Patent Application
20230314585
The present disclosure is in the field of radar technology.
A conventional radar system is illustrated in
Non-linear distortion of the transmit waveform by the RF power amplifier (PA) in a conventional radar system can reduce the performance of the radar, by introducing errors into the radar channel estimates the system produces.
Thus, in the present disclosure, a method is described for mitigating the impact of non-linear transmitter distortion, by using the received radar signals to adaptively estimate the distortion introduced by the transmitter. This distortion can then be properly accounted for when the radar channel is estimated, improving the quality of the estimates (which are then used for subsequent core radar processing tasks such as detection and tracking).
In general terms, the disclosed method starts by using a parametric polynomial series expansion (e.g. a memory polynomial) to approximate the non-linear power amplifier response. A radar waveform is transmitted, and the received radar signal and an initial estimate of the distorted transmit waveform are used to obtain an estimate of the radar channel by deconvolution. This radar channel estimate is then used to improve the estimate of the distorted transmit waveform, by updating the parameters of the polynomial function. This process is repeated iteratively and converges upon an accurate representation of the transmit waveform. It is inherently adaptive, and hence can track changes in the response of the PA and other analogue circuitry.
Aspects of the disclosure are potentially applicable to a variety of radar applications, including full duplex pulse compression weather radar systems, aerospace radar systems and joint radar & communication systems.
The user interface 102 integrates with a radar control computer 104 which controls the operation of a radar signal processor 106. The radar signal processor 106 is configured to generate a transmit signal for transmission by a transmitter 108. The transmitter 108 takes the transmit signal and puts it into condition to cause a radar emission at an antenna 114. This can include transposition of the transmit signal to an appropriate transmit frequency, and power amplification.
A beam steering controller 112 operates to ensure that the transmit signal is transmitted at the antenna 114 using beam shaping, to provide focus of the radar on an area of interest. This enables, for instance, a sweep effect of the radar signal across the environment of interest, such that reflections and backscatter can be made to correspond with objects in the environment.
A receiver 110 receives signals at the antenna and conditions them for processing at the radar signal processor 106.
Wideband radars use modulated waveforms (such as chirp signals) to strike a balance between peak transmit power, sensitivity and spatial resolution. They are widely across a range of traditional radar sensing applications, such as aerospace and weather, and are growing in popularity in new applications such as automotive.
In the following description, all mathematical signal models given are written in complex baseband equivalent form. For ease of illustration, however, illustrated examples are of real parts of waveforms.
In simple terms, the radar transmitter 108 transmits the waveform, xT[n], and then the receiver 110 receives the reflected/backscattered signal, y[n].
As shown, the radar transmit waveform 120 is processed (step 1-2) through an RF front end 122, and then the transmitted radar signal passes through a radar channel 140. The received signal at the receiver 110 (step 1-4) is the convolution between the transmitted waveform and the radar channel impulse response, hR[n], plus receiver noise, w [n]
y[n]=x
T
[n]*h
R
[n]+w[n]
This can be equivalently written in matrix-vector form,
y=X
T
h
R
+w
where:
y=H
R
x
T
+w
where:
A fundamental radar processing task is to use the received signal to estimate the radar channel impulse response, ĥR=f(y), from which information about the target environment can then be attained (step S1-6). Channel estimation 130 is indicated as a block in
A classical approach to channel estimation is matched filtering, whereby the received signal is correlated with the original transmit signal.
ĥ
R
=X
T
H
y
This method maximises the return signal to noise ratio (SNR) from an individual scatterer within the environment, and hence is good for detecting weak radar returns. However, the sidelobes present in the matched filter output reduce the spatial resolution, and can lead to masking of weak scatterers by stronger scatters in adjacent range cells.
An alternative approach to impulse response estimation is deconvolution. A variety of deconvolution techniques have been developed for radar applications. Many of the deconvolution approaches are based on the least squares criteria
ĥ
R=argmin∥y−XThR∥22+θ/(hR)
where θ(⋅) is a suitable regularisation function. When the regularisation is omitted this reduces to a simple linear least squares estimator,
ĥ
R=(XTHXT)−1XTHy
This achieves high spatial resolution but typically suffers from noise amplification, leading to poor SNR which can significantly impact the ability to detect targets.
Using the assumption of a sparse radar impulse response (i.e. scatterers are present in only some of the range cells), a popular approach is to solve the above problem with an L1 norm regularisation term included:
ĥ
R=argmin∥y−XThR∥22+λ∥hR∥1
This is a non-linear problem known as least absolute shrinkage and selection operator (LASSO) or basis pursuit denoising (BPD). It generally produces a sparse solution that suppresses noise, with the degree of sparsity controlled by A. The BPD approach can lead to a good balance between spatial resolution and SNR, but comes at the expense of an increase in computational complexity since iterative methods are required to solve the regularised minimisation. From basic convex optimisation theory, for appropriate choice of ∈ this is exactly equivalent to solving
ĥ
R=argmin∥hR∥1 subject to ∥y−XThR∥22≤∈
And for appropriate ζ exactly equivalent to solving
ĥ
R=argmin∥y−XThR∥22 subject to ∥hR∥1≤ζ
Other regularisation functions, θ(hR), that do not exploit sparsity are also possible, as well as deconvolution methods that do not use the least squares formulation—such as the well-known ‘CLEAN’ method.
When performing deconvolution using the above (or other) methods, it is generally assumed that the transmit waveform, xT[n], is perfectly known. This is a reasonable assumption in many cases, since the transmit waveform is often generated digitally within the radar.
However, when a radar system suffers from transmitter impairments, the signal radiated from the antenna may differ from the ideal (digitally-generated) waveform, x[n]. In particular, when the waveform does not have a constant envelope (i.e when the instantaneous power varies), non-linearities in the transmitter power amplifier (PA) distort the waveform. A typical example of this is illustrated in
The output of the non-linear PA can be modelled as a non-linear function with memory L:
x[n]=g(x[n],x[n−1], . . . ,x[n−L+1]),
An illustrative example non-linear function with memory L=1 is shown in
If the non-linear distortion is not accounted for, the mismatch between the ideal waveform and the actual transmit waveform can lead to significant errors during deconvolution. This is illustrated in
Examples disclosed herein provide a method for accurately & adaptively estimating the non-linearly distorted transmitted signal, so that accurate deconvolution of the radar return channel can be achieved.
The non-linear function associated with a PA can generally be well-approximated by a polynomial expansion, such as a memory polynomial
This function contains a linear sum of non-linear terms, and is fully parameterised by the coefficients al,p. A variety of other non-linear models with similar structures can also be used (e.g. the Volterra series).
Using the above, the transmit waveform, xT[n], can be written in vector form as
x
T
=X
NL
a
where each column of XNL contains a vector generated using the ideal waveform, x[n], and a single polynomial term, for example x[n−l]|x[n−l]|2p. For a given waveform, the matrix XNL is fixed and the non-linear function depends on the coefficients al,p contained in the vector a.
The method, as before, commences by transmitting the radar waveform xT[n], with unknown non-linear distortion, from the transmitter RF front end 122 (step S2-2). The radar return signal is received at the receiver 130 (step S2-4). The algorithm starts (step S2-6) by assuming some initial estimate of the transmit signal is available,
{circumflex over (x)}
T
(i)
=X
NL
â
(i)
This transmit signal estimate is used to estimate the radar return channel using some deconvolution method, such as BPD:
Other deconvolution techniques could also be used. Providing the initial estimate {circumflex over (x)}T(i) is reasonably close to the true waveform, a reasonably accurate radar channel estimate ĥR can be obtained.
A decision is then taken (S2-8) as to whether to update the estimate of the distorted transmit waveform. This decision is based on whether the estimate has become impaired. This can be determined based on SNR. In general terms, in one embodiment, the update is performed when the level of noise exceeds a pre-set threshold. That threshold may be equal to the minimum power of the echo signal. In a specific embodiment, the threshold may be set at −108 dBm. So, when the SNR has become degraded to the threshold, the estimate is updated.
The radar channel estimate can then be used to update the estimate of the transmit signal (step S2-10). This is done by formulating a regularised least squares problem to estimate â(i+1):
The regularisation term here is used to ensure that the new estimate is close to the old estimate, helping prevent overfitting and reducing noise. The degree of similarity is controlled by the γ, and setting γ=0 removes the regularisation constraint. The parameter γ could optionally be changed at each iteration. Other related variants of regularised least squares optimisation could also be used to obtain â(i+1).
The solution to the above least squares problem, and updated estimate of a, is given by:
â
(i+1)
=â
(i)
+W(y−ĤRXNLâ(i))
where
W=(XNLHĤRHĤRXNL+γI)−1XNLHĤRH
Here it will be noted that the columns of the matrix ĤRXNL represent convolutions, and hence can be computed very efficiently using fast convolution techniques. Therefore, the main computational burden is the matrix inversion operation in W. This can be kept low by appropriately limiting the number of memory polynomial terms used in the model. Other numerical optimisations to minimise the computational complexity of solving the above problem efficiently may be possible.
To further mitigate the impact of noise and overfitting, a damping factor, 0<μ≤1, may optionally be introduced:
â
(i+1)
=â
(i)
+μW(y−ĤRXNLâ(i))
The new transmit waveform estimate is then formed:
{circumflex over (x)}
T
(i+1)
=X
NL
â
(i+1)
={circumflex over (x)}
T
(i)
+μX
NL
W(y−ĤR{circumflex over (x)}T(i))
To ensure the transmit waveform maintains the correct power scaling, a scaling factor can optionally be used, but may not be required.
{circumflex over (x)}
T
(i+1)=β(i+1)XNLâ(i+1)
This power constraint could also be enforced in some other way, for example by introducing an additional constraint directly into the least squares problem.
The new estimate of the transmit signal should be used for deconvolution of the next received radar signal (S2-12), and the process repeated. Once the method has converged to an accurate estimate of the transmit signal, re-estimation of the transmit signal can be performed periodically to track any changes to the non-linear function that may occur due to heating effects & drift in the PA.
Using the disclosed method, an accurate reconstruction of the non-linearly distorted waveform can be obtained, as illustrated in
The improved waveform estimate enables better radar channel estimates to be obtained. This is illustrated
The convergence of the disclosed method is shown in
The matrix XNL will often have correlated columns, which can lead to poor conditioning of the matrix ĤRXNL. To reduce numerical errors and noise in the waveform estimate, it can be useful to instead use an orthonormal basis to represent xT,
x
T
=X
NL
a=Q
NL
z
where the columns of QNL are mutually orthogonal and span the same column space as XNL (calculated using the QR decomposition, for example). The model is now defined by the parameter vector z, and the problem can be restated as
leading to the update
{circumflex over (x)}
T
(i+1)=β(i+1)({circumflex over (x)}T(i)+μQNLWU(y−ĤR{circumflex over (x)}T(i)))
with
W
Q=(QNLHĤRHĤRQNL+γI)−1QNLHĤRH
The reader will recognise that this does not give the same solution to the original formulation at each iteration, but will converge to a similar overall solution. Other related least square formulations for estimating the polynomial coefficients are also possible, and should be covered by this patent.
Note that the method of the present disclosure can also be applied in a context where the ideal transmit waveform changes, which can be accounted for by updating the matrix XNL. This could be applicable, for example, to a joint communications & radar systems.
Variations in how the above procedure is implemented are also possible. For example, a single estimated radar channel could be used to update the distorted waveform estimate, which could then be used to re-estimate the radar channel from the same received signal (i.e. rather than just using it for subsequent received signals).
Whilst certain embodiments have been described, these embodiments have been presented by way of example only, and are not intended to limit the scope of the inventions. Indeed, the novel devices, and methods described herein may be embodied in a variety of other forms; furthermore, various omissions, substitutions and changes in the form of the devices, methods and products described herein may be made without departing from the spirit of the inventions. The accompanying claims and their equivalents are intended to cover such forms or modifications as would fall within the scope and spirit of the inventions.
