GB2579239A - Method for generating an array antenna and the array antenna thereof - Google Patents

Abstract

A method of making a sparse antenna array, comprises: generating first 1203 and second 1205 orthogonal rectangular matrices by determining a Kronecker product of a linear vector 1202 containing 1 values and a seed matrix 1201 containing 1 and 0 values with at least a 1 value per line and per column, for each respective matrix, and making an antenna array equivalent to that of the Kronecker product of the first and second rectangular matrices 1206. At least one of the first and/or second orthogonal matrices may be dilated and the seed matrix may be a diagonal or anti-diagonal matrix. The second orthogonal rectangular matrix 1205 may be a transposition of the first orthogonal rectangular matrix 1203. The sparse antenna array arrangement may be a MIMO arrangement with a first matrix used in transmission and a second matrix used in reception. A single antenna transmission element and a reception matrix according to a Kronecker product of the first and second orthogonal rectangular matrices may be used. An antenna array formed by the method is disclosed. The sparse antenna array may provide a large field of view, low side-lobes, low grating-lobes, good resolution with a low number of antenna elements for detecting the angle of arrival of signals in a radar system.

Description

METHOD FOR GENERATING AN ARRAY ANTENNA AND THE ARRAY ANTENNA

THEREOF

The present disclosure concerns millimetre wave radars, in particular radars able to determine the direction of arrival (DOA) or angle of arrival (AOA) images of echo signals based on reflections of an emitted radar wave on target objects, also called scatterers.

More specifically, the present invention provides a method for designing and generating a sparse antenna array providing a resolution at least as good as a corresponding full antenna array of same length, or equivalently of same aperture. Radars antenna comprising multiple antenna elements are known. In particular, it is known that two linear arrays of antenna elements, one of transmission antenna elements and one for reception antenna elements may be equivalent to one transmission antenna element and a two-dimensional array of receiving antenna elements.

A radar antenna is characterized by its radiating pattern. A typical antenna radiating pattern exhibits a main peak, or lobe, in the operating direction and side lobes of lower energy in some other directions.

The main features of a multi-antenna radar are the resolution, the field of view, the side lobes and the number of antenna elements. The resolution is a measure of the capabilities of the radar to discriminate two close targets. It is related to the shape of the main peak of the antenna radiating pattern. A thinner main beam corresponds to a better resolution. High-energy side lobes may lead to false target detection, non-detection of secondary targets and noise in the resulting image. A large field of view requires that the grating lobes are distributed the further apart possible. Regularly spacing the antenna elements, thus reducing the number of elements is adverse to the large field of view as grating lobes appears. Removing some of the elements, thus reducing the number of antenna elements, is also adverse to the achievement of low sidelobes. Reducing the number of antenna elements is advantageous, not only regarding the spare of antenna elements by themselves, but also by the spare of signal processing electronic needed to treat the signals behind the antenna elements. The challenge in the multi-antenna design is to get a design with a low number of antenna elements while keeping a good resolution, a large field of view and low sidelobes.

The reduction of the number of antenna elements in an array antenna is an important issue. To obtain images with a sufficient resolution in range direction, the modulation frequency must have a large bandwidth to insure a good definition of range steps. Also the aperture of the antenna must be wide, to achieve a small angular resolution. It is not uncommon to find frequencies above 60 GHz and antenna arrays of more than 100 elements.

The present invention has been devised to address one or more of the foregoing concerns.

According to a first aspect of the invention there is provided a method of manufacturing an array antenna comprising the following steps: generating a first rectangular matrix by applying a Kronecker product of a first linear vector containing 1 values and a first seed matrix, the first seed matrix containing only 1 and 0 values, the first seed matrix containing at least a 1 value per line and per column; generating a second rectangular matrix by applying a Kronecker product of a second linear vector containing 1 values and a second seed matrix, the second seed matrix containing only 1 and 0 values, the second seed matrix containing at least a 1 value per line and per column, the first and second rectangular matrices being orthogonal; manufacturing the array antenna equivalent to the array antenna represented by the Kronecker product of the first and second rectangular matrices.

In an embodiment, the method further comprises: dilating the first or second rectangular matrix by applying translations to lines and columns of the dilated rectangular matrix, the distance between two successive rows and respectively columns in the dilated rectangular matrix being lower or equal to the number of rows, respectively columns, of the non-dilated rectangular matrix minus one.

In an embodiment, the distance between two successive rows and respectively columns in the dilated rectangular matrix is equal to the number of rows, respectively columns, of the non-dilated rectangular matrix minus one.

In an embodiment, the seed matrix is a diagonal, or anti-diagonal, matrix.

In an embodiment, the second rectangular matrix is a transposition of the first rectangular matrix.

In an embodiment, the generated antenna is a MIMO antenna comprising a first and second array antenna represented by the first and second rectangular matrices, one array antenna being used in transmission, the other one in reception.

In an embodiment, the generated antenna comprises one antenna element and an array antenna represented by the Kronecker product of the first and second rectangular matrices, one of the antenna element and the array antenna being used in transmission, the other in reception.

According to a first aspect of the invention there is provided an array antenna manufactured according to the invention.

Embodiments of the invention will now be described, by way of example only, and with reference to the following drawings in which: Figure 1 illustrates an antenna constituted by a linear array of equally spaced antenna elements; Figure 2 illustrates a polar representation of the diagram of emission of such antenna according to the array factor; Figure 3 illustrates grating lobes generated by an array antenna where the antenna elements are spaced by a distance greater than half the wavelength; Figure 4 illustrates the array factor of an antenna corresponding to a full antenna array where each antenna element is spaced by a distance of half the wavelength but where some antenna elements are missing, or are deactivated; Figure 5 illustrates the equivalence between a MIMO antenna of two one- dimensional arrays of transmission, respectively reception, antenna arrays and a two-dimensional array of reception antenna elements and one transmission antenna; Figure 6 illustrates the architecture of a MIMO radar that can be used for implementing an antenna according to embodiments of the invention; Figure 7 illustrates a variant of the architecture illustrated by Figure 6; Figure 8 illustrates the behaviour of a two dimensional array antenna; Figure 9 illustrates the effect of the MIMO operation for 2D antenna arrays, when the operation does not correspond to a Kronecker product; Figure 10 illustrates the effect of the MIMO operation for two dimension antenna arrays, when the operation does correspond to a Kronecker product; Figure 11 illustrates the main steps of a method to generate an antenna according to embodiments of the invention; Figure 12 illustrates a first example of application of the method according to the invention; Figure 13 illustrates another example of application of the method according to the invention; Figure 14 illustrates another example of application of the method according to the invention.

Figure 1 illustrates an antenna constituted by a linear array of equally spaced antenna elements. The wavelength of the carrier frequency of the emitted signal is noted A and the distance between two antenna elements is noted d. An array of antenna elements 102 receives signals 101 reflected by a target with an angle of arrival 8.

The near field and far field are regions of the electromagnetic field (EM) around an object, such as a transmitting antenna, or the result of radiation scattering off an object. Non-radiative 'near-field' behaviors of electromagnetic fields dominate close to the antenna or scattering object, while electromagnetic radiation 'far-field' behaviors dominate at greater distances.

The energy is received by each of the antenna elements with a delay due to the different times of flight of the signal. For each direction 0, the far field energy, also called array factor or AF, can be calculated as: AF = 2n=0 e 0.n.k.d.sin(8)); Where k =27/A, 2 being the carrier frequency, d is the distance between the antenna elements, and N is the number of antenna elements.

Figure 2 illustrates a polar representation of the diagram of emission of such antenna according to the array factor (AF) as indicated by the above equation. The antenna factor is the name given to the radiating pattern of the antenna while the element factor is the name of the radiating pattern of an antenna element. The antenna factor is the product of the array factor and the element factor. As a radiating dot radiates isotropically, the antenna factor here is also representative of the array factor.

The diagram indicates the relative intensity of the electromagnetic field along the different directions. Generally, 0° indicates the direction orthogonal to the antenna plan, assuming a planar antenna. From this diagram, two characteristics of the antenna can be determined. The first characteristic corresponds to its 3dB beam width. The 3dB beam width is the angle corresponding to a division of the peak energy by a factor of two. When the antenna array is full, each antenna element being distant from its neighbor of a distance corresponding to half the wave length of the carrier signal, the 3dB beam width BW expressed in radian can be approximated by the equation: BW = sin-1(2IN); The second characteristic is the null beam width, which is the angle corresponding to a reduction of the peak energy to zero on each side of the peak. These beam width characteristics are tied to the number of antenna elements spaced by half the wavelength. A larger antenna with a larger number of antenna elements leads to smaller 3dB beam width and null beam width, meaning to a narrower 10 beam.

Figure 3 illustrates grating lobes generated by an array antenna where the antenna elements are spaced by a distance greater than half the wavelength. This figure illustrates the antenna factor of two array antennas as Figure 2. The representation is rectangular as opposed to the polar representation of Figure 2. The plain line corresponds to the same antenna already illustrated on Figure 2 where the antenna elements are spaced by half the wavelength. The dotted line corresponds to an antenna array have the same number of antenna elements but spaced by a distance corresponding to the wavelength. At direction corresponding to angles 90 and 180 degrees, lobes with a same amplitude as the main lobe appear. These lobes are grating lobes generated by the fact that the Shannon sampling theorem is not respected. The other secondary lobes observed on both the plain and the dotted lines with an energy of 13.7 dB below the main lobe are due to the spatial sampling process, they are called side lobes.

Figure 4 illustrates the array factor of an antenna corresponding to a full antenna array where each antenna element is spaced by a distance of half the wavelength but where some antenna elements are missing, or are deactivated. The plain line corresponds to the full antenna array while the dotted line corresponds to the same antenna with missing or deactivated antenna elements. It can be seen that the levels of the sidelobes are increased when some of the antenna elements are missing. The peak to side lobe ratio (PSLR) is now lower than 13.7 dB.

When no more antenna elements are spaced by half the wavelength, grating lobes also appear. To avoid grating lobes, it is important that at least some of the distances between antenna elements are fixed to half the wavelength or less.

In the literature, an array antenna where some antenna elements are missing or deactivated is called a sparse antenna.

The array factor diagram of Figure 2, 3 and 4 are calculated considering that the antenna is emitting. An antenna is a reversible object and the diagrams may be interpreted as the sensitivity of the antenna to an electromagnetic field incoming in various directions.

In these diagrams, the direction of the main lobe is orthogonal to the main direction defined by the antenna array. In some embodiments, this direction may be controlled by weighting differently the outgoing or incoming energies on each antenna 10 element.

The angle of arrival of a signal received by an array antenna can be determined based on the array manifold. A signal received by an array antenna is received by each antenna element with a delay depending on the angle of arrival 8. For a regular linear antenna with N elements spaced by a distance d, the array manifold can be defined as the vector: ad e7.z.A a(0) = n.c.f e sin(6) This array manifold is the expression of the array response of the antenna to a unit signal with one of the external antenna element taken as a reference. By applying proper delays to signals received by each antenna element, the signals can be all in phase and their addition provides the best possible signal to noise ratio.

For example, forming a dot product I a(0)H. a(00) I provides the value carrying the best possible signal to noise ratio for the value 8 corresponding to the angle of arrival Igo of the signal. This means that the evaluation of the dot product for all possible values of 8 allows determining the angle of arrival, which corresponds to the highest value of the dot product.

Methods for determining the angle of arrival generally use a weight vector W. Each output of the receiving signal processing chain is weighted and summed to obtain a beamformer output. The weight vector depends on an angle O. Simplifying by assuming the received signal is a unit gate, the output is in the form p(0)= IW(0)" .a(90)I. When 0 is identical to 00, p(0) will present a maximum. The weight vector can be the array manifold, but not necessarily.

When the weight vector uses the array manifold the output is: N-1 N-1 P(°) =expO rt 2.1r 2.Tr T d(sin(9)). expO Tn d sin(00)) n 0 n=O N-1 2.Tr expo -n d sin(9)) . 22= 0 Not surprisingly, we recognize the array factor in the equation. In this case, the output of the method to determine the angle of arrival is dependent on the array manifold.

Thus, the angle of arrival answer also depends on the shape of the antenna array, and will be similar, at a multiplication by a complex number, with the Array Factor corresponding to the antenna shape.

It can be seen that the resolution, or the ability for the system to separate two direction of incoming signals is related to the notion of beam widths exposed above. The larger the antenna, the larger the number of antenna elements and the better the resolution.

To realise images with a sufficient range resolution, the range resolution being the ability of the radar to distinguish two close targets, the baseband signal must have a large bandwidth to insure a good definition of range steps. Such a large bandwidth will require a carrier frequency with a very high frequency. The angular resolution, meaning the ability to distinguish two targets forming a small angle with the antenna, depends on the aperture of the antenna which is the width of the antenna, the distance between the two most spaced antenna elements. It is not uncommon to find frequencies above 60 GHz and array antennas of more than 100 elements to meet the requirements.

Each antenna element is associated with a signal processing chain used to process the received signals. These signal processing chains are costly. Decreasing the number of antenna elements and corresponding signal processing modules is therefore an issue in array antenna design.

Considering a reference distance d < 212, where A is the wavelength of the signal and considering a line with a graduation at every distance d, it is possible to formalize an array antenna by a vector comprising a one value if the corresponding graduation is associated with an active antenna element and a zero value if the corresponding graduation is associated with a deactivated, or missing, antenna element.

For example, a full array of aperture, meaning width, of 6.d can be noted [1 1 1 1 1 1 1]. An example of sparse array antenna can be noted [1 0 0 0 1 0 1]. An array antenna with antenna elements spaced by the wavelength distance A may be noted [1 0 1 0 1 0 1].

The co array of the antenna can be defined corresponding to the vector obtained by making the convolution of the vector representation of the antenna and its flipped representation. For example, the co array of the antenna represented by [1 1 1] is the vector [1 2 3 2 1]. The co array indicates the number of times each delay is present in the antenna. In the above example, the delay 0 is present 3 times (one for each antenna element). The delay d.sin(e) is present 2 times (one for each pair of neighbour antenna element). The delay 2d.sin(e) is present 1 time (between the two extremum antenna elements).

Some array antennas are known to allow a reduction of the number of antenna elements while preserving correct properties of the antenna. Among these known antenna design, we can mention the non uniform linear arrays (NLAs) where the antenna elements are placed at integer multiples of a reference distance d. The non redundant non uniform linear arrays are non uniform linear arrays having the property that the co array of the antenna contains only zero and ones except at the middle position. For example, the array antenna represented by the vector [1 0 0 1] has a corresponding co array [1 0 0 2 0 0 1]. This array presents a lack of visibility at zero position which correspond to some delay that are not present in the antenna. Consequently, grating lobes are present.

An interesting kind of non uniform linear array is the minimum redundant non uniform linear array (MRNLA) which presents no zeros in their co array, with the largest possible aperture. For example, the antenna represented by the vector [1 1 0 1] has the co array [1 1 1 3 1 1 1]. This antenna has a good response as the redundancy is limited to one except for the zero delay.

These studies concern one dimension array antennas but can be extended to two dimension array antennas.

The problem in designing an array antenna is to optimize the four following properties of the antenna: high resolution, large field of view, low side lobes and a small number of active antenna elements. This optimisation must deal with the fact that a high resolution requires a high number of antenna elements, and with the fact that a large field of view requires that the grating lobes are distributed the further apart possible. Regularly spacing the antenna elements is adverse to the large field of view as it induces the apparition of grating lobes. Removing some of the antenna elements is also adverse to the obtention of low sidelobes. The challenge is therefore to determine a design allowing the reduction of the number of antenna elements while limiting the loss in resolution and field of view, meaning limiting the side lobes and the grating lobes.

The needed field of view depends on the contemplated application. The field of view is large enough as soon as the contemplated targets are encompassed by the radar. Accordingly the proposed design seeks a reduction of the number of antenna elements that keeps the resolution of a full array antenna while allowing a decrease in the field of view.

A MIMO (Multiple Input Multiple Output) radar with a transmitter equipped with M antenna elements and a receiver equipped with N antenna elements receives a signal, at each antenna element indexed by n, corresponding to the summation;JO Xmr,t,1 an,nt(Pm(r) where (pat(t)is the transmitted waveform and amt.?, is the channel coefficient of the transmission channel between the transmitting antenna element m and the receiving antenna element n. 0 k

The transmitted signals are said orthogonal when f cpk(t)coRt) dt = [SW 1 k = 1-When the transmitted signals are orthogonal, the incoming waveform can be separated using correlation: St = f x(t)co (t) dt. Thus, even if the emission is done simultaneously by all the transmission chains, there is a total of MxN distincts paths at the reception. Considering the output of the MxN correlations being y=[S_11,S_12,...S_MN]; The orthogonality of signals can be obtained either by using different frequencies, different code words belonging to a set of orthogonal codes, or simply by sending all signals sequentially.

Figure 5 illustrates the equivalence between a MIMO antenna of two one-dimensional arrays of transmission, respectively reception, antenna arrays and a two-dimensional array of reception antenna elements and one transmission antenna. The MIMO antenna 100 comprises a first one-dimensional array 101 of transmission antenna elements and a second one-dimensional array 102 of reception antenna elements. It is equivalent to the antenna 110 comprising a single transmission antenna element 111 and a two-dimensional array of reception antenna elements 112. The real antenna 100 corresponds to the virtual array antenna 110. It is to be noted that the two one-dimensional arrays of the MIMO antenna do not have to comprise the same number of antenna elements. Similarly, the two-dimensional array of reception antenna elements does not have to comprise the same number of rows and columns.

Let A be an M x N matrix, B a P x Q matrix: a11B * * a1NB The Kronecker product is defined as A®B = i %. i which is a MP x QN aM1B aMNB matrix.

It is known that a MIMO operation over two one dimension antenna arrays may realize a Kronecker product of the two array manifolds, and that the resulting array factor is the multiple of the 2 array factors.

Using one dimension antenna arrays, where the Kronecker product is realized, the aperture of the antenna is enlarged. If the first antenna with M antenna elements has an aperture of (M-1) x u x X/2, the inter element distance of first antenna is u x X/2 the second antenna with N antenna elements an aperture of (N-1) x v x X/2, the inter element distance of first antenna is v x X/2 the resulting antenna will have an aperture of (M-1) x u x X/2 + (N-1) x v x X/2. Since the aperture increases, the resolution becomes sharper.

Using two dimensions antenna arrays, the MIMO operation may or may not realize a Kronecker product. Reversely, a two dimensions antenna array may or may not be the result of a Kronecker product. As explained later in relation to Figures 9 and 10, in case the two dimensions antenna array is not the result of a Kronecker product, the desired resolution may not be obtained.

Figure 6 illustrates the architecture of a MIMO radar that can be used for implementing an antenna according to embodiments of the invention. The described radar comprises a first set 201 of antenna elements dedicated for transmission and a second set 207 of antenna elements dedicated for reception. Signal to feed the transmission antenna elements are generated by signal generators 203a to 203c as baseband signals. The generated signals are transmitted to frequency transposition modules 202 in charge of transposing the frequency carrier of the signal to a desired frequency for transmission. A carrier generator 204 is in charge for generating the carrier at the desired frequency to feed the frequency transposition modules 202. The carrier generator is typically a unique controlled oscillator operated under the control of control module 209, which can control the frequency of the carrier to be used by the frequency transposition modules 202.

Using this transmission architecture, each antenna element can transmit a different signal at a same frequency at a given instant. Frequency hopping can be realized by successively changing the frequency of the carrier during time.

Signals 220 emitted by the transmission antenna elements 201 may be reflected by a target 208 in reflected signals 221 received by reception antenna elements 207. The received signals are transposed down in frequency to baseband by the frequency transposition module 206. The frequency transposition module 206 receive the frequency value of the carrier used for transmission from the carrier generator 204.

Baseband signals are processed in the receiving units 205a to 205c.

This architecture may be used for two different types of radar. A first type of radars is known as FMCW (Frequency Modulated Continuous Wave) mode radars. In this case, the signal generated by the signal generators 203a to 203c are continuous non-null signals. The signals received by the receiving units 205a to 205c are the beat signals representing the difference of frequency in time between the received signal and the actual frequency generated by the signal generators 203a to 203c or by the carrier generator 204. The AOA module 210 determines the phase differences of the signals coming out of the receiving units 205a to 205c. From these phase differences, an angle of arrival is determined according to known methods.

A second type of radars is known as pulse compression mode radars. In this mode, the generated signals emitted by the signal generators 203a to 203c are short pulses of signal. These pulses are typically encoded with codes like, for example, Barker sequences of codes or Golay codes. The successive pulses may be emitted at different frequencies to realize a scan of the frequency band in a mechanism known as frequency hopping. A pulse controller 211 is in charge of synchronizing the pulses, controlling the codes to be used and the frequencies of the carrier sent to the control module 209. The received signals are correlated with the corresponding emitted signals generated by the signal generators 203a to 203c by the receiving units 205a to 205c. Codes are used to discriminate signals from the different transmission antennas using code division multiplexing technics. Targets are identified by detecting correlation peaks in the result of the correlation. The position of the peak being related to the distance of the target. Known technics, like trilateration for example, can be used on the resulting signals by the AOA module 210 to retrieve the angle of arrival of the signal giving the direction of the target.

The receiving units 205a to 205c are used to apply the matching filter. In case of pulse compression mode radars, the matching filtering is made with a correlator to correlate the received signal with the emitted one. In case of FMCW radars, a whitening filter may be used.

Operation of FMCW or coded pulse radars are well known by the person skilled in the art.

Figure 7 illustrates a variant of the architecture illustrated by Figure 6.

The architecture of Figure 7 differs from the one illustrated in Figure 6 in that it comprises a single signal generator 303 and a single receiving unit 305 to replace the signal generators 203a to 203c and the receiving units 205a to 205c. A second difference is that the antennas elements are switched in both transmission and reception using the switches 313a to 313c and 314a to 314c. This means that only one antenna element is allowed to transmit, or receive, at a given instant. Simultaneous transmission of code division multiplexed signals by the transmission antenna elements is no longer possible. Typically, time division multiplexing is used with this architecture. For example, a pulse radar using this architecture will transmit the different pulses by each transmission antenna elements successively in time. This second architecture is therefore simpler but requires more time to proceed.

Mixed architectures may be used with, for example, a single signal generator and multiple receiving units. The number of antenna and corresponding signal generators and receiving units is not limited to the three illustrated on the figures. Any number of antenna elements may be contemplated.

Figure 8 illustrates the behaviour of a two dimensional array antenna. Circles 410 represent the antenna elements on a grid spaced by a reference distance d, typically half the wavelength. The antenna elements are distributed along two directions x and y.

Methods for determining the angle of arrival are generally applied based on the covariance matrix. The covariance matrix is the result of the multiplication of a vector constituted by the signals received at each active antenna element, and its Hermitian transpose. The resulting matrix contains all the different delays that could exist from one antenna element to another. The angle of arrival is then obtained by multiplying the covariance matrix with the antenna manifold at various angles. When all delays are in phase, the maximum signal to noise ratio is obtained. It is therefore possible to determine the angle of arrival. Obviously, the delays between the antenna elements depend on the distance between the antenna elements.

Refering to antenna 401, for the x direction, 6 signals with a delay 0, 5 distances with a delay dx, 4 distances with a delay 2.dx, 3 distances with a delay 3.dx, 4 distances with a delay 4.dx and 1 distance with a delay 5.dx may be observed. For the y direction, 3 distances with a delay 0 and 3 distances with a delay dy can be observed.

Antenna 402 corresponds to antenna 401 where one antenna element has been removed. Referring to antenna 402, for the x direction, 5 signals with a delay 0, 3 distances with a delay dx, 1 distances with a delay 2.dx, 2 distances with a delay 3.dx, 2 distances with a delay 4.dx and 1 distance with a delay 5.dx may be observed. For the y direction, 3 distances with a delay 0 and 2 distances with a delay dy can be observed. Both antennas 401 and 402 cover all possible delays. Antenna 401 is the Kronecker product of [1 1 1] and [1 13] meaning that it can be realized using two LO antennas represented by [1 1 1] and LO 01 and comprising together 5 antenna elements.

Using these 5 antenna elements, an antenna corresponding to a virtual antenna with 6 antenna elements is achieved.

Antenna 402 does not correspond to a Kronecker product. This antenna can only be realized using 5 antenna elements and does not correspond to a virtual antenna of 6 antenna elements. So, no gain in the number of antenna element is achieved.

Considering the measure of the different delays, both antenna cover all delays. No delay is missing. This is of importance as a missing delay means that no measure of this delay will be obtained and this results in an increased signal to noise ratio. Antenna 401 exhibits more redundancy in the measure of the different delays. Each delay may thus be measured by averaging each measure. By averaging more measures of each delay antenna 401 allows a better signal to noise ratio compared to antenna 402.

These examples illustrate the fact that a two dimensions antenna generated by a Kronecker product is preferable to any other two dimensional antenna, even if both antennas cover all possible delays.

Figure 9 illustrates the effect of the MIMO operation for 2D antenna arrays, when the operation does not correspond to a Kronecker product. The MIMO operation of the antenna array 501 over the antenna array 502 corresponds to a virtual array 503. The coverage is augmented as the virtual antenna is the result of the tiling of the 2 antennas.

The operation may be seen as reporting the configuration of antenna 501 at each antenna element of 502. It results in superposition of antenna elements in the corresponding virtual array antenna. The aperture is augmented from 2.d to 3.d in both directions. The number of antenna elements in the virtual antenna 503 is 7. Using 2 antennas of 3 elements created a virtual array of 7 elements with a small gain of 7/6. It uses 6 antenna elements for a total number of delay coverage of 49. The total number of delay coverage is the sum of all delay coverages, i.e. the sum of the coverage with the distance d, added to the sum of coverage with the distance 2.d, added to the sum of coverage with the distance 3.d, and so on.

Figure 10 illustrates the effect of the MIMO operation for two dimension antenna arrays, when the operation does correspond to a Kronecker product. The MIMO operation of the antenna array 601 over the antenna array 602 corresponds to the virtual array 603. One of the antenna arrangements has supported a geometric transformation.

This transformation corresponds to a dilation that allows the virtual antenna elements not to be superposed. This transformation is the translation of one or several alignements of antenna elements, following the x and y directions. With these operations of translation the MIMO now operates a Kronecker operation in two dimensions. As a result the aperture of the antenna is augmented from 3.d to 5.d in the y direction, but is augmented to 4.d in the x direction.

The number of antenna elements in the virtual antenna 603 is 9. Using 2 antennas of 3 antenna elements created a virtual array of 9 antenna elements with a better gain of 9/6 compared to the previous example.

As the number of virtual antenna elements is now N x M, obviously the gain will be enhanced for a larger number of antenna elements. The total coverage number is here 53 for 6 antenna elements, again a gain compared to the previous example.

Figure 11 illustrates the main steps of a method to generate an antenna according to embodiments of the invention.

The described method is based on the matrix representation of array antennas as previously described. Matrices contains 0 and 1 value to represent the position of activated antenna elements on a square grid based on the reference distance d, which is typically half the wavelength of the signal used by the radar.

In step 1101, a first rectangular matrix is generated. The generation of the first rectangular matrix is typically done by a Kronecker product of a linear array containing only 1 values with a seed two dimensions matrix. The seed matrix can be a diagonal, or anti-diagonal, matrix containing 1 values on the diagonal and 0 values elsewhere. Alternatively, a rectangular seed matrix may be used. The seed matrix must follow the following rule: it must contain at least a 1 value per line and per column. In some embodiments, the first rectangular matrix may be a square matrix.

In step 1102, a second rectangular matrix is generated. The generation of the second rectangular matrix is similar to the generation of the first rectangular matrix. When the first and second rectangular matrix are not square matrices, then the first rectangular matrix and the second rectangular matrix are orthogonal, meaning that if the first rectangular matrix has longest rows than columns, the inverse will be true for the second rectangular matrix. This may be obtained by transposing the result of the Kronecker product of the linear arreay and the seed matrix used to generate the second rectangular matrix or by using a vertical linear array instead of a horizontal one. In an embodiment, the second rectangular matrix corresponds to the transposition of the first rectangular matrix.

The first and second rectangular matrices are intended to represent two dimension antennas of a MIMO antenna. For example, the first rectangular matrix represents the transmission antenna elements of the MIMO antenna while the second rectangular matrix represents the reception antenna elements of the MIMO antenna, or vice-versa. This MIMO antenna is equivalent to the two dimensions antenna represented by the Kronecker product of the first and second rectangular matrices. As explained above, the Kronecker product may be seen as inserting the pattern of one matrix at each position with a 1 value in the other matrix. As illustrated by Figure 9 and 10, this Kronecker product is likely to lead to superposition of antenna elements. While the resulting antenna is effective, it does not offer all the potential given by the first and second rectangular matrices. This superposition limits the gain in term of number of antenna elements and in term of aperture of the resulting antenna.

In some embodiments, it is possible to overcome at least partially these limitations by applying an optional dilation step 1103 to one of the first and second rectangular matrix. This dilation step consists in translation applied to rows and columns of the matrix. The translation factor depends on the row and column it is applied to. This dilation step has the effect to move away from each other the antenna elements represented by 1 values in the matrix. By doing so, the insertion of the pattern of the other matrix realized by the Kronecker product results in less superposition of antenna elements. It also enlarges the resulting antenna corresponding to its aperture. The dilation step therefore improves the gain in term of the number of antenna elements and in term of aperture of the resulting antenna. The limit to the dilation is to avoid creating some empty rows or empty columns in the resulting antenna as such empty rows or columns generate some grating lobes prejudicial to the operation of the resulting antenna. This means that the distance between two successive rows and respectively columns in the dilated rectangular matrix being lower or equal to the number of rows, respectively columns, of the non-dilated rectangular matrix minus one. The embodiment where the dilation generates exactly the space for the pattern of the other matrix between the 1 values of the first matrix gives the maximum gain. It means that the distance between two successive rows and respectively columns in the dilated rectangular matrix is equal to the number of rows, respectively columns, of the non-dilated rectangular matrix minus one.

In step 1104, the actual antenna design is obtained from the first and second rectangular matrices. In a first embodiment, the antenna is designed to correspond to a MIMO antenna where the transmission two dimensions antenna and the reception two dimensions antenna correspond to the antennas represented by the first and second rectangular matrices. In a second embodiment, the antenna is designed to correspond to the array antenna represented by the Kronecker product of the first and second rectangular matrices. The antenna may be manufactured from the obtained design.

Antennas designed according to the proposed method exhibits a high gain in term of the number of antenna elements while preserving a good aperture and the resolution of the obtained images. For a same number of active antenna elements, antenna designed according to the invention achieved better performance over other designs. In the preferred embodiment where the dilation corresponds exactly to the size of the pattern of the first rectangular matrix, the covariance matrix used in the method for determining the angle of arrival is invertible. Compared to other designs, the coverage of the different delays is increased resulting of an improvement of the signal to noise ratio. Compared to MIMO antennas based on one dimension arrays of antenna elements, the proposed design is more compact as the antenna elements are gathered on several lines, or columns. As the multiplicative property of array factor is conserved in the proposed two dimension arrays, the sharpness of the resolution can be easily calculated.

Figure 12 illustrates a first example of application of the method according to the invention. A seed matrix of size 2x2 has been chosen. For sparsity reason, the choice has been made to use the matrix [01 (11 as the seed matrix 1201. The linear array used is the vector 1202 [1 1 1]. The first rectangular matrix 1203 is obtained by applying a Kronecker product to matrices 1201 and 1202.

In this example, the second rectangular matrix 1204 is obtained by a transposition of 1203.

Next, a dilation step is applied to matrix 1204 to obtained a dilated matrix 1205. The dilation consists in translation of the lines and columns of 1204 in x and y directions. The translation vectors have an oriented length of i.d in the y direction for lines indexed by i from 0 to 5. The translation vectors have an oriented length of 0 and j.5.d in the x direction for the two columns of matrix indexed by j. It may be noted that the pattern of the first rectangular matrix 1203 has a size of 1=2 lines and J=6 columns. To allow an exact insertion of the pattern between positions of antenna elements in the second rectangular matrix 1205, the translations of each line must be i.(I-1).d and the translation of each column must be j.(J-1).d. Lower translations may be used but will lead to lower gain in term of antenna elements and aperture. Higher translations must not be used, as they will generate empty lines or columns in the resulting matrix 1205, and thus grating lobes in the corresponding antenna. Alternatively, the dilation may have been applied to the first rectangular matrix 1203 instead of the second rectangular matrix 1204.

The two final rectangular matrices 1203 and 1205 being obtained, the antenna may be designed based on these matrices. In a first embodiment two antennas are build corresponding to the two rectangular matrices 1203 and 1205, used one for transmission and one for reception according to a MIMO scheme. The MIMO antenna is equivalent to an antenna represented by the Kronecker product 1206 of the two rectangular matrices 1203 and 1205. In a second embodiment, an antenna is build based on the Kronecker product 1206 of the two rectangular matrices 1203 and 1205, for example in reception an additional antenna element being used in transmission or vice-versa. Both embodiments have the same properties. The resulting antenna has good properties as no empty lines or empty columns are created in the Kronecker product 1206 of the two rectangular matrices 1203 and 1205. It has to be noted that there is no element inter distance of A/2 in one direction. Grating lobes will be created in this direction and hence, the field of view of this antenna shall be limited. Adding one or two antenna elements anywhere in the pattern of 1203 eliminates the grating lobes. As the proposed design seeks a reduction of the number of antenna elements that keeps the resolution of a full array antenna while allowing a decrease in the field of view, the design makes the economy of these antenna elements.

Figure 13 illustrates another example of application of the method according to the invention. This example is similar to the previous one with the exception that the second rectangular matrix 1304 has been extended with two additional lines. The resulting antenna corresponding to matrix 1306 is therefore no more square but rectangular. The second rectangular matrix 1304 is dilated similarly to the second rectangular matrix 1206. The resulting antenna presents a different resolution in azimuth and elevation.

Figure 14 illustrates another example of application of the method according to the invention. This example is similar to the previous one with the exception that the seed Fl 0 matrix is now the matrix 0 1. Accordingly, the first rectangular matrix 1403 has now 3 1 0 lines. The second rectangular matrix 1404, being here the transposition of the first rectangular matrix 1403 has 3 columns. This second rectangular matrix 1404 is dilated according to the same rules to obtained a dilated second rectangular matrix 1405. The antenna will correspond to the Kronecker product 1406. Here again, the resulting antenna has good properties has the Kronecker product 1406 does not contain any empty line or column.

Figure 15 illustrates another example of application of the method according to an embodiment of the invention. When a large field of view is necessary, the addition of 2 antenna elements to one of the antenna is sufficient to eliminate the grating lobes that appears in the antenna factors with the examples of the previous figures, at large angles. In this case, the sparsity is no longer 50% compared to a fully populated antenna.

A seed matrix of size 2x2 has been chosen. For sparsity reason, the choice has been made to use the matrix E0 1l 1. The linear array used is the vector [1 1 1 1 1]. A first rectangular matrix is obtained by applying a Kronecker product to these matrices. The antennas are then designed based on these matrices, following the steps described in figure 11.

To obtain a large field of view, 2 antenna elements must be added on the antenna that has not been dilated, represented here by the set 1500. The other dilated set is unchanged and is not represented. Here element 1501 and element 1502 are added to the set originally obtained by the Kronecker product, aligned to the x and y direction inter distances. Thus, antenna elements at a distance below or equal the half wave are added, and no grating lobe will appear when the antenna factor is realized, even if the antenna factor is calculated for a range of -90° to 90°.

Any step of the algorithms of the invention may be implemented in software by execution of a set of instructions or program by a programmable computing machine, such as a PC ("Personal Computer"), a DSP ("Digital Signal Processor") or a microcontroller; or else implemented in hardware by a machine or a dedicated component, such as an FPGA ("Field-Programmable Gate Array") or an ASIC ("Application-Specific Integrated Circuit").

Although the present invention has been described hereinabove with reference to specific embodiments, the present invention is not limited to the specific embodiments, and modifications will be apparent to a skilled person in the art which lies within the scope of the present invention.

Many further modifications and variations will suggest themselves to those versed in the art upon making reference to the foregoing illustrative embodiments, which are given by way of example only and which are not intended to limit the scope of the invention, that being determined solely by the appended claims. In particular the different features from different embodiments may be interchanged, where appropriate.

Each of the embodiments of the invention described above can be implemented solely or as a combination of a plurality of the embodiments. Also, features from different embodiments can be combined where necessary or where the combination of elements or features from individual embodiments in a single embodiment is beneficial.

Each feature disclosed in this specification (including any accompanying claims, abstract and drawings) may be replaced by alternative features serving the same, equivalent or similar purpose, unless expressly stated otherwise. Thus, unless expressly stated otherwise, each feature disclosed is one example only of a generic series of equivalent or similar features.

In the claims, the word "comprising" does not exclude other elements or steps, and the indefinite article "a" or "an" does not exclude a plurality. The mere fact that different features are recited in mutually different dependent claims does not indicate that a combination of these features cannot be advantageously used.

Claims (8)

1. CLAIMS1. A method of manufacturing an array antenna comprising the following steps: generating a first rectangular matrix by applying a Kronecker product of a first linear vector containing 1 values and a first seed matrix, the first seed matrix containing only 1 and 0 values, the first seed matrix containing at least a 1 value per line and per column; generating a second rectangular matrix by applying a Kronecker product of a second linear vector containing 1 values and a second seed matrix, the second seed matrix containing only 1 and 0 values, the second seed matrix containing at least a 1 value per line and per column, the first and second rectangular matrices being orthogonal; manufacturing the array antenna equivalent to the array antenna represented by the Kronecker product of the first and second rectangular matrices.
2. 2. The method of claim 1, wherein the method further comprises: dilating the first or second rectangular matrix by applying translations to lines and columns of the dilated rectangular matrix, the distance between two successive rows and respectively columns in the dilated rectangular matrix being lower or equal to the number of rows, respectively columns, of the non-dilated rectangular matrix minus one.
3. 3. The method of claim 2, wherein the distance between two successive rows and respectively columns in the dilated rectangular matrix is equal to the number of rows, respectively columns, of the non-dilated rectangular matrix minus one.
4. 4. The method of any one of claims 1 to 3, wherein the seed matrix is a diagonal, or anti-diagonal, matrix.
5. 5. The method of any one of claims 1 to 4, wherein the second rectangular matrix is a transposition of the first rectangular matrix.
6. 6. The method of any one of claims 1 to 5, wherein the generated antenna is a MIMO antenna comprising a first and second array antenna represented by the first and second rectangular matrices, one array antenna being used in transmission, the other one in reception.
7. 7. The method of any one of claims 1 to 5, wherein the generated antenna comprises one antenna element and an array antenna represented by the Kronecker product of the first and second rectangular matrices, one of the antenna element and the array antenna being used in transmission, the other in reception.
8. 8. An array antenna manufactured according to any one of claims 1 to 7.