The present disclosure relates to a method and an apparatus for detecting signals. In particular, it relates to a method of and apparatus for using a transducer array and an adaptive beamformer to detect signals.
In the field of signal detection, the key problem which must be solved, is how to distinguish between noise alone, and the presence of one or more signals together with noise. This is a well known problem and many methods and devices are known for solving it. Conventional beamformers have been used to provide a more sensitive solution to the signal detection problem. However, they are typically used in the traditional manner of forming a directional beam and looking for signals in a particular direction. Spatial diversity methods which use multiple transducers have also been previously proposed. Neither of these techniques provides optimum energy detection sensitivity.
In a first aspect, the present disclosure provides a method for detecting signals using an adaptive transducer arrangement, the arrangement including a transducer array having a plurality of transducers, a beamformer, and an energy detector, the method comprising: determining weights to be applied by the beamformer to signals emitted from each transducer in order to maximise a performance metric; applying the determined weights to the signals emitted from each transducer; measuring the energy received at the energy detector; comparing the measured energy with a predetermined value and based on said comparison determining whether or not one or more signals are present.
In a second aspect, the present disclosure provides a signal detection apparatus, comprising: a transducer array having plurality of transducers; a beamformer for applying weights to signals emitted from each transducer; an energy detector for measuring the energy of the combined signals received from the beamformer; a processor; wherein the beamformer is further for determining the weights to apply to the signals emitted from the transducers in order to maximise a performance metric; the processor is for comparing the measured energy with a predetermined value and determining, based on said comparison, whether or not one or more signals are present.
Further features are provided in the appended claims and accompanying description.
The present disclosure will now be described by way of example only and with reference to the accompanying drawings, in which:
The adaptive antenna array 100 also includes a beamformer 103. The beamformer 103 includes gain and phase adjusters 104. In particular, the beamformer 103 includes gain and phase adjusters 104-1, 104-2 through to 104-N. Each of the respective antenna output lines 102 is connected to a respective gain and phase adjuster 104. The beamformer 103 is arranged to apply adaptive complex weights to the antenna signals using the gain and phase adjusters 104. This will be described in more detail below. The beamformer 103 also includes gain and phase adjuster outputs 105. In this example, the array includes gain and phase adjuster outputs 105-1, 105-2 through to 105-N. Each of the respective gain and phase adjusters 104 is coupled to a respective gain and phase adjuster output 105.
The beamformer 103 also includes the summing circuit 106. The summing circuit 106 is arranged to sum the signals which are output from the gain and phase adjusters 104. The adaptive antenna array 100 includes a summation circuit output 107 which is coupled to the summing circuit 106. Finally the adaptive antenna array 100 includes an energy detector 108 which is coupled to the summation circuit output 107.
Before describing the operation of the adaptive antenna array 100 in detail, a brief overview of the process will be described in connection with
Prior to energy detection, the array 100 must be set up in order to maximise a performance metric at the input to the energy detector 108. In order to achieve this, the weights applied by the gain and phase adjusters 104 must be established. This process will be described with reference to
For the N element array shown in
x(t)=As(t)+n(t)
where AεCN×K is the array manifold matrix, s(t)εCK×1 is the received signals vector, and n(t)εCN×K is the noise vector. As shown in
Without loss of generality, the model represents the received signals at complex baseband. For the purposes of this embodiment, it is assumed that the band of interest has already been mixed down from the carrier frequency. It is also assumed that the baseband received signal has been pre-filtered by a low-pass filter to limit the average noise power. The noise vector models both externally generated noise, as well as noise generated within the system, such as thermal noise. The noise may be spatially correlated.
The signal at the output of the beamformer is given by:
y(t)=wHx(t)
where w=[w1, w2, . . . , wN]TεCN×1 is the complex weight vector containing all N adaptive weights. As shown in
As noted above, in order to detect one or more signals, a performance metric must be used. The proposed performance metric for the adaptive beamformer 103 prior to energy detection is defined as: the ratio of the total signals plus noise power to the total noise power at the beamformer 103 output (S300). This is expressed as
where the received signal covariance matrix is defined as Rx=E{x(t)x(t)H} and Rn=E{n(t)n(t)H} is the noise covariance matrix.
Maximizing the performance metric (S301) with respect to w
which simplifies to
Substituting for λ we obtain a generalized eigenvector equation
R
x
w=λR
n
w
So the optimum weight vector is equal to the generalized eigenvector associated with the maximum generalized eigenvalue of the matrix pencil (Rx, Rn).
To calculate this optimum weight vector, estimates of both Rx and Rn are required. Matrix Rx is estimated by directly taking the expectation of the outer product of the received signals vector x(t) with itself over a suitable averaging period. Rn may be obtained by estimating Rx when it is known that no signals are present, because in the absence of any signals Rn=Rx. Alternatively, the expectation of the outer product of the received signals vector with itself can be calculated for unoccupied adjacent frequency channels, and then the elements of the covariance matrices thus generated can be interpolated into the frequency channel of interest to provide an estimate of Rn. Finally, if direct measurement is not feasible, then Rn can be estimated by modelling the noise characteristics of the receiver equipment and the external noise environment.
Accordingly, for a given set of signal data, we are able to determine the optimum weight vector (S302).
Following determination of the optimum weight vector, the weights are applied to the same set of signal data. Accordingly, the ratio of the total power of the received signals plus noise to the total noise power arriving at the energy detector is maximised. The process of energy detection with be described with reference to
For an energy based signal detector, we need to choose between the following two hypotheses:
The test statistic for the energy detector, V, is equal to the square of the beamformer 103 output signal integrated over a finite time interval T:
A practical energy detection threshold should be proportional to the noise power at the output of the beamformer 103, which is given by:
γ=kwHRnw
where k is a scalar which may be used to adjust the false alarm rate. Consequently, the detection test hypotheses can now be expressed as:
H
0
:V≦γ
H
1
:V>γ
In other words, if the measured energy is greater than the energy due to noise, then one or more signals may assumed to be present. The first step in the process is to measure V at the energy detector 108 (S400). V is then compared against γ, which has been determined in advance (S401). If V≦γ then it is determined that the beamformer output 103 is noise alone (S402). If V>γ then it is determined that the beamformer output 103 is noise plus one or more signals (S403).
This adaptive array energy detector provides up to 10 log10 N dB coherent gain and a maximum of N orders of diversity. Furthermore, if some of the noise is external to the detection system and is correlated between the antenna elements, then the beamformer 103 described above will act to cancel the correlated noise and further gains in detection sensitivity are possible.
Of course, this is only possible if a good estimate of Rn is available for the generalized eigenvector calculation. If only a poor estimate of Rn is available then a different approach using another performance metric (which is not dependent on Rn) can provide better results. In a second embodiment, the ratio of the total signals plus noise power at the beamformer 103 output to the norm of the weight vector is optimized:
To maximize λ′ the following standard eigenvector equation needs to be solved:
R
x
w=λ′w
This time the optimum weight vector is equal to the eigenvector associated with the maximum eigenvalue of Rx. The test statistic and detection threshold are then calculated as for the first version of this adaptive array energy detector. This simplified version of the adaptive array energy detector provides up to 10 log10 N dB coherent gain and a maximum of N orders of diversity, but does not act to cancel any spatially correlated noise which might be present.
A third embodiment of the present disclosure will now be described with reference to
The adaptive antenna array 500 also includes a beamformer 503. The beamformer 503 includes gain and phase adjusters 504. In particular, the beamformer includes gain and phase adjusters 504-1 through to 504-N. In this embodiment, antenna 501-m is not coupled to the beamformer 503, and hence the output line 502-m is not coupled to a gain and phase adjuster. Each of the respective antenna output lines 502 is connected to a respective gain and phase adjuster 504, except for output line 502-m. The beamformer 503 is arranged to apply adaptive weights to the antenna signals using the gain and phase adjusters 504. This will be described in more detail below. The beamformer 503 also includes gain and phase adjuster outputs 505. In this example, the array includes gain and phase adjuster outputs 505-1 through to 505-N. Each of the respective gain and phase adjusters 504 is coupled to a respective gain and phase adjuster output 505. In particular, gain and phase adjuster 504-1 is coupled to output 505-1 and gain and phase adjuster 505-N is coupled to output 505-N.
The output of antenna 501-m is fed to cross correlator 509, via line 502-m. In practise, the cross correlator may be implemented in software. As will be described in more detail below, the cross correlator cross-correlates the output of the antenna 501-m and the outputs of the other antennas in order to determine a weight vector to apply to the gain and phase adjusters 504.
The beamformer 503 also includes the summing circuit 506. The summing circuit is arranged to sum the signals which are output from the gain and phase adjusters 504. The array 500 includes a summation circuit output 507 which is coupled to the summing circuit 506. Finally the array 500 includes an energy detector 508 which is coupled to the summation circuit output 507.
The first stage in the process is to determine the adaptive weight vector for a given set of data. Starting with the standard received signal model for an N element array, the array is partitioned so that dm(t) is the signal from the mth array element and x
x
(t)=A
where A
d
m(t)=sT(t)am+m(t)
where am is the mth column of AT and nm(t) is the mth element of the noise vector. We now consider dm(t) to be the reference signal and x
r
x
d
=E{x
(t)dm*(t)}
The subarray beamformer weight vector is then set to:
so that the signal at the output of the beamformer is:
y
m(t)=w
The test statistic which is thresholded to decide whether signal energy is present is then given by:
and the detection threshold is:
γm=kw
where Rn
To understand the effect of this beamformer note that dm(t) contains a linear combination of all of the signals incident upon the receiving array. Consequently, by forming w
While the above examples have been described in the context of radio signals and an adaptive antenna array, the disclosure is also applicable to acoustic or sonar applications using arrays of microphones or hydrophones. The term “transducer” is used to refer to an antenna, microphone, hydrophone, or any other suitable sensor.
A summary of the mathematical notation used in this specification is provided below:
Number | Date | Country | Kind |
---|---|---|---|
1115312.9 | Sep 2011 | GB | national |