Signal detection before’ Prewhitening’ (Determina- tion of the maxima of the spectrogram at each time instant) 

Contexts in source publication

Context 1

... Detection, Broadband Digital Receiver, Extreme Value Statistics, PALES In this paper an adaptive prewhitening method is proposed to obtain an uniform transfer function of the used broadband receiver. Then we describe a new detection scheme which is based on extreme value statistics. The discussed methods are applied to real data measured by the PALES experimental system. In a hostile environment an active radar mode should be avoided. Thus, passive radar modes without an own transmis- sion of radar pulses are of current research interest. Besides a bistatic radar mode and possibly PCL (‘Passive Coherent Lo- cation’) processing, also the classical tasks of an ESM receiver (‘Electronic Support Measurement’) should be inte- grated in a future radar system (“Shared Aperture”). To fulfil all wanted tasks like radar imaging or ESM, broadband aspects are becoming more important. In ESM the system should cover the frequency range between 2 and 18 GHz, while in radar bandwidths of up to 2 GHz are wanted for imaging and target recognition tasks. If an active radar mode can not be circumvented, the transmitted energy has to be chosen as low as possible. In this case a listening system (ESM) should have a high antenna gain to compensate the decrease of the transmitted power. High antenna gain requires narrow antenna beams. To guarantee a simultaneous overview of the whole interesting field of view, beam switching is not an ap- propriate measure. Alternatives are fully digitized arrays [5] or beamforming networks. The high numerical load and the costs of broadband receivers, imply a preference of beamforming networks. Because Butler and BLAS matrices can only be realized for narrowband systems, electromagnetic lenses are a possible choice. Especially Rotman lenses are of great interest (comp. [2], [4]). Because Rotman lenses are based on true time delays they are “natural” broadband devices. Applying a fitted shading low sidelobes can be obtained. A realization as an optical device (comp. [6]), reduces the needed space and weight of future systems. To check the capabilities of a ‘shared aperture’, at FGAN the PALES experimental system ([12], [13], [14]) is built up. Especially signal processing with a multibeam system is in- vestigated. The first step in signal processing is the detection of received signals. Having a digital receiver with a wide in- stantaneous bandwidth the detection of a received narrowband signal at a given time can be a problem because of the signal to noise ratio. Besides the wide bandwidth, the transfer function of the analogue part of the receiver has to be taken into account. In this paper at first we discuss an adaptive prewhitening method to obtain an uniform transfer function of the used broadband receiver. Then we describe a new detection scheme which is based on extreme value statistics. To validate the proposed methods the whitening procedure and the following detection procedure are applied to measured data of the PALES experimental system. In the PALES experimental system the received data of four neighbouring channels are digitized at IF with a rate of up to 6 GHz and a depth of 8 bit. The theory of detection as described in this paper, is based on investigations of the data of only one receiver channel. In the experiments (figure 1) the bandwidth of the digital receiver was 500 MHz. To validate the theoretical results and to show the problems, we measured transmitted signals which were generated by an AWG (‘arbitrary waveform generator’) and/or a commercial signal synthesizer. To describe the problems of digital broadband receivers, at first usual signal detection methods are applied to the received signals of our system. Each value of the time function, shown in figure 2, is the received mean power of several hun- dred data samples. Though the signals of 2 transmitters were received, in the observed time interval only the signals of one transmitter can be detected. The signals of a second transmitter having a small signal power are not detected by the applied conventional methods. Detection by Likelihood ratio tests (comp. [10]) fails if the frequency of the received signals is not taken into account. To take the frequency of received narrowband signals into account and to enhance the detection properties, often time frequency representations of the received signals are consid- ered. If the spectral power for a given frequency and time crosses a detection threshold, we assume that we have received a signal. Being interested only in signal detection, it should be sufficient to check if the maximal spectral power at a given time crosses a given threshold. Because real receivers usually don’t have a uniform transfer function, detection of signals with a small SNR (“Signal to Noise power Ratio”) is quite difficult. In figure 3 the normalized spectrogram of the measured data without a received signal, i.e. noise only, is shown. The received power at a given time (x axis) and for a given frequency (y axis) is colour coded. The higher sensitivity of the receiver at the centre frequencies deteriorates the detection of target signals. To show the effects of the receiver transfer function to signal detection, we consider the spectrogram of the data of figure 2, which is shown in figure 4. Though at 85 MHz the pulses of the second radar can be assumed to be present, an automatic detection method does not work. Taking the maximum of the spectrogram at each time instant with respect to the signal powers at the different frequencies we obtain the time function shown in figure 5. Similar to figure 2 in figure 5 the pulses of the second radar cannot be detected. Following, at first we consider a method to eliminate the in- fluences of the receiver transfer functions and then in a second step we derive the probability density function of the maxima of the columns of the spectrogram to obtain a detection thresholds with given false alarm rates. The consideration of the maxima or minima, i.e. extreme values, of a ‘large’ set of random values (in our case the power values at 512 frequencies at a given time instant of the spectrogram), and their statistical properties are the topic of extreme value theory. To match the receiver transfer function and to suppress the coloured noise, optimal filtering [11] is applied to the received data. To derive the prewhitening method we start by a description of the signal model, which was checked by statistical tests. We assume that at a given time the received signal x(t) can be described ...

Context 2

... Detection, Broadband Digital Receiver, Extreme Value Statistics, PALES In this paper an adaptive prewhitening method is proposed to obtain an uniform transfer function of the used broadband receiver. Then we describe a new detection scheme which is based on extreme value statistics. The discussed methods are applied to real data measured by the PALES experimental system. In a hostile environment an active radar mode should be avoided. Thus, passive radar modes without an own transmis- sion of radar pulses are of current research interest. Besides a bistatic radar mode and possibly PCL (‘Passive Coherent Lo- cation’) processing, also the classical tasks of an ESM receiver (‘Electronic Support Measurement’) should be inte- grated in a future radar system (“Shared Aperture”). To fulfil all wanted tasks like radar imaging or ESM, broadband aspects are becoming more important. In ESM the system should cover the frequency range between 2 and 18 GHz, while in radar bandwidths of up to 2 GHz are wanted for imaging and target recognition tasks. If an active radar mode can not be circumvented, the transmitted energy has to be chosen as low as possible. In this case a listening system (ESM) should have a high antenna gain to compensate the decrease of the transmitted power. High antenna gain requires narrow antenna beams. To guarantee a simultaneous overview of the whole interesting field of view, beam switching is not an ap- propriate measure. Alternatives are fully digitized arrays [5] or beamforming networks. The high numerical load and the costs of broadband receivers, imply a preference of beamforming networks. Because Butler and BLAS matrices can only be realized for narrowband systems, electromagnetic lenses are a possible choice. Especially Rotman lenses are of great interest (comp. [2], [4]). Because Rotman lenses are based on true time delays they are “natural” broadband devices. Applying a fitted shading low sidelobes can be obtained. A realization as an optical device (comp. [6]), reduces the needed space and weight of future systems. To check the capabilities of a ‘shared aperture’, at FGAN the PALES experimental system ([12], [13], [14]) is built up. Especially signal processing with a multibeam system is in- vestigated. The first step in signal processing is the detection of received signals. Having a digital receiver with a wide in- stantaneous bandwidth the detection of a received narrowband signal at a given time can be a problem because of the signal to noise ratio. Besides the wide bandwidth, the transfer function of the analogue part of the receiver has to be taken into account. In this paper at first we discuss an adaptive prewhitening method to obtain an uniform transfer function of the used broadband receiver. Then we describe a new detection scheme which is based on extreme value statistics. To validate the proposed methods the whitening procedure and the following detection procedure are applied to measured data of the PALES experimental system. In the PALES experimental system the received data of four neighbouring channels are digitized at IF with a rate of up to 6 GHz and a depth of 8 bit. The theory of detection as described in this paper, is based on investigations of the data of only one receiver channel. In the experiments (figure 1) the bandwidth of the digital receiver was 500 MHz. To validate the theoretical results and to show the problems, we measured transmitted signals which were generated by an AWG (‘arbitrary waveform generator’) and/or a commercial signal synthesizer. To describe the problems of digital broadband receivers, at first usual signal detection methods are applied to the received signals of our system. Each value of the time function, shown in figure 2, is the received mean power of several hun- dred data samples. Though the signals of 2 transmitters were received, in the observed time interval only the signals of one transmitter can be detected. The signals of a second transmitter having a small signal power are not detected by the applied conventional methods. Detection by Likelihood ratio tests (comp. [10]) fails if the frequency of the received signals is not taken into account. To take the frequency of received narrowband signals into account and to enhance the detection properties, often time frequency representations of the received signals are consid- ered. If the spectral power for a given frequency and time crosses a detection threshold, we assume that we have received a signal. Being interested only in signal detection, it should be sufficient to check if the maximal spectral power at a given time crosses a given threshold. Because real receivers usually don’t have a uniform transfer function, detection of signals with a small SNR (“Signal to Noise power Ratio”) is quite difficult. In figure 3 the normalized spectrogram of the measured data without a received signal, i.e. noise only, is shown. The received power at a given time (x axis) and for a given frequency (y axis) is colour coded. The higher sensitivity of the receiver at the centre frequencies deteriorates the detection of target signals. To show the effects of the receiver transfer function to signal detection, we consider the spectrogram of the data of figure 2, which is shown in figure 4. Though at 85 MHz the pulses of the second radar can be assumed to be present, an automatic detection method does not work. Taking the maximum of the spectrogram at each time instant with respect to the signal powers at the different frequencies we obtain the time function shown in figure 5. Similar to figure 2 in figure 5 the pulses of the second radar cannot be detected. Following, at first we consider a method to eliminate the in- fluences of the receiver transfer functions and then in a second step we derive the probability density function of the maxima of the columns of the spectrogram to obtain a detection thresholds with given false alarm rates. The consideration of the maxima or minima, i.e. extreme values, of a ‘large’ set of random values (in our case the power values at 512 frequencies at a given time instant of the spectrogram), and their statistical properties are the topic of extreme value theory. To match the receiver transfer function and to suppress the coloured noise, optimal filtering [11] is applied to the received data. To derive the prewhitening method we start by a description of the signal model, which was checked by statistical tests. We assume that at a given time the received signal x(t) can be described ...