GB2462876A

GB2462876A - Estimating the component of a signal via random sampling

Info

Publication number: GB2462876A
Application number: GB0815454A
Authority: GB
Inventors: Andrei Popescu
Original assignee: Cambridge Silicon Radio Ltd
Current assignee: Qualcomm Technologies International Ltd
Priority date: 2008-08-26
Filing date: 2008-08-26
Publication date: 2010-03-03
Also published as: GB0815454D0; TW201025950A; WO2010023469A1

Abstract

A system and method for estimating a component of a signal, such as the DC offset of a received radio signal, comprises sampling the signal at random times 101 to generate a decimated signal, then filtering the decimated signal 102 using a low-pass filter to generate the estimate. The sample may be taken and passed to the low-pass filter with a probability of 1/M, where M is the decimation factor. Passing the sample to the filter may include generating a random number, and passing the sample if that number equals a predefined value. Alternatively, the predefined value may be compared with the value of a counter, or the two mechanisms may be combined.

Description

METHOD OF MEASURING A DC COMPONENT

BackQ round Some circuits which are used to process a signal add an unwanted constant or very low frequency component to the signal due to imperfections I non-idealities in those circuits. This unwanted component is referred to as a DC offset.

DC offset compensation is often implemented in radio receivers, for example in zero-IF (intermediate frequency) and low-IF receivers, in order that the DC offset does not reduce the useful dynamic range of the receiver circuit. The DC offset, or DC component of a signal (which may be referred to as the reference signal) is estimated so that the compensation can occur.

The DC offset is measured by low-pass filtering the signal. This separates the DC from the other frequency components of the signal. The specification of the filter used and the computational effort required to implement the filtering depend on both the sampling rate of the signal and the expected frequency contents of the signal. As the sampling rate increases, 1 5 the computational intensity required to implement the filter can become high. Where taking a signal sample has a cost, the cost of sampling the signal per unit of time also increases with the sampling rate.

The embodiments described below are not limited to implementations which solve any or all of the disadvantages of known methods of DC offset estimation.

Summary

This Summary is provided to introduce a selection of concepts in a simplified form that are further described below in the Detailed Description. This Summary is not intended to identify key features or essential features of the claimed subject matter, nor is it intended to be used as an aid in determining the scope of the claimed subject matter.

A method of measuring a very low frequency component of a signal is described. The method comprises sampling the signal at random times to generate a decimated' signal, and then filtering the decimated signal using a low-pass filter. There are many different methods which may be used to sample the signal at random times, and in one example, a sample of the signal may be taken and then passed to the low-pass filter with a probability of 1IM, where M is the decimation factor.

A first aspect provides a method of estimating a component of a signal comprising: receiving a signal; sampling the signal at random times to generate a decimated signal; and filtering the decimated signal using a low-pass filter to generate an estimate of the component of the signal.

Sampling the signal at random times to generate a decimated signal may comprise: taking a sample of the signal; and passing the sample to the low-pass filter with a defined probability.

The defined probability may be varied in order to control the bandwidth of the filtering step.

Passing the sample to the low-pass filter with a defined probability may comprise: generating a random number; and if the random number equals a predefined value, passing the sample to the low-pass filter.

Sampling the signal at random times to generate a decimated signal may comprise: 1 0 generating a random number; and if the random number equals a predefined value, taking a sample of the signal and passing the sample to the low-pass filter.

Generating a random number may comprise: generating a first random number comprising a first plurality of bits; and generating a second random number from the first random number by selecting a subset of the first plurality of bits. Generating a random number may also 1 5 comprise: generating a third random number from the second random number by selecting at least one bit from the subset of the first plurality of bits.

Sampling the signal at random times to generate a decimated signal may comprise: initialising a counter to a value; updating the value of the counter at a first rate; and when the value of the counter equals a predefined value, passing a sample of the signal to the low-pass filter.

The method may further comprise: selecting a number from a range of numbers with a uniform probability distribution; and wherein the counter is initialised to the number selected and the predefined value is zero. Alternatively, the counter may be initialised to zero and the predefined value may be the number selected.

The signal may be one of a discrete-time signal and a continuous-time signal.

A second aspect provides a computer program comprising computer executable code arranged to perform any of the methods described herein when executed. The computer program may be embodied on a computer readable medium (e.g. a tangible computer readable medium).

The computer executable code may be hardware description language.

A third aspect provides a system for estimating a component of a signal comprising: a decimating element arranged to receive a signal and sample the signal at random times to generate a decimated signal; and a low-pass filter arranged to filter the decimated signal to generate an estimate of the component of the signal.

The decimating element may comprise: a selector element arranged to pass a sample of the signal to the low-pass filter with a defined probability.

The decimating element may further comprise a random number generator and the selector element may be arranged to pass the sample to the low-pass filter if a random number generated by the random number generator equals a predefined value.

The decimating element may further comprise a sampling element arranged to take a sample of the signal.

1 0 The decimating element may comprise: a counter; a sampling element arranged to take a sample of the signal; and a selector element arranged to trigger the sampling element to sample the signal when the counter equals a predefined value.

The decimating element may further comprise a random number generator arranged to select a number from a range of numbers with a uniform probability distribution.

1 5 In an example, the counter may be initialised to the number selected and the predefined value is zero. In another example, the counter may be initialised to zero and the predefined value is the number selected.

Further aspects provide a method substantially as described with reference to any of figures 1-4 of the drawings and a system substantially as described with reference to figure 6 of the drawings.

The methods described herein may be performed by firmware or software in machine readable form on a storage medium. The software can be suitable for execution on a parallel processor or a serial processor such that the method steps may be carried out in any suitable order, or simultaneously.

This acknowledges that firmware and software can be valuable, separately tradable commodities. It is intended to encompass software, which runs on or controls "dumb" or standard hardware, to carry out the desired functions. It is also intended to encompass software which "describes" or defines the configuration of hardware, such as HDL (hardware description language) software, as is used for designing silicon chips, or for configuring universal programmable chips, to carry out desired functions.

The preferred features may be combined as appropriate, as would be apparent to a skilled person, and may be combined with any of the aspects of the invention.

Brief Description of the DrawinQs

Embodiments of the invention will be described, by way of example, with reference to the following drawings, in which: Figure 1 is a flow diagram of an improved method of estimating a DC component of a signal; Figure 2 is a flow diagram of an example method of random decimation; Figure 3 is a flow diagram of an example method of random number generation; Figure 4 is a flow diagram of further example methods of random decimation; 1 0 Figure 5 is graph comparing the variance of the DC estimates obtained with uniform and random decimation; and Figure 6 shows a block diagram of a system which may be used to estimate a DC component of an input signal.

Common reference numerals are used throughout the figures to indicate similar features.

1 5 Detailed Description

Embodiments of the present invention are described below by way of example only. These examples represent the best ways of putting the invention into practice that are currently known to the Applicant although they are not the only ways in which this could be achieved.

The description sets forth the functions of the example and the sequence of steps for constructing and operating the example. However, the same or equivalent functions and sequences may be accomplished by different examples.

Figure 1 is a flow diagram of an improved method of estimating a DC or very low frequency component of a signal, such as a DC offset. The method comprises sampling the signal at random times (block 101), a process which is referred to herein as random decimation, and then low-pass filtering the resulting decimated signal (block 102).

The term decimation' is used herein to refer to a process of reduction in the sample rate of a signal, where this signal may be already a discrete-time signal but may alternatively be a continuous-time signal. Where the signal is a continuous-time signal, the term decimation, as used herein, refers to a processing in which the signal is sampled at a rate, or average rate, lower than the minimum sample rate that would be necessary to prevent aliasing when sampling that signal.

The sampling of the signal at random times (in block 101) may include converting the sample from analogue to numeric format.

By decimating the signal (in block 101), the computational intensity required to estimate the DC component is reduced and the random nature of the decimation preserves the DC component whilst spreading the spectrum of all other signal components that have narrow-band frequency contents (as described in more detail below with reference to figure 5). As a result the DC estimate does not depend strongly on narrow-band frequency components (e.g. 1 0 tones) within the signal.

In an example, the average decimation factor, M, which is used may be given by: M=2N. The value of M or N may be programmable and the value of M or N may be selected for a particular application or implementation and in a particular example, N=8 (so M=256).

Smaller values of N (and hence of M) result in a reduction in the benefit of reduced 1 5 computational complexity; whilst larger values of N (and M) may be suitable where the DC component of the signal is stable over a long period of time. In other examples, however, M may not be a power of two. Where the estimated DC component is used in a feedback (or control) loop (e.g. to perform DC offset compensation), the properties of the loop may determine the value of N and/or M that is used (e.g. where the estimation must be updated quickly enough to enable the loop to operate).

The average decimation factor (and hence the rate of the decimated signal, which is referred to herein as the decimated sampling rate) may be varied as a means to control the bandwidth of the low-pass filtering operation.

The random decimation process described herein (e.g. in block 101) goes against conventional signal processing thinking, which considers that aliasing should normally be prevented by sampling a signal at a rate greater than the signal bandwidth.

There are a number of different techniques which may be used to implement the random decimation (in block 101) and figures 2 and 4 show flow diagrams of two example methods of random decimation. In the example shown in figure 2, reference signal samples are taken at a rate referred to herein as the reference sampling rate, (block 201) and these samples are passed to the low-pass filter with a probability of 1/M (block 202). This is convenient where the reference signal readily has a discrete-time representation, uniformly sampled at the reference sampling rate.

A similar approach may be used when the reference signal is continuous-time, in which case the operations of taking a reference signal sample and passing it to the low-pass filter may be grouped so that they are both performed at the decimated sampling rate. When the reference signal is continuous-time, the reference sampling rate may be chosen using any suitable technique; for example it may be chosen to be equal to the reference signal bandwidth.

The probability with which samples are passed to the low-pass filter (in block 202) may be varied as a means to control the bandwidth of the low-pass filtering operation.

An example implementation of the second process step (block 202) is also shown in figure 2 and this comprises generating a random number (block 211), for example using a pseudo- 1 0 random number generator (PRNG) and then if the number generated equals a predefined value, passing the sample to the low-pass filter (block 212). The predefined value (Y) may be fixed or may be variable.

In the example of figure 2, the random number X is selected with a uniform probability distribution from a range of values, which may, for example, be the integer numbers between 0 and M-1 (e.g. 0 <X < M-1). In this example the number Y is fixed, e.g. Y = M-1.

The sequence of random numbers, X, may be generated directly by a PRNG (in block 211), e.g. a N-bit LFSR (linear feedback shift register) PRNG. Alternatively, additional randomisation steps may be used to prevent short-term periodicity in the sequence of numbers X that are generated. An example of such a process is shown in figure 3 and any one or more of the method blocks 301-303 may be used. In an example, a P bit number 31 may be generated using a PRNG (block 301), a K bit random number 32 may then be generated from the P bit number (block 302), e.g. by selecting K bits at random from the P bit number 31. R bits are then selected, to generate a R bit random number 34, (block 303), for example by using an AND operation between the K bit number and a number 33 (e.g. a K bit number) with a variable number of bits set to one (where this variable number may be less than or equal to R). In some examples R=N and varying R in this way is a means of varying the bandwidth of the low-pass filtering operation.

The selection of the K bits from the P bit number (in block 302) may be performed using any suitable technique. In an example, the same technique may be used as is used in block 303, i.e. the P bit number may undergo an AND operation with a number with a variable number of bits set to one (where this variable number may be less than or equal to K). In some implementations of this example, K=N.

Whilst in the above example, the number 33 is described as having a variable number of bits set to one, in other examples the number of bits set to one may be fixed (e.g. at R in the first example above or at K in the previous example).

In a variation of the method shown in figure 3, a subset of the method blocks may be used.

For example, a P bit number may be generated (block 301) and then R bits may be selected from the P bit number (block 303), e.g. by using an AND operation, as described above. In other example variations, additional randomisation steps may be included, in addition to, or instead of, those shown in figure 3.

Figure 4 shows two variations on an example method in which the reference signal is 1 0 sampled at random intervals T(k), where T(k) = mT where T is the reference signal sampling period and m is an integer variable which is selected from the range 1 to 2M-1 with a uniform probability distribution. In the two implementations shown in figure 4, a counter is used which runs at the reference sampling rate (e.g. 1/Ta Hz, where T is in seconds), and the reference signal is sampled at a lower rate (the decimated sampling rate, e.g. 1/T0 Hz, where T0 is the 1 5 average value of T(k) and is in seconds).

In the method shown in figure 4, the value m is selected (block 401) from a defined range (e.g. between 1 and 2M-1). The value may, for example, be selected using a PRNG and/or using the methods described above with reference to figure 3. Having selected the value of m, the counter is initialised (block 402 or 403). The counter may be initialised either to the value m (as in block 402) or to zero (as in block 403). The counter is then decremented from m towards zero (block 404) or incremented from zero towards m (block 405). The counter is decremented / incremented (in blocks 404 and 405) at the reference sampling rate. When the counter reaches the target value, be it zero (Yes in block 406) or m (Yes in block 407), a sample of the signal is passed to the low-pass filter (block 408).

In the example of figure 4, the value m is selected with a uniform probability distribution from a range of values, which may, for example, be between 1 and 2M-1 (e.g. 1 <X < 2M-1).

It will be appreciated that although figure 4 shows the value of m being determined before the counter is initialised, in some examples the counter may be initialised first. For example, where the counter is initialised to zero (in block 403), this may be performed prior to selecting avalueofm (in block4Ol).

Whilst the two techniques shown in figures 2 and 4 are not equivalent, both approaches result in an average decimation factor of M. The implementation shown in figure 4 has the counter and sampling decision logic running at the reference sampling rate, whilst the sampling, filtering and random number generator run at the lower rate (the decimated sampling rate).

By comparison, the implementation shown in figure 2 has the random number generator running at the reference sampling rate, but does not require a counter. Another difference between the two techniques is that when sampling the reference signal at random intervals, T(k) (as in figure 4), the maximum time between two consecutive samples is 2M-1, whereas when sampling with a probability 1/M (as in figure 2) the time between consecutive samples can exceed 2M-1.

It will be appreciated that the examples shown in figure 2 and 4 and described above provide example methods of performing random decimation. Other implementations may alternatively be used and any suitable method may be used to perform random decimation.

1 0 The example methods described above involve random decimation, i.e. the decimation is performed by sampling the signal at random times. In an alternative method, the decimation may be performed by sampling the signal at uniform time intervals, i.e. uniform decimation.

However, when using uniform decimation the estimate of the DC component may be strongly corrupted by the aliasing of reference signal components whose frequency contents are 1 5 concentrated around multiples of the decimated sampling rate, as shown in the graph of figure 5. When the user is not aware whether the conditions are met which cause the corruption of the estimate, use of uniform decimation is unreliable.

Figure 5 is a graph comparing the variance of the DC estimates obtained with uniform and random decimation (traces denoted 501 and 502 respectively). In this particular example, the reference signal consists of DC of magnitude 0.1 plus a tone with peak amplitude 1. The variance of the DC estimate is typically higher when using random decimation but it does not depend on the tone frequency, whereas with uniform decimation some tone frequencies cause a very large degradation of the DC estimate, e.g. as indicated by arrow 503. The DC plus tone' reference signal used in this example is a good model for an FM receiver IF signal.

The decimation, whether random or uniform, results in aliasing (or folding) of the reference signal spectrum in the post-decimation signal. The spreading of the spectrum which occurs when random decimation is used can be described using the random sampling scheme (of figure 4) by way of example. As detailed above, the reference signal sampling period is denoted T and the time T(k) between consecutive samples is a random variable (T(k)= mT).

The average value of T(k) may be denoted T0, where T0 = MT. Simulation indicates that components of the reference signal with frequency higher than 1I(2T0) are effectively whitened' by the random sampling. This can be expected because with T(k) random, the value of each sample of such a component is not correlated to that of the previous sample.

For reference signal components with frequencies lower than 1I(2T0), consecutive samples are correlated because the variation of these reference signal components is limited within a time T0.

Assuming that: * apart from DC and components with frequencies above 1/(2T0), the reference signal contains only components of negligible power, and * the low-pass filter is kept unchanged, the variance of the random sampling' DC estimate is independent of M. Because the variance of the post-decimation signal is equal to that of the reference signal and the non-DC contents of the decimated signal have a flat spectrum, the estimate variance depends only on 1 0 the filter used. If the samples of the low-pass filter impulse response are denoted h_n and the variance of non-DC components of the reference signal is denoted P, then, the random sampling' DC estimate variance is sum((h_n)2)P.

The methods described above provide an efficient way to estimate the DC component of a signal, such as a DC offset. The resulting estimate may be used in many different ways, e.g. 1 5 to compensate for the DC component, to drive a control loop etc. The method ensures that the available computational cycles in a device are not wasted and where computational resources are limited may enable the estimation to be performed and/or may enable other processes to be performed in parallel to determining the estimate. Where it is difficult to perform uniform sampling of the reference signal at a sufficiently high frequency to prevent aliasing, the method provides a way to estimate low frequency components of the reference signal by sampling the reference signal more slowly, while limiting the effect of aliasing.

Whilst the methods are described above as being used to compute the DC component of a signal or other very low frequency signal component, such as the DC offset in a FM signal (or the IF signal in an FM receiver), the methods are applicable to estimating the magnitude of any signal component that is stable over time (e.g. an additive constant) or which varies slowly compared to the frequency at which the signal is sampled. The use of random decimation (as opposed to uniform decimation) is particularly suited to applications where the signal comprises periodic components of unknown frequency which might corrupt an estimate generated using uniform decimation.

The methods described above may be implemented in an IC, within software or in any other suitable manner. In an example, the methods described above may be implemented in digital hardware (e.g. a HDL-described implementation).

Figure 6 shows a block diagram of a system which may be used to estimate a DC component of an input signal, which is referred to herein as the reference signal. This system may be implemented in hardware, software, firmware or any combination thereof. The system comprises a decimating element 601 and a low-pass filter 602. The decimating element 601 receives the reference signal 61, which may be an analogue or digital signal and which may already have been sampled at the reference sampling rate. The decimating element 601 processes the signal (e.g. as described above) and outputs samples of the reference signal at the lower decimated rate 62 to the low-pass filter 602. The low-pass filter 602 filters the signal 62 and outputs an estimate of the DC component 63.

1 0 The decimating element 601 may comprise any combination of some or all of the elements shown in figure 6 and the elements may depend on the decimating method used (e.g. as shown in figures 2 and 4). The elements comprise a PRNG 611, a counter 612, a sampling element 613 and a selector 614. The operation of PRNG is described above with reference to figures 2-4 and the operation of the counter 612 is described above with reference to figure 4. The sampling element 613 is used to sample the input signal (e.g. as in block2Ol or 408).

The selector 614 may be used to pass samples (e.g. as generated by the sampling element 613) to the low-pass filter with a probability of 1/M (e.g. as in block 202) and/or to compare the counter value to a defined value (e.g. as in blocks 406 and 407).

Those skilled in the art will realize that storage devices utilized to store program instructions can be distributed across a network. For example, a remote computer may store an example of the process described as software. A local or terminal computer may access the remote computer and download a part or all of the software to run the program. Alternatively, the local computer may download pieces of the software as needed, or execute some software instructions at the local terminal and some at the remote computer (or computer network).

Those skilled in the art will also realize that by utilizing conventional techniques known to those skilled in the art that all, or a portion of the software instructions may be carried out by a dedicated circuit, such as a DSP, programmable logic array, or the like.

Any range or device value given herein may be extended or altered without losing the effect sought, as will be apparent to the skilled person.

It will be understood that the benefits and advantages described above may relate to one embodiment or may relate to several embodiments. The embodiments are not limited to those that solve any or all of the stated problems or those that have any or all of the stated benefits and advantages.

Any reference to an item refers to one or more of those items. The term comprising is used herein to mean including the method blocks or elements identified, but that such blocks or elements do not comprise and exclusive list and a method or apparatus may contain additional blocks or elements.

The steps of the methods described herein may be carried out in any suitable order, or simultaneously where appropriate. Additionally, individual blocks may be deleted from any of the methods without departing from the spirit and scope of the subject matter described herein. Aspects of any of the examples described above may be combined with aspects of any of the other examples described to form further examples without losing the effect sought.

It will be understood that the above description of a preferred embodiment is given by way of example only and that various modifications may be made by those skilled in the art.

1 0 Although various embodiments have been described above with a certain degree of particularity, or with reference to one or more individual embodiments, those skilled in the art could make numerous alterations to the disclosed embodiments without departing from the spirit or scope of this invention.

Claims

Claims 1. A method of estimating a component of a signal comprising: receiving a signal; sampling the signal at random times to generate a decimated signal (101); and filtering the decimated signal using a low-pass filter to generate an estimate of the component of the signal (102).
2. A method according to claim 1, wherein sampling the signal at random times to generate a decimated signal comprises: taking a sample of the signal (201); and passing the sample to the low-pass filter with a defined probability (202).
3. A method according to claim 2, wherein the defined probability is varied in order to control the bandwidth of the filtering step.
4. A method according to claim 2 or 3, wherein passing the sample to the low-pass filter with a defined probability comprises: generating a random number (211); and if the random number equals a predefined value, passing the sample to the low-pass filter (211).
5. A method according to claim 1, wherein sampling the signal at random times to generate a decimated signal comprises: generating a random number; and if the random number equals a predefined value, taking a sample of the signal and passing the sample to the low-pass filter.
6. A method according to claim 4 or 5, wherein generating a random number comprises: generating a first random number comprising a first plurality of bits (301); and generating a second random number from the first random number by selecting a subset of the first plurality of bits (302).
7. A method according to claim 6, wherein generating a random number further comprises: generating a third random number from the second random number by selecting at least one bit from the subset of the first plurality of bits (303).
8. A method according to claim 1, wherein sampling the signal at random times to generate a decimated signal comprises: initialising a counter to a value (402, 403); updating the value of the counter at a first rate (404, 405); and when the value of the counter equals a predefined value (406, 407), passing a sample of the signal to the low-pass filter (408).
9. A method according to claim 8, further comprising: selecting a number from a range of numbers with a uniform probability distribution (401); and wherein the counter is initialised to the number selected (402) and the predefined value is zero (406).
10. A method according to claim 8, further comprising: selecting a number from a range of numbers with a uniform probability distribution (401); and wherein the counter is initialised to zero (403) and the predefined value is the number selected (407).
11. A method according to any of the preceding claims, wherein the signal is one of a discrete-time signal and a continuous-time signal.
12. A computer program comprising computer executable code arranged to perform a method according to any of the preceding claims when executed.
13. A computer program according to claim 12 embodied on a computer readable medium.
14. A system for estimating a component of a signal comprising: a decimating element (601) arranged to receive a signal (61) and sample the signal at random times to generate a decimated signal (62); and a low-pass filter (602) arranged to filter the decimated signal (62) to generate an estimate of the component of the signal (63).
15. A system according to claim 14, wherein the decimating element (601) comprises: a selector element (614) arranged to pass a sample of the signal to the low-pass filter (602) with a defined probability.
16. A system according to claim 15, wherein the decimating element further comprises a random number generator (611) and wherein the selector element (614) is arranged to pass the sample to the low-pass filter (602) if a random number generated by the random number generator (611) equals a predefined value.
17. A system according to claim 15 or 16, wherein the decimating element further comprises: a sampling element (613) arranged to take a sample of the signal (61).
18. A system according to claim 14, wherein the decimating element (601) comprises: a counter (612); a sampling element (613) arranged to take a sample of the signal (61); and a selector element (614) arranged to trigger the sampling element to sample the signal when the counter equals a predefined value.
19. A system according to claim 18, wherein the decimating element (601) further comprises: a random number generator (611) arranged to select a number from a range of numbers with a uniform probability distribution, and wherein the counter is initialised to the number selected and the predefined value is zero.
20. A system according to claim 18, wherein the decimating element (601) further comprises: a random number generator (611) arranged to select a number from a range of numbers with a uniform probability distribution, and wherein the counter is initialised to zero and the predefined value is the number selected.
21. A method substantially as described with reference to any of figures 1-4 of the drawings.
22. A system substantially as described with reference to figure 6 of the drawings.