ACE's (1 - 3) have an update coefficient, μ, that varies with the environment of the device. The process for determining μ is described in co-pending application titled "A Method for Optimization of Adaptive Filter Update Coefficient" (Docket No. CE00473R) to Kevin Baum and as¬ signed to Motorola, Inc. The update coefficient will remain constant during a single TDMA data burst.

The three ACE's (1 - 3) are identical except for having different frequency offset dither generators, a dither generator being the source of the reference signal. ACE 2 uses the base¬ band received signal that has been mixed (9) with the numeri¬ cally controlled oscillator (NCO) (8) signal as the reference signal. ACE's 1 and 3 mix (11 and 12) this reference signal with frequency offsets before using it as a reference signal. The frequency offsets, ete* and e-i⁰¹*, and their relation¬ ship to the desired residual frequency offset, ω^*, are illustrated graphically in FIG. 3. These offsets are located on either side of the frequency offset estimate, -α>v. ACE's 1 and 3 act as residual frequency offset "probes"; relative to ACE 2, ACE 1 acts as a "high" frequency probe and ACE 3 acts as a "low" fre¬ quency probe. ACE's 1 and 3 estimate two points on the MSE curve. ACE 2 performs the actual desired adaptive filtering function.

The k term of the frequency offset denotes the time in- dex of the sample. The ®d term is application dependent, ©d should be chosen as small as possible while still allowing a difference in the mean square errors (MSE) to be detected. ®d could also vary with time by setting it to a larger value initially to speed acquisition and then reduced to get the most accurate frequency offset estimate. In the preferred embodiment, < i is set to a value of 5 x (2π) radians/second. In operation, the process of the present invention ini¬ tially removes the current estimated frequency offset, -<*>v, from the baseband received signal by mixing (9) the signal with the NCO (8) output, ei<°*. Initially, the NCO (8) fre- quency, ∞v, is set to zero if there is no prior knowledge of the initial frequency offset. This is indicated by the initial accu¬ mulator (7) value being zero.

This signal is then operated on by a detection algorithm (10) that is driven by the ACE 2 output. The resulting symbol decision signal, α, is input to the three ACE's (1 - 3).

The ACE's (1 - 3) generate error signals that are the dif¬ ference between the filtered output and the associated refer¬ ence signals that are discussed above. Two of the error sig¬ nals, error 1 and error3, are input to MSE estimators (4 and 5) that operate as follows:

where k is the same as in the frequency offset and n is the number of samples of the error signal. As an example, if k = 1 and n s 10 for the first estimation cycle, k will start at 12 for the next cycle. The difference between the estimated MSE's,

E_d = Eτι - ETC , provides an indication of which direction to move along the frequency offset axis, illustrated in FIG. 3, to get closer to the minimum MSE point (residual offset = 0). For example, if the residual frequency offset is greater than 0, Eχι will be larger than ETC thus making E_d < 0. The negative value of Ed indicates that °>v is too large and should be decre¬ mented. In the preferred embodiment, E is input to a compara¬ tor (6) where it is compared to 0. In this case, the comparator has an output function, f(E_d), as follows:

flE_d) = ΔwhenE_d > 0, flJ__d) = -Δ whenE_d < 0, fl.E_d) = 0 whenE_d = 0,

where Δ is application dependent and determines the resolu- tion of the AFC and also the adaptation speed of the AFC. Δ can be chosen as a very small value for a system with a coarse AFC. In an alternate embodiment, Δ could vary with time by setting it to a larger value initially to speed acquisition and then reduced to get the most accurate frequency offset esti- mate. In the preferred embodiment, Δ is set to a value of 2π radians/second.

In an alternate embodiment, E_d is input to a filter in¬ stead of a comparator. The filter provides a time varying step size (compared to the fixed step size of Δ) that is responsive to the size of the error difference signal. For example, when the error difference signal becomes large, the step size automati¬ cally increases resulting in faster convergence of the algo¬ rithm. Using the filter, however, increases the complexity of the invention and may cause stability problems if a higher order filter is used. A first order digital infinite impulse re¬ sponse (IIR) filter is preferred due to stability and simplicity considerations. The output of the filter is used to update the frequency offset estimate.

The output of the comparator (6) (or filter) is input to an accumulator (7) that adds the new input value to the previ¬ ously stored value. The accumulated value is then used to control the frequency, ωv, of the NCO (8). Since the MSE's n and E ₃ are estimated over blocks of n samples, E and the outputs of the comparator (7) and accumulator (8) are cal- culated every n iterations. The NCO (8) frequency, therefore, is updated once every n iterations. As illustrated graphically in FIG. 3, after several NCO (8) update cycles, ^β v will be approximately equal to -ω^* and the residual frequency offset will be approximately zero. If the frequency offset changes, the process of the present invention detects and tracks the change.

The operation of the process of the present invention can be seen in graphically FIG. 4. The process is using an LMS adaptive channel estimator with an initial frequency offset of 50 Hz. The bit error rate of the detector in this example is 1%. Note that the residual frequency offset quickly declines to nearly 0 Hz. The slope of the initial change from 50 Hz can be changed by modifying Δ. A larger value for Δ will cause a faster acquisition and, therefore, a steeper slope.

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. Another alternate embodiment can use only two adap¬ tive filters by not using the second adaptive filter. In this em¬ bodiment, the output of one of the filters replaces the second filter's output. The resulting AFC value will be biased by Δ/2. Still another alternate embodiment, illustrated in FIG. 6, can use adaptive equalizers in place of the channel estima¬ tors. In this embodiment, the reference signal and the symbol decision signal, α, are input to the equalizer. The adaptive equalizers (601 - 603) are operative to remove the ISI from the respective dithered received signals. The adaptive equalizer may have some inherent delay until an output responsive to the current input is available. The symbol decisions, α, are delayed (604 - 606) until the equalizer output corresponding to that decision is available. The difference between the symbol decisions and the corresponding equalizer output forms an error signal. The error signal is used in the same way as the preferred embodiment to update the NCO frequency. In summary, a process of automatic frequency control in a changing environment has been described. By compar¬ ing the performance of each adaptive algorithm to determine how to change the oscillator frequency, the frequency offset can be reduced to almost zero. The process of the present in¬ vention is not affected by inter-symbol interference since the adaptive channel equalizers take the ISI into account in their estimates. Communication devices using the process of the present invention can out-perform devices using only coarse AFC.

Claims

1. A method for generating an automatic frequency control signal in an apparatus having a plurality of adaptive algo- rithms, each adaptive algorithm having a reference signal with an associated frequency dither, the method comprising the steps of: comparing performances of each of the plurality of adaptive algorithms; and modifying the automatic frequency control signal in re¬ sponse to a difference in the performances.

2. A method for automatic frequency control in an apparatus having a received signal, oscillating means for generating an oscillator signal, and symbol detection means for generating a symbol decision signal, the method comprising the steps of: generating a plurality of reference signals in response to the received signal, the oscillator signal, and a plurality of offset signals; generating a plurality of error signals in response to the symbol decision signal, an update coefficient, and the plural¬ ity of reference signals; estimating a plurality of mean square error signals in response to the plurality of error signals; modifying the oscillator signal in response to a differ¬ ence between the plurality of mean square error signals; and repeating from the first step until the difference be¬ tween the plurality of mean square error signals is substan¬ tially zero.

3. The method of claim 1 wherein the plurality of offset sig¬ nals have the same magnitude.

4. The method of claim 1 wherein the oscillating means is a numerically controlled oscillator.

5. The method of claim 1 wherein a first reference signal is generated by the step of multiplying the received signal with the oscillator signal.

6. The method of daim 5 wherein a second reference signal is generated by the step of multiplying the first reference signal by a first offset signal.

7. The method of daim 6 wherein a third reference signal is generated by the step of multiplying the first reference signal by a second offset signal having a magnitude equal to the first offset signal.

8. A method for automatic frequency control in a system hav- ing a baseband received signal, oscillating means for generat¬ ing an oscillator signal, and symbol detection means for gen¬ erating a symbol dedsion signal, the method comprising the steps of: multiplying the baseband received signal with the osril- lator signal to produce a first reference signal; multiplying the first reference signal by a first offset signal, having a first magnitude, to produce a second refer¬ ence signal; multiplying the first reference signal by a second offset signal, having a second magnitude equal to the first magni¬ tude, to produce a third reference signal; generating a first error signal in response to the symbol dedsion signal, an update coeffident, and the first reference signal; generating a second error signal in response to the symbol dedsion signal, the update coeffident, and the second reference signal; generating a third error signal in response to the sym¬ bol dedsion signal, the update coeffident, and the third refer- ence 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; modifying the oscillator signal in response to the mean square error difference; and repeating from the first step until the mean square er- ror difference is substantially zero.

9. An apparatus for automatic frequency control in a device having a received signal, oscillating means for generating an oscillator signal, and symbol detection means for generating a symbol dedsion signal, the apparatus comprising: a plurality of multiplying means for produdng a plural¬ ity of reference signals in response to the received signal, the oscillator signal, and a plurality of offset signals; a plurality of adaptive filtering means, each means coupled to the symbol detection means and a different multi¬ plying means, for producing a plurality of error signals; a plurality of mean square error estimation means, each means coupled to a different adaptive filtering means, for producing a plurality of mean square error estimates; summing means, coupled to the plurality of mean square error estimation means, for produdng a difference signal; comparing means, coupled to the summing means, for comparing the difference signal to a predetermined value to produce a delta signal; and accumulation means, coupled to the comparing means and the osrillator means, for accumulating the delta signal.

10. The apparatus of daim 9 wherein the plurality of adaptive filtering means are adaptive channel estimators.