METHOD AND APPARATUS FOR SIGNAL REGENERATION

Abstract

A method (10) of regenerating a signal is provided. The method involves sampling (13) a received signal to obtain a plurality of samples each having an associated magnitude. The samples are sorted (15) to obtain a statistical distribution (which may be a histogram). Known distributions are fitted to the statistical distribution using a fitting operation (16, 17), and for each a measure of similarity is obtained. A matched distribution is then determined from the measures of similarity (18), that is subsequently used to regenerate a signal (12) that itself is statistically representative of the originally sampled signal. Such a method mitigates the storage burden associated with the recording and subsequent regeneration of representative wireless signal environments for wireless device testing. Also relates to an apparatus for the same.

Claims

1. A method of regenerating a signal, comprising the steps of: a) Sampling a received signal to obtain a plurality of samples each having an associated magnitude; b) Sorting the samples to obtain a statistical distribution of the magnitudes; c) Fitting a plurality of known distributions to the statistical distribution using a fitting operation, and in each case obtaining a measure of similarity; d) Determining a matched distribution from the plurality of known distributions, the matched distribution corresponding to an optimum value of the measure of similarity; e) Synthesising a regenerated signal using the matched distribution; and then f) Outputting the regenerated signal.

2. The method of claim 1, further comprising the step of determining a phase distribution from the matched distribution, such that the matched distribution and the phase distribution can be used to synthesise the regenerated signal.

3. The method of claim 1, wherein the step of sorting the samples comprises the step of binning the magnitudes to generate the statistical distribution.

4. The method of claim 3, wherein the step of binning the magnitudes comprises the step of selecting a bin width according to Scott's Reference Rule.

5. The method of claim 1, wherein the known distributions comprise a plurality of different distributions.

6. The method of claim 5, wherein the known distributions comprise a normal distribution, Weibull distribution, Rayleigh distribution and Nakagami distribution.

7. The method of claim 1, wherein the step of sorting the samples further comprises the step of normalising the magnitudes.

8. The method of claim 7, wherein the step of fitting a plurality of known distributions comprises applying a hypothesis test.

9. The method of claim 8, wherein a plurality of hypothesis tests are applied.

10. The method of claim 9, wherein the hypothesis tests are Kolmogorov Smirnov, Anderson Darling, Chi Squared and Lilliefors tests.

11. The method of claim 1, wherein the step of synthesising a regenerated signal comprises the step of a configuring a random number generator to operate with a probability distribution corresponding the matched distribution, and generating therefrom a plurality of synthesised samples.

12. The method of claim 11, wherein the step of synthesising a regenerated signal further comprises the step of arranging the synthesised samples as a waveform.

13. The method of claim 1, wherein the step of sampling a received signal comprises the steps of: a) Generating a spectrogram of the received signal; and b) Selecting a plurality of samples corresponding to a predetermined frequency.

14. Apparatus for regenerating a signal, comprising transceiver means for receiving and transmitting a signal connected to a means for processing data, wherein the means for processing data is configured to: a) Sample a received signal from the transceiver means to obtain a plurality of samples each having an associated magnitude; b) Sort the samples to obtain a statistical distribution of the magnitudes; c) Fit a plurality of known distributions to the statistical distribution using a fitting operation, and in each case obtaining a measure of similarity; d) Determine a matched distribution from the plurality of known distributions, the matched distribution corresponding to an optimum value of the measure of similarity; e) Synthesise a regenerated signal using the matched distribution; and then f) Transmit the regenerated signal using the transceiver means.

15. The apparatus of claim 14, wherein the means for processing data is further configured to determine a phase distribution from the matched distribution, and to synthesise the regenerated signal using the matched distribution and the phase distribution.

16. A computer program comprising instructions which, when the program is executed by a computer, cause the computer to carry out the method of claim 1.

17. A computer-readable data carrier having stored thereon the computer program of claim 16.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Embodiments of the invention will now be described by way of example only and with reference to the accompanying drawings in which:

[0019] FIG. 1 illustrates for a relatively simple waveform the steps involved in regenerating a signal;

[0020] FIG. 2A illustrates the relatively simple waveform operated on using the method of FIG. 1;

[0021] FIG. 2B illustrates the results of a fitting operation on the relatively simple waveform of FIG. 2A;

[0022] FIG. 3 illustrates for a complex waveform the steps involved in regenerating a signal.

DETAILED DESCRIPTION

[0023] FIG. 1 illustrates an embodiment of a method 10 of regenerating a signal, in flow diagram form. The method 10 comprises two stages: the processing of a received signal 11; and the generation of a regenerated signal 12. In the processing stage 11 a first step comprises sampling a received signal 13 to obtain 400 waveform samples. The received signal is a time based electromagnetic signal, and as such is received by an antenna and transceiver, then sampled by a computer system using an input/output data acquisition card. Each of the 400 samples has an associated magnitude. The waveform samples are normalised in a subsequent step 14 by the computer system to ensure any statistical tests are performed in a consistent manner, and are then processed into a histogram 15 and stored as an array in computer memory. The histogram has a bin width set by Equation 1. Known distributions Normal, Weibull, Rayleigh, Nakagami, are fitted to the histogram 16 to obtain optimally matched versions of each distribution. This is achieved by trialling a plurality of each distribution against the histogram data using a least squares or other fitting algorithm. A plurality of hypothesis tests are then performed 17 with the null hypothesis that the best fitting Normal, Weibull, Rayleigh, or Nakagami, reflects the true statistical behaviour of the received signal magnitude variations with a confidence interval of 95%. The hypothesis tests are Kolmogorov Smirnov, Anderson Darling, Chi Squared, and Lilliefors tests, and are all provided as algorithms within the computer system. Each hypothesis test outputs a measure of similarity in the form of a p-value. The maximum p-value represents the most likely to be true statistical behaviour, which in this embodiment is a Rayleigh distribution. The precise form of the Rayleigh distribution is stored in computer memory as the matched distribution 18. When the received signal needs to be regenerated in the laboratory the second stage 12 of ‘generation’ is performed. This involves configuring a random number generator 19 with a probability density function corresponding to the matched distribution 18. The random number generator is then used to synthesise samples 20 in accordance with the probability density function. These samples can then be plotted 21 as a waveform, and rescaled 22 for instance my multiplying a maximum value of the un-normalised samples. A shape parameter obtained from a maximum likelihood estimate of the un-normalised samples may also be applied. The regenerated waveform may then be played back over-the-air using the transceiver and antenna 23.

[0024] FIG. 2A shows a relatively simple signal 24 received and processed in the method of FIG. 1. FIG. 2B shows the results of a fitting operation applied to the signal 24 of FIG. 2A. An optimal normal 25, Weibull 26, Rayleigh 27 and Nakagami 28, distribution is shown fitted to the normalised binned samples 29, prior to hypothesis testing.

[0025] FIG. 3 illustrates for a complex signal the method steps 30 involved in signal regeneration. The method steps 30 are divided into three stages: pre-processing 31; processing 32; and generation 33. Each of stages is performed in a computer system. In the pre-processing stage 31 a spectrogram of an electromagnetic signal is obtained 34. The spectrogram shows the frequencies present in a received signal. The spectrogram is thresholded 35 to identify the frequencies having magnitudes above a predetermined level. This allows the primary frequencies of the received signal to be identified for further analysis (for instance signals above a noise floor). In this embodiment a single frequency is selected for analysis, and the plurality of samples in that frequency bin are extracted from the spectrogram 36 for further analysis. Each of the samples has a respective magnitude, and these magnitudes are normalised 37 in the processing stage 32. The normalised samples are then binned using Equation 1 to generate a histogram 38. A fitting operation 39 is applied to the histogram, using a least squares or other fitting algorithm to fit Normal, Weibull, Rayleigh, Nakagami known distributions to the histogram. Each fitted known distribution is then used in a null hypothesis in Kolmogorov Smirnov, Anderson Darling, Chi Squared, and Lilliefors tests 40, in each case obtaining measures of similarity (p-value). For a given hypothesis test, the known distribution achieving the maximum p-value is deemed to be the distribution representing the statistical behaviour of the received signal at the chosen frequency—the matched distribution. The matched distribution is stored in computer memory 41. In this embodiment the matched distribution is a Rayleigh distribution. The computer system used contains a look-up table matching the known distributions with corresponding phase distributions. A phase distribution is generated using a look-up operation, to associate the Rayleigh matched distribution with a uniform phase distribution (each phase has an equal probability of being present in a given sample) 42. In the generation stage 33, the matched distribution is used to configure a random number generator 43. Synthesized samples are generated by the random number generator 44. A complex signal is generated 45 having both amplitude and phase components, and modulated with the frequency selected from the spectrogram. The synthesised samples are used to scale the amplitude component of the complex signal 46. The phase distribution is used to adjust the phase component of the complex signal 46. The regenerated signal is then output 47 as an electromagnetic signal using an antenna and transceiver.

[0026] Complex signals may be generated in the time domain or the frequency domain. A complex signal may comprise many frequencies and the regeneration process may be performed for a plurality of frequencies, the signals being superimposed once regenerated to form a statistically representative version of the received signal. Additional steps of retesting the regenerated signals may be applied prior to their output or transmission. This is to ensure the newly generated waveforms have the same statistical behaviour as the received signal. This may comprise the steps of re-binning the generated samples and applying similar fitting operations as were performed to analyse the received signal.