GB2568741A

GB2568741A - Optimized transmission scheme for radar using mutually orthogonal complementary codes

Info

Publication number: GB2568741A
Application number: GB1719653.6A
Authority: GB
Inventors: Achir Mounir; Thoumy Francois; Le Bars Philippe
Original assignee: Canon Inc
Current assignee: Canon Inc
Priority date: 2017-11-27
Filing date: 2017-11-27
Publication date: 2019-05-29
Anticipated expiration: 2037-11-27
Also published as: GB201719653D0; GB2568741B

Abstract

A method comprises transmitting radar pulses encoded with mutually orthogonal complementary sets of code, each set comprising at least a first and second code. Pulses encoded with the first codes are transmitted in a first timeslot and pulses encoded with the second codes are transmitted in a second timeslot. The method further comprises receiving the first and second echoes of the pulses and determining and applying a filter to obtain the separate signals by cross-correlating the received echoes. The filter may be determined specifically by calculating the cross correlations of the first code with the first echo and the second code with the second echo. The calculated cross-correlations corresponding to a same set of codes are summed to obtain respective summed correlation signals. The summed correlation signals may then themselves be summed to obtain the desired filter. An angle-of-arrival algorithm may be applied to the obtained separated signals.

Description

OPTIMIZED TRANSMISSION SCHEME FOR RADAR USING MUTUALLY ORTHOGONAL COMPLEMENTARY CODES

FIELD OF THE INVENTION

The invention relates to the field of radar apparatuses, in particular the transmission and reception of complementary codes with ΜΙΜΟ (Multiple Input Multiple Output) radar.

Range resolution relates to the ability of a RADAR (“RAdio Detection And Ranging”) system to distinguish between two targets that are close to each other. For pulsed radar systems, which transmit signals comprising regular pulses at a given frequency, the range resolution depends on the bandwidth of the transmitted/received signal, which is inversely proportional to the pulse duration: the shorter the pulse, the lower (better) the range resolution. However, the strength of the received signal is proportional to the pulse duration: the longer the pulse, the higher the received signal strength, and thus the greater the detection range.

A technique known as “pulse compression” helps to solve this incompatibility by transmitting a long pulse which has a bandwidth corresponding to a short pulse, by coding the original pulse and modulating the transmitted signal. For example, a Barker B7 code [1110 0 10] may be generated, and the transmitted signal has a phase modulated carrier and a bandwidth depending on the width of the sub-pulses (duration of each bit). The energy used for the target detection depends on the width of the coded pulse, i.e. the duration of the entire code, here seven times the duration of the sub pulse.

The received signal, after processing, comprises a main lobe with high amplitude providing information about the distance (range) to the target, and is well adapted to detecting a single target. However, side lobes of lower amplitudes on each side of the main lobe also result, interfering with the detection of two or more targets, depending on their Radar Cross Section (RCS). As an example, if a first target is at 20 meters, a second target is at 22 meters, and the targets have the same RCS, two main peaks will be visible, allowing detection of the two targets. However, if the targets have different RCS, such as a car with a high RCS due to the large metallic frame that reflects waves well and a person with a small RCS due to a small non-metallic frame that does not reflect waves well, a main peak at 20 meters will be visible, with disturbed side-lobes, which may relate to the weak detection of a second target or be simply due to noise. The second target is thus poorly distinguished or not at all.

The appearance of side-lobes may thus be problematic in some cases, in particular for the detection of targets close to each other with different RCS values. Various methods have been developed to suppress side-lobes, in particular the use of “complementary codes” such as Golay codes or Spano codes, wherein several pulses are successively sent, each pulse being encoded with a specific code.

Upon reception, matched filters are applied to each pulse and the outputs of the matched filters are summed (cross-correlation). Cross-correlation is applied by convolving the incoming signal with a conjugated and time-reversed version of the transmitted signal. Thanks to the property of the complementary codes, the correlation signal, after cross-correlation, comprises a main lobe with a multiplied amplitude (such as by two if two complementary codes are sent) while the side-lobes cancel each other out.

A radar apparatus can also estimate an “Angle of Arrival” of echoes coming from targets by means of an antenna array with specific signal processing. MultipleInput Multiple-Output or “ΜΙΜΟ” radars can be used to estimate the Angle of Arrival. A ΜΙΜΟ Radar uses several transmitting antenna elements and several receiving antenna elements in order to simulate a virtual array antenna having a larger number of receiving antenna elements arranged as an array of receiving antenna elements.

A steering vector represents the delays in the reception of a plan signal at each of the receiving antenna elements in the array. From the steering vector, known methods allow the azimuth and elevation angles of the source of the plan signal to be estimated. In radar application, the source of the plan signal is the target. Being able to compute the steering vector of the simulated array antenna from the signals reflected by the target allows the radar to compute the “angle of arrival”, and thus the position of the target.

A “cross antenna” configuration comprises a transmitting antenna comprising antenna array elements arranged in a linear vertical manner, and a receiving antenna comprising antenna array elements arranged in a linear horizontal manner.

Figures 1A, 1B schematically present corresponding equivalent antenna arrays.

The first example, as shown in Figure 1A, presents two transmitting antenna elements TA1, TA2 arranged vertically and two receiving antenna elements RA1, RA2 arranged horizontally.

The second example, as shown in Figure 1B, presents one transmitting antenna element TA1 in the center of a square arrangement of four receiving antenna elements RA1, RA2, RA3, RA4 forming an array antenna.

These two examples may be shown as equivalent by computing a steering vector, which represents the set of phase delays a plane wave experiences, evaluated by a set of array antenna elements. The phases are specified with respect to an arbitrary origin.

In the following:

dT is the distance between two transmitting antenna elements TA; dR is the distance between two receiving antenna elements RA; λ (Greek letter lambda) is the wavelength of an electromagnetic wave; j is the square root of -1;

Θ (Greek letter theta) is an elevation angle;

φ (Greek letter phi) is an azimuth angle;

X1 is the signal transmitted from the antenna element TA1;

X2 is the signal transmitted from the antenna element TA2;

Y1 is the signal (echo) received at the antenna element RA1; and

Y2 is the signal (echo) received at the antenna element RA2.

The steering vector matrix A at the transmission is as follows:

The steering vector matrix B at the reception is as follows:

g _ N g-7.2rc.d/?.sin(<p)/Al [matrix 2]

The relation between X1, X2, Y1, Y2 is given by the following matrix:

= B^T.A.

[matrix 3] wherein B^T is the transpose of matrix B.

If X1, X2 are orthogonal or de-correlated (temporally) then:

wherein xcorr is the cross-correlation function.

By de-correlated it is meant that X1, X2 are transmitted at different times/periods.

It may be noted that the arrangement of the antennas TA, RA may be changed, but the steering vectors would be modified accordingly.

From the above equations, the two-dimensional (2D) steering vector can be computed corresponding to the steering vector of the one transmitting antenna element ΤΑ (TA1) and four receiving antenna elements RA (RA1, RA2, RA3, RA4) forming an array antenna as shown in Figure 1B. The 2D steering vector is provided by the following matrix:

B^T.A = g-j .2n.dR.sln(pp')/A g-j.2n.dT.sin(9)/i g-j .2n.(dT.sln(e)+dR.sln((p))/A [matrix 4]

It has been demonstrated here that the “cross antenna” configuration shown in

Figure 1A is equivalent to the “array antenna” configuration shown in Figure 1B, and that the 2D steering vector corresponding to the array antenna is applicable. Conventional Angle of Arrival methods that assume an array antenna configuration may therefore be applied on Yv1, Yv2, Yv3, Yv4 in order to estimate Θ (theta) and φ (Phi).

This result can be generalized to show that a “cross antenna” configuration with K transmitting antenna elements and K receiving antenna elements (Figure 1A) is similarly equivalent to an array antenna with one transmitting antenna element and an array of K * K antenna elements (Figure 1B). Thus, if the transmitting and receiving antenna elements are generalized to K elements (K TA and K RA), the steering vector

A at the transmission is as follows:

A = [1 g-7.2rc.dT.sin(0)/A ^-/.2.2rc.dT.sin(0)/A

[matrix 5]

The steering vector at the reception is as follows:

B = [1 g-j.2n:.dR.sin(<p)^ g- j .2.2Tt.dR.sin(rp)IX

[matrix 6]

The 2D steering vector is given by:

1 g-/.2n.dT.sin(e)/'A g-j .2π.άΚ.5ΐη(φ)/λ	ρ-].(Κ-1).2π:.άΤ.5ίη(θ)/λ
g-p(K-l).2n.dR.si.n(rp)/A	g-j.(K-l).2n.(dR.sin(rp)+dT.sin(9)')/A_

[matrix 7]

It is to be noted that the method for estimating an angle of arrival assumes an array antenna of size K * K. As such, it takes as input K * K received signals that are used with the corresponding 2D steering vector to estimate the azimuth (phi) and elevation (theta) angles of arrival. When using a “cross antenna” configuration with K receiving antenna elements and K transmitting antenna elements, at a given moment, meaning that during a given timeslot, only K signals have been received, each received signal being the sum of the corresponding K transmitted signals.

It has been shown here that a cross antenna with K transmitting antenna elements and K receiving antenna elements is equivalent to a K x K array antenna with one transmitting antenna and K x K receiving antenna elements. It is possible to compute the K x K steering vector corresponding to the K x K array antenna using the signal received by the cross antenna with the condition that, at reception, signals from the K different transmitting antenna elements may be discriminated, in other words separated.

A simple way of fulfilling this condition is to separate in time the transmission by the transmitting antenna elements, that is to say, the transmitting antenna elements transmit their signals successively at different time intervals. Nevertheless, this solution is time consuming (e.g., the time for image reconstruction is high), and may be improved.

In the example of the “cross antenna” configuration of Figure 1A, where K = 2, if transmitting antenna elements TA1 and TA2 each transmit a signal at the same time, the receiving antenna elements RA1 and RA2 receive respectively echoes combining the two transmitted signals. In order to use the estimation of angle of arrival method, the signal transmitted by each transmitting antenna needs to be discriminated (that is to say, separated) at each receiving antenna element, in order to obtain the two received signals.

Golay pairs are used to generate mutually orthogonal complementary codes, wherein a code is a sequence of bits.

The following is an example of four codes (A1, A2, B1, B2) of four bits (b1, b2, b3, b4) each:

	b1	b2	b3	b4
A1	1	1	1	-1
A2	1	-1	1	1
B1	1	1	-1	1
B2	1	-1	-1	-1

Table 1: Go ay Pairs Matrix G1

A pair of codes (e.g. a pair of binary sequences with the same finite length) is complementary if the sum of their respective auto-correlation functions is zero for all non-zero offsets. The complementary property can be demonstrated by computing the cross-correlation xcorr of each of the codes of the Golay Pairs matrix: xcorr(A1, A1) + xcorr(A2, A2) [equation 2A] = [-1 0 1 4 1 0 -1] + [1 0 -1 4 -1 0 1 ] = [0 0 0 8 0 0 0] xcorr(B1, B1) + xcorr(B2, B2) [equation 2B] = [1 0-1 4-1 0 1 ] + [-1 0 1 4 1 0 -1] = [0 0 0 8 0 0 0]

One can see that A1 and A2 are complementary with each other, and B1 and B2 are complementary with each other since the values other than the middle value (4) are opposite each other, canceling each other out (0), while the middle values (4) are the same such that the sum is doubled (8). Consequently, in an ideal case, the use of complementary codes allows a correlation signal to be obtained with a main lobe having a multiplied (doubled) amplitude, while the side-lobes are canceled out after processing ofthe received echoes.

To find the cross-correlation of a code, the bits are sequentially compared with each other. If the bits are the same (both 1 or both -1) a 1 results, and if the bits are different (one 1 and one -1), a -1 results. The values are summed, and then the sequence is shifted, and the comparison repeats.

For example, the cross-correlation of A1 [111 -1] with itself is as follows, for the bits b1 (1), b2(1), b3(1), b4(-1), from the following configuration (shifted so only first and last bits are aligned):

			1	1	1	-1
1	1	1	-1

Table 2A: First cross-correlation of A1, A1

The comparison of bits b1 (1) of the first line and b4(-1) of the second line provides a value of -1, the first value of xcorr(A1, A1). Next, from the following configuration (shifted so the first and third bits are aligned).

		1	1	1	-1
1	1	1	-1

Table 2B: Second cross-correlation of A1, A1

The comparison of bits b1(1) and b3(1) provides a value of 1, and the comparison of bits b2(1) and b4(-1) provides a value of -1, such that their sum is 0, the second value of xcorr(A1, A1). The shifting, comparison, and summation continue until all bits have been compared.

The orthogonal property can be demonstrated also by computing the crosscorrelation of the codes of the Golay Pairs matrix: xcorr(A1, B1) + xcorr(A2, B2) [equation 3A] = [1 0 1 0 3 0 -1] + [-1 0 -1 0 -3 0 1 ] = [0 0 0 0 0 0 0] xcorr(B1, A1) + xcorr(B2, A2) [equation 3B] = [-1 0 3 0 1 0 1] + [1 0-3 0-1 0 -1 ] = [0 0 0 0 0 0 0]

Hence (A1, A2) and (B1, B2) are mutually orthogonal, having zero crosscorrelation.

From the above equations, one can conclude that: xcorr(A1, A1+B1) + xcorr(A2, A2+B2) [equation 4A] = xcorr(A1, A1) + xcorr(A1, B1) + xcorr(A2, A2) + xcorr (A2, B2) = xcorr(A1, A1) + xcorr(A2, A2)

It may be noted that a cross-correlation of a sum is equal to a sum of crosscorrelations, such that xcorr(A1, A1+B1) may be considered as equivalent to xcorr(A1,A1) + xcorr(A1, B1). From the second line above, the xcorr(A1, B1) + xcorr(A2, B2) values cancel each other out, leaving simply xcorr(A1, A1) + xcorr(A2, A2).

Likewise, for the B values:

xcorr(B1, A1+B1) + xcorr(B2, A2+B2) [equation 4B] = xcorr(B1, A1) + xcorr(B1, B1) + xcorr(B2, A2) + xcorr (B2, B2) = xcorr(B1, B1) + xcorr(B2, B2)

It is to be noted here that A1+B1 will represent the echo received by a receiving antenna element when two transmitting antenna elements transmit simultaneously pulses encoded respectively with code A1 and code B1. It means that the cross correlation of the received signal with A1 added to the cross correlation with A2 allows to retrieve the contribution of the first antenna element to the received signal. The contribution of the second antenna element being canceled thanks to the orthogonality property. The contribution of the second antenna element to the received signal may be retrieved similarly with cross correlation with B1 and B2. Consequently, codes A1 and B1 can be simultaneously transmitted, and codes A2 and B2 can also be simultaneously transmitted, since they may be separated during processing.

It is thus possible to transmit two different signals by two antenna elements simultaneously and still be able to separate at reception the transmitted signals, by coding the two transmitted signals using a pair of orthogonal codes. It is therefore possible to reduce the transmission time by two, compared to the simplest solution (one code at a time), by allowing pairs of transmitting antenna elements to transmit simultaneously. A radar using this technique will be twice as fast to detect a target along with its position.

Figure 2 illustrates an example of transmitting mutually orthogonal complementarycodes. Two different codes are simultaneously transmitted on two (or more) transmitting antenna elements, instead of transmitting a code antenna element by antenna element. The different complementary codes have some orthogonal properties necessary for separating, upon reception, the simultaneously transmitted signals.

In Figure 2, Golay pairs are used to generate the mutually orthogonal complementary codes. Pulses encoded with codes A1, A2, B1, B2 are transmitted, codes A1, A2 being complementary with each other, and codes B1, B2 being complementary with each other, as described above.

During a timeslot TS1, pulses encoded with codes A1, B1 are simultaneously transmitted by means of first and second transmitting antenna elements TA1, TA2 respectively. During a timeslot TS2, pulses encoded with codes A2, B2 are simultaneously transmitted by means of the same transmitting antenna elements TA1, TA2. It is to be noted that when it is indicated that an antenna element transmits code X, it simply a manner of indicating that the antenna element transmits pulse(s) encoded with code X.

Receiving antenna elements RA1, RA2 are active during the entire transmission, the receiving antenna elements being configured to receive echoes Xij (i being an index of the timeslot, j being an index of the receiving antenna element). During a timeslot TS1’ (slightly delayed with respect to timeslot TS1 of the transmission), echoes X11, X12 are simultaneously received by means of the first and second receiving antenna elements RA1, RA2 respectively.

It may be noted that echoes X11, X12 do not correspond directly to pulses encoded with codes A1, B1 respectively, but rather are combined signals (resulting from the combination of pulses simultaneously transmitted) received by each antenna element, slightly delayed with respect to A1 and B1, but for the sake of simplicity, it will be considered that X11 = A1 + B1, X12 = A1 + B1, X21 = A2 + B2, X22 = A2 + B2.

Once the pulses have been transmitted and the echoes received, the echoes can be processed by known methods.

In particular, equations 4 (4A, 4B) described above are applied on the received echoes X11, X12, X21, X22. The pulses simultaneously transmitted by each transmitting antenna element (TA1, TA2) are each cross-correlated with the echoes received in the same timeslot. For example, for transmitting antenna element TA1, transmitted code A1 is cross-correlated with X11 (A1 + B1), and transmitted code A2 is cross-correlated with X21 (A2 + B2) [equation 4A], to obtain the sum of crosscorrelations (A1, A1) + (A2, A2), providing detected target(s), as described in relation with equation 2A, and likewise for the transmitting antenna element TA2 [equations 4B - mutual orthogonality, and 2B - complementarity].

However, the method of Figure 2 does not allow more than two pairs of codes to be simultaneously transmitted.

As a consequence, the invention aims at finding transmission schemes that improve the time necessary for a ΜΙΜΟ radar to detect targets and determine their positions.

SUMMARY OF THE INVENTION

Embodiments of the invention relate to a method of receiving echoes by means of a radar receiving device comprising receiving antenna elements, the receiving antenna elements being configured to receive echoes of transmitted pulses; wherein the transmitted pulses are encoded by mutually orthogonal complementary sets of codes, each set comprising at least a first code and a second code; and wherein pulses encoded with the first codes are transmitted in a first timeslot, and pulses encoded with the second codes are transmitted in a second timeslot.

The receiving method comprises the steps of:

receiving, by each of the receiving antenna elements, a first echo resulting from the reflection off of at least one target of the pulses transmitted in the first timeslot;

receiving, by each ofthe receiving antenna elements, a second echo resulting from the reflection off of the at least one target of the pulses transmitted in the second timeslot;

determining a filter to be applied to a correlation signal resulting from crosscorrelations performed upon the received echoes to obtain separated signals, each separated signal corresponding to a single transmitted signal; and applying the determined filter to obtain the separated signals.

According to one embodiment, the filter is determined by:

calculating the cross-correlations of each first code with the first echo; calculating the cross-correlations of each second code with the second echo; summing the calculated cross-correlations corresponding to a same set of codes to obtain a summed correlation signal for each set of codes; and summing at least two summed correlation signals to obtain the filter.

According to one embodiment, all the summed correlation signals are summed to obtain the filter.

According to one embodiment, only two of the summed correlation signals are summed to obtain the filter, the summed correlation signals relating to mutually orthogonal pairs.

According to one embodiment, the filter is applied to each summed correlation signal.

According to one embodiment, the method further comprises a step of applying an angle of arrival algorithm on the obtained separated signals.

According to one embodiment, the number of receiving antennas is greater than two.

According to one embodiment, the number of receiving antennas is a power of two.

According to one embodiment, the total number of receiving antennas is an uneven number, and a Golay matrix for determining the pulses to transmit is obtained by determining the next higher power of two greater than the number of receiving antennas.

According to one embodiment, a sub-matrix of the obtained Golay matrix is determined to encode pulses.

Embodiments of the invention also relate to a method of transmitting pulses by means of a radar transmitting device comprising transmitting antenna elements; wherein the transmitted pulses are encoded by mutually orthogonal complementary sets of codes, each set comprising at least a first code and a second code.

The transmitting method comprises the steps of:

transmitting, by each of the transmitting antenna elements, pulses encoded with the first codes in a first timeslot; and transmitting, by each of the transmitting antenna elements, pulses encoded with the second codes in a second timeslot.

Embodiments of the invention also relate to a radar receiving device comprising receiving antenna elements configured to receive echoes of transmitted pulses; wherein the transmitted pulses are encoded by mutually orthogonal complementary sets of codes, each set comprising at least a first code and a second code; and wherein pulses encoded with the first codes are transmitted in a first timeslot, and pulses encoded with the second codes are transmitted in a second timeslot.

The radar receiving device is configured to:

receive, by each of the set of receiving antenna elements, a first echo resulting from the reflection off of at least one target of the pulses transmitted in the first timeslot;

receive, by each of the receiving antenna elements, a second echo resulting from the reflection off of the at least one target of the pulses transmitted in the second timeslot;

determine a filter to be applied to a correlation signal resulting from crosscorrelations performed on the received echoes to obtain separated signals, each separated signal corresponding to a single transmitted signal; and apply the determined filter to obtain the separated signals.

According to one embodiment, the filter is determined by:

calculating the cross-correlations of each first code with the first echo;

calculating the cross-correlations of the each second code with the second echo;

summing the calculated cross-correlations corresponding to a same set of codes to obtain a summed correlation signal for each set of codes; and summing at least two summed correlation signals to obtain the filter.

According to one embodiment, the device is further configured to apply an angle of arrival algorithm on the obtained separated signals.

Embodiments of the invention also relate to a radar transmitting device comprising transmitting antenna elements configured to transmit pulses; wherein the transmitted pulses are encoded by mutually orthogonal complementary sets of codes, each set comprising at least a first code and a second code.

The transmitting device is configured to:

transmit, by each of the transmitting antenna elements, pulses encoded with the first codes in a first timeslot; and transmit, by each of the transmitting antenna elements, pulses encoded with the second codes in a second timeslot.

Embodiments of the invention also relate to a radar apparatus comprising a radar receiving device according to an embodiment of the invention and a radar transmitting device according to an embodiment of the invention.

BRIEF DESCRIPTION OF THE DRAWINGS

Other particularities and advantages of the invention will also emerge from the following description, illustrated by the accompanying drawings, in which:

Figures 1A, 1B, schematically present corresponding equivalent antenna arrays;

Figure 2, previously described, illustrates a conventional transmitting scheme;

Figure 3 shows a transmitting scheme according to an embodiment of the invention;

Figure 4 shows a transmitting scheme according to another embodiment of the invention;

Figure 5 is a flowchart of a transmitting method, according to the transmitting scheme of Figure 3;

Figure 5 is a flowchart of a receiving and processing method, according to the transmitting scheme of Figure 3; and

Figure 6 is a schematic block diagram of a computing device for implementing one or more embodiments of the invention.

DETAILED DESCRIPTION OF THE INVENTION

Embodiments of the invention relate to an improved radar transmitter/receiver based on the generation, transmission, reception and processing of complementary codes.

Such a radar allows an improved (decreased) refresh time (the time required to construct an image) for a same Pulse Repetition Interval PRI and a same number of averaging to provide the target range more quickly, an improved (increased) PRI for a same refresh time and a same number of averaging to provide an increased maximum range, or an increased number of averaging for a same refresh time and a same PRI to provide a better signal-to-noise ratio.

By extension of the method described in relation with Figure 2 to four or more simultaneously-transmitted codes (A1, B1, C1, D1 for example, as described in relation with the matrix G2 presented in Table 4 below), application of the processing described above in relation with this figure would not allow a signal to be completely separated from the other, since considering signal A for example, the C components could be canceled out thanks to the orthogonality, but the B and D components could not be canceled out using the conventional processing. It is thus necessary to find another method to process the simultaneously transmitted/received codes.

In particular, embodiments of the invention relate to an increased number of simultaneous transmissions of codes by transmitting two or more pairs (A and C, B and D, and so forth) of orthogonal codes, which are then simultaneously received and processed to separate out the individual codes by exploiting the complementary and orthogonal properties.

More specifically, a filter is determined and applied to the cross correlation of the received echoes with each transmitted code, to isolate each component (A, B, C, D...) in turn. The filter is equal to the sums of correlations between the transmitted codes and the received echoes. This filtering allows the transmitted signals to be recovered, and thus separated, for example to then calculate a steering vector and apply Angle of Arrival methods.

To this end, it is considered that an antenna (transmitting or receiving) comprises T transmitting antenna elements for sending codes and T receiving antenna elements for receiving echoes. However, in some embodiments, the numbers of transmitting and receiving elements are not necessarily identical.

If the total T of antenna elements is a power of two (2, 4, 8, 16...), then all T antenna elements may be active antenna elements K, thus T = K. The associated Golay matrix is thus of size 2K * 2K. As an example, if K = 8 (2^Λ3), the associated Golay matrix is of size 16 * 16 (thus eight pairs of codes A1, A2... H1, H2 for a total of sixteen codes of sixteen bits each, sent and received by eight antenna elements).

If however the total number T of antenna elements is not a power of two, then the next higher H power of two greater than the total T is determined, and the resulting Golay matrix of size 2H * 2H is obtained, each row of the matrix corresponding to a Golay code. As an example, if T = 7, the next higher H power of two is 2^Λ3 = 8, and the associated Golay matrix is of size 2H * 2H, here 16*16 again.

However, a sub-matrix of the Golay matrix is determined to encode pulses, since all codes cannot be sent (only seven antenna elements). The next lower L even number (or the number T if T itself is even, such as 10) is chosen, so that a maximum number of antenna elements out of the total T number of antenna elements available are utilized to simultaneously transmit/receive the codes.

In this case, considering T = 7, the next lower number L is 6, thus six out of seven antenna elements are utilized. The resulting submatrix is of size 2L * 2N = 12 * 16 (six sets of codes A1, A2... F1, F2 for a total of twelve codes, each code being of sixteen bits each, since only six antenna elements can simultaneously transmit).

As previously indicated, Golay codes may be used to increase the number of simultaneous transmissions, and as such will be exploited to allow a radar transmitter to transmit an increased number of codes, and to allow a radar receiver to receive and process an increased number of codes. As shown in Figure 2, pairs of codes (A1, A2) (B1, B2) comprising a first code (A1, B1) and a second code (A2, B2) may be transmitted, the first and second codes of a same pair being complementary, and the pairs being mutually orthogonal. In this manner, the processing is relatively straightforward in order to separate the transmitted codes.

It may be noted that the mutually orthogonal complementary Golay codes may be extended to eight or more codes with eight or more bits as necessary. The following is an example with eight codes (A1 to D2) of eight bits (b1 to b8), forming a matrix G2 of Golay Pairs:

	b1	b2	b3	b4	b5	b6	b7	b8
A1	1	1	1	-1	1	1	-1	1
A2	1	-1	1	1	1	-1	-1	-1
B1	1	1	-1	1	1	1	1	-1
B2	1	-1	-1	-1	1	-1	1	1
C1	1	1	1	-1	-1	-1	1	-1
C2	1	-1	1	1	-1	1	1	1
D1	1	1	-1	1	-1	-1	-1	1
D2	1	-1	-1	-1	-1	1	-1	-1
	rable 4: Golay Pairs Mai	.rix G2

As described above, for T = K = 4 (a total of four antenna elements, four being a power of two, thus T = K), the Golay matrix is 8 * 8 as above (four pairs of codes A1, A2... D1, D2 for a total of eight codes, each code of eight bits, to be sent and received by four antenna elements).

The complementary property can be demonstrated by computing the crosscorrelation of the codes of the Golay Pairs matrix:

xcorr(A1, A1) + xcorr(A2, A2) = [0 00000016000000 0] xcorr(B1, B1) + xcorr(B2, B2) = [0 0 0 0 0 0 0 16 0 0 0 0 0 0 0] xcorr(C1, C1) + xcorr(C2, C2) = [0 00000016000000 0] xcorr(D1, D1) + xcorr(D2, D2) = [0 00000016000000 0] [equations 7]

It may be noted that A1, A2 are complementary, B1, B2 are complementary, C1, C2 are complementary, and D1, D2 are complementary since for each pair, the values other than the middle value are opposite each other, canceling each other out (0), while the middle values are the same (8) such that the sum is doubled (16). Consequently, the use of complementary codes allows the amplitude of the main lobe to be doubled while the side-lobes are canceled out.

The orthogonal property can also be found by computing the cross-correlation of the codes of the Golay Pairs matrix:

xcorr(A1, C1) + xcorr(A2, C2) = [0 0000000000000 0] xcorr(B1, D1) + xcorr(B2, D2) = [0 0000000000000 0] [equations 7]

Hence, (A1, A2) and (C1, C2) are mutually orthogonal, and (B1, B2) and (D1, D2) are mutually orthogonal:

From the above equations, one obtains:

xcorr(A1, A1+C1) + xcorr(A2, A2+C2) = xcorr(A1, A1) + xcorr(A2, A2) xcorr(C1, A1+C1) + xcorr(C2, A2+C2) = xcorr(C1, C1) + xcorr(C2, C2) xcorr(B1, B1+D1) + xcorr(B2, B2+D2) = xcorr(B1, B1) + xcorr(B2, B2) xcorr(D1, B1+D1) + xcorr(D2, B2+D2) = xcorr(D1, D1) + xcorr(D2, D2) [equations 8]

It may be noted that (A1, A2) is not mutually orthogonal with (B1, B2) nor with (D1, D2) since:

xcorr(A1, B1) + xcorr(A2, B2) = [0 0080000000800 0] xcorr(A1, D1) + xcorr(A2, D2) = [0 0080000000800 0] [equations 9] Likewise, (B1, B2) is not mutually orthogonal with (C1, C2).

Consequently, pulses encoded with A1 and C1 can be simultaneously transmitted, pulses encoded with A2 and C2 can be simultaneously transmitted, pulses encoded with B1 and D1 can be simultaneously transmitted, and pulses encoded with B2 and D2 can be simultaneously transmitted. By using the known method as described in relation with Figure 2, it is not possible to simultaneously transmit A1 and B1, C1 and D1, nor A2 and B2, C2 and D2.

However, it will be demonstrated that, pulses encoded with all of the first codes (A1, B1, C1, D1) can be simultaneously transmitted during a timeslot, and pulses encoded with all of the second codes (A2, B2, C2, D2) can be simultaneously transmitted during another timeslot, if the received echoes are processed on the receiver end so as to separate out the different codes, as will be explained in relation with Figure 6 thanks to the filtering according to the invention.

Figure 3 illustrates a transmitting scheme by a radar transmitter device, according to an embodiment of the invention. The radar transmitter device has four transmitting antenna elements TA1, TA2, TA3, TA4 and the radar receiving device has four receiving antenna elements RA1, RA2, RA3, RA4. The radar devices may be separate entities or integrated into a single radar apparatus.

As explained above, a plurality of encoded pulses may be simultaneously transmitted as codes by a plurality of transmitting antenna elements.

By “simultaneously”, it is considered the difference in transmission time of the “codes” is less than a predetermined time interval (or timeslot). More particularly, in case of codes comprising a plurality of pulses (for example, the transmission of one or more codes A1 and one or more codes B1 simultaneously), the transmission time of the first pulse of the code A1 minus the transmission time of the last pulse of the code B1 is less than the predetermined time interval.

During a timeslot TS1, pulses encoded with codes A1, B1, C1, D1 are simultaneously transmitted by the four transmitting antenna elements (one by each antenna element). During a timeslot TS2, pulses encoded with codes A2, B2, C2, D2 are simultaneously transmitted by the same antenna elements. The process then repeats.

During a timeslot TS1’ (slightly delayed with respect to timeslot TS1), echoes Xij (again, i being an index of the timeslot, j being an index of the antenna - X11, X12, X13, X14) are simultaneously received by the four receiving antenna elements (one by each antenna). During a timeslot TS2’, echoes X21, X22, X23, X24 are simultaneously received by the same antenna elements. The process then repeats.

The codes A1, B1, C1, D1, A2, B2, C2, D2 are codes obtained from the Golay Matrix M2 above. As previously indicated, (A1, A2) are complementary codes, (B1, B2) are complementary codes, (C1, C2) are complementary codes, and (D1, D2) are complementary codes, (A1, A2) and (C1, C2) are mutually orthogonal pairs of codes, and (B1, B2) and (D1, D2) are mutually orthogonal pairs of codes.

The transmitting scheme illustrated in Figure 3 thus allows pulses encoded with four codes to be simultaneously transmitted [(A1, B1, C1, D1) OR (A2, B2, C2 , D2)], yet the total number of transmissions is limited to eight (A1, B1, C1, D1, A2, B2, C2, D2) in two sequential timeslots. This is as opposed to a total number of four transmissions but with only two codes simultaneously transmitted (A1, B1 OR A2, B2) as shown in Figure 2.

It may be noted that the invention may be generalized to a complementary set of more than two codes, where the sum of the cross-correlations of the codes in a set for all non-zero offsets (that is to say, for all values except the middle value, which corresponds to the main lobe). Likewise, two or more sets of codes are mutually orthogonal amongst themselves.

Figure 4 illustrates a transmitting scheme by a radar transmitter device, according to another embodiment of the invention. The radar transmitter device has eight transmitting antenna elements TA1, TA2, TA3, TA4, TA5, TA6, TA7, TA8 and eight receiving antenna elements (RA1, RA2, RA3, RA4, RA5, RA6, RA7, RA8 - not shown). During a timeslot TS1, the codes A1, B1, C1, D1, E1, F1, G1, H1 are simultaneously transmitted by the eight transmitting antenna elements (one by each antenna element). During a timeslot TS2, the codes A2, B2, C2, D2, E2, F2, G2, H2 are simultaneously transmitted by the eight transmitting antenna elements.

	b1	b2	b3	b4	b5	b6	b7	b8	b9	b10	b11	b12	b13	b14	b15	b16
A1	+ 1	+1	+ 1	-1	+ 1	+ 1	-1	+ 1	+ 1	+ 1	+1	-1	-1	-1	+ 1	-1
A2	+ 1	-1	+ 1	+1	+ 1	-1	-1	-1	+ 1	-1	+1	+ 1	-1	+1	+ 1	+ 1
B1	+ 1	+1	-1	+1	+ 1	+ 1	+ 1	-1	+ 1	+ 1	-1	+ 1	-1	-1	-1	+ 1
B2	+ 1	-1	-1	-1	+ 1	-1	+ 1	+ 1	+ 1	-1	-1	-1	-1	+1	-1	-1
C1	+ 1	+1	+ 1	-1	-1	-1	+ 1	-1	+ 1	+ 1	+1	-1	+ 1	+1	-1	+ 1
C2	+ 1	-1	+ 1	+1	-1	+ 1	+ 1	+ 1	+ 1	-1	+1	+ 1	+ 1	-1	-1	-1
D1	+ 1	+1	-1	+1	-1	-1	-1	+ 1	+ 1	+ 1	-1	+ 1	+ 1	+1	+ 1	-1
D2	+ 1	-1	-1	-1	-1	+ 1	-1	-1	+ 1	-1	-1	-1	+ 1	-1	+ 1	+ 1
E1	+ 1	+1	+ 1	-1	+ 1	+ 1	-1	+ 1	-1	-1	-1	+ 1	+ 1	+1	-1	+ 1
E2	+ 1	-1	+ 1	+1	+ 1	-1	-1	-1	-1	+ 1	-1	-1	+ 1	-1	-1	-1
F1	+ 1	+1	-1	+1	+ 1	+ 1	+ 1	-1	-1	-1	+1	-1	+ 1	+1	+ 1	-1
F2	+ 1	-1	-1	-1	+ 1	-1	+ 1	+ 1	-1	+ 1	+1	+ 1	+ 1	-1	+ 1	+ 1
G1	+ 1	+1	+ 1	-1	-1	-1	+ 1	-1	-1	-1	-1	+ 1	-1	-1	+ 1	-1
G2	+ 1	-1	+ 1	+1	-1	+ 1	+ 1	+ 1	-1	+ 1	-1	-1	-1	+1	+ 1	+ 1
H1	+ 1	+1	-1	+1	-1	-1	-1	+ 1	-1	-1	+1	-1	-1	-1	-1	+ 1
H2	+ 1	-1	-1	-1	-1	+ 1	-1	-1	-1	+ 1	+1	+ 1	-1	+1	-1	-1

Table 5: Golay Pairs Matrix G3

Other embodiments using larger Golay matrices, known to the skilled person, are possible.

Figure 5 is a flowchart of a method 500 of transmitting encoded pulses 10 according to an embodiment of the invention. The method 500 comprises steps 501, 502.

The method 500 relates to the transmitting scheme illustrated in relation with

Figure 3, that is to say with four transmitting antenna elements and four receiving antenna elements, but it may be extended to transmitting schemes with more antenna 15 elements, for example that illustrated in relation with Figure 4 with eight transmitting antenna elements and eight receiving antenna elements or for any number K of transmitting and receiving antenna elements.

In step 501, the radar transmitter device simultaneously transmits, during timeslot TS1, pulses encoded with the code A1 on the first antenna element TA1, with the code B1 on the second antenna element TA2, with the code C1 on the third antenna element TA3, and with the code D1 on the fourth antenna element TA4.

In step 502, the radar transmitter device simultaneously transmits, during timeslot TS2, pulses encoded with the code A2 on the first antenna element TA1, with the code B2 on the second antenna element TA2, with the code C2 on the third antenna element TA3, and with the code D2 on the fourth antenna element TA4.

Figure 6 is a flowchart of a method 600 of receiving and processing echoes according to an embodiment of the invention. The method 600 comprises steps 601 to 607.

The method 600 relates to the transmitting scheme illustrated in relation with Figure 3, that is to say with four transmitting antenna elements and four receiving antenna elements, but it may be extended to transmitting schemes with more antenna elements, for example that illustrated in relation with Figure 4.

In step 601, the radar receiver device receives, during timeslot TS1’, an echo X1j on the receiving antenna element RAj (that is to say, each receiving antenna RAj receives a corresponding echo X1j - X11, X12, X13, X14 by receiving antenna elements RA1, RA2, RA3, RA4 respectively). Each echo X1j (X11, X12, X13, X14) corresponds to a simultaneous transmission of pulses (e.g. encoded with A1, B1, C1, D1) transmitted in step 501 of the transmitting method 500 of Figure 5. The echo X1j received by the receiving antenna element RAj and the echo X1 (j+1) received by the receiving antenna element RA(j+1) may be phase shifted due to the time delay related to the distance between the two receiving antenna elements.

In step 602, the radar receiver device receives, during timeslot TS2’, an echo X2j on the receiving antenna RAj. Each echo X2j (X21, X22, X23, X24) corresponds to a simultaneous transmission of pulses (e.g., encoded with A2, B2, C2, D2) transmitted in step 502 of the transmitting method 500 of Figure 5. The echo X2j received by the receiving antenna element RAj and the echo X2(j+1) received by the receiving antenna element RA(j+1) may be phase shifted due to the time delay related to the distance between the two receiving antenna elements.

In step 603, the radar receiver device processes the received corresponding echoes X1j and X2j (that is to say echoes X11 and X21, echoes X12 and X22, echoes X13 and X23, echoes X14 and X24), preferably in parallel.

In a first step, the cross-correlation of each transmitted code and the corresponding echo are calculated and summed, to obtain a summed correlation signal. In particular, the following cross-correlations are computed:

Corr_Aj = xcorr(A1, X1j) + xcorr(A2, X2j) = xcorr(A1, X11) + xcorr(A2, X21)

Corr_Bj = xcorr(B1, X1j) + xcorr(B2, X2j)

Corr_Cj = xcorr(C1, X1j) + xcorr(C2, X2j)

Corr_Dj = xcorr(D1, X1j) + xcorr(D2, X2j)

For the purpose of illustration, for N = 8 bits (corresponding to the transmitting scheme of Figure 3):

Corr_Aj = xcorr[A1, (A1+B1+C1+D1)] + xcorr[(A2, (A2+B2+C2+D2)] = [0 000000 16 000 16 00 0]

Corr_Bj = xcorr[B1, (A1+B1+C1+D1)] + xcorr[B2, ( A2+B2+C2+D2)] = [0 000000 16 000 16 00 0]

Corr_Cj = xcorr[C1, (A1+B1+C1+D1)] + xcorr[C2, (A2+B2+C2+D2)] = [000 0000 16000-16 000]

Corr_Dj =xcorr[D1, (A1+B1+C1+D1)] + xcorr[D2, (A2+B2+C2+D2)] = [0000 000 16000-160 0 0]

One of the non-zero values (16) corresponds to the amplitude of a detected target, while the other non-zero value (16, -16) corresponds to a side lobe.

It is thus necessary to separate the signals in order to identify the value (lobe) associated with the detected target.

In step 604, the radar receiver device computes a filter that is to be applied to the summed correlation signals obtained in step 603. The filter is used to determine the lobe(s) corresponding to the detected target(s) and to remove side lobes.

The filter may be computed in several manners.

In a first embodiment, the filter is a sum of all the summed correlation signals, calculated as follows:

Corr_filter = corr_Aj + corr_Bj + corr_Cj + corr_Dj

As a numerical example:

Corr_filter = Corr_Aj + Corr_Bj + Corr_Cj + Corr_Dj = [0 000000 64 000000 0]

Such a filter allows the impact of noise to be reduced.

In a second embodiment, the filter is a sum of only correlation signals (for example A and C or B and D), calculated as follows:

Corr_filter = corr_Aj + corr_Cj = [0 000000 32 000000 0] since A1 and A2 are complementary, and C1 and C2 are complementary, or:

Corr_filter = corr_Bj + corr_Dj = [0 000000 32 000000 0] since B1 and B2 are complementary, and D1 and D2 are complementary.

Thus, the complementarity of the codes (A1, A2), (B1, B2), (C1, C2) and/or (D1, D2) is exploited to obtain a main lobe, while the orthogonality of the codes, (e.g., (A1, A2) with (C1, C2) or (B1, B2) with (D1, D2)), is exploited to reduce the side lobes. Nevertheless, certain side lobes may remain, due to the cross-correlations of A and C with B and D when applying the filter in the following step. The number of crosscorrelation signals to be summed is thus reduced.

In step 605, the filter computed in step 604 is applied to cross-correlations computed in step 603 as follows:

YAj = corr_filter * corr_Aj

YBj = corr_filter * corr_Bj

YCj = corr_filter * corr_Cj

YDj = corr_filter * corr_Dj

As a numerical example:

YAj = Corr_filter * Corr_Aj = [0 000000 64 000000 0] *[0 000000 16 000 16 00 0] = [000 0000 1024000 0 000]

YBj = Corr_filter * Corr_Bj = [000 0000 1024000 0 000]

YCj = Corr_filter * Corr_Cj = [000 0000 1024000 0 000]

YDj = Corr_filter * Corr_Dj = [000 0000 1024000 0 000]

One target is thus identified by the main lobe at amplitude 1024. Each transmitted signal has been separated at the level of each receiving antenna. In a particular example, the separation being completed, the computation of the angle of arrival may be performed, since the signals obtained after processing are similar to those received by the method wherein the transmissions by the transmitting antenna elements are separated in time (each transmitting antenna element transmits its signal successively at different time intervals).

In step 606, the radar receiving device supplies on output the computed signals YAj, YBj, YCj, YDj obtained during step 605.

In step 607, the radar receiving device is able to apply an Angle of Arrival algorithm on the obtained signals by determining a steering vector, the size of which is equal to the number of antenna elements squared Κ^Λ2. The following table presents a signal matrix that may be used to determine a steering vector, which represents the delays in the reception of a plan signal at each of the receiving antenna elements in the array.

YA1	YB1	YC1	YD1
YA2	YB2	YC2	YD2
YA3	YB3	YC3	YD3
YA4	YB4	YC4	YD4
Table 6: Obt	ained signal matrix

However, other signal processing algorithms may be applied to the separated signals.

The determination of the Angle of Arrival is thus improved, since an increased number of transmitted signals and received echoes are implemented, thus allowing a more precise determination of the target. The detection of targets and the computation of the position of the detected targets have been performed by using only two timeslots whatever the number of simultaneous transmissions, i.e. the number of antenna elements constituting the antenna. Therefore, the time operation of a radar using this technique is highly improved over the known prior art, as illustrated in relation with Figure 2.

Figure 7 is a schematic block diagram of a computing device 700 for implementing one or more embodiments ofthe invention.

The computing device 700 may be a device such as a micro-computer, a workstation or a light portable device.

The computing device 700 comprises:

- a communication bus 710;

- a central processing unit 720 or CPU, such as a microprocessor;

- a random access memory 730 or RAM;

- a read only memory 740 or ROM;

- a network interface 750 or Nl;

- a user interface 760 or Ul;

- a hard disk 770 or HD; and

- an input/output module 780 or I/O.

The RAM 730 stores the executable code of the method of embodiments of the invention as well as the registers adapted to record variables and parameters necessary for implementing the method according to embodiments of the invention, the memory capacity thereof can be expanded by an optional RAM connected to an expansion port for example.

The ROM 740 stores computer programs for implementing embodiments of the invention.

The network interface 750 is typically connected to a communication network over which digital data to be processed are transmitted or received. The network interface 750 can be a single network interface, or composed of a set of different network interfaces (for instance wired and wireless interfaces, or different kinds of wired or wireless interfaces). Data packets are written to the network interface for transmission or are read from the network interface for reception under the control of the software application running in the CPU 720.

The user interface 760 may be used for receiving inputs from a user or to display information to a user, the hard disk 770 may be provided as a mass storage device, and the I/O module 780 may be used for receiving/sending data from/to external devices such as a video source or display (not shown).

The executable code may be stored either in the ROM 740, on the hard disk 770, on a removable digital medium such as a disk, or even received by means of a communication network, via the network interface 750, in order to be stored in one of the storage means of the communication device 770, such as the hard disk 770, before being executed.

The central processing unit 720 is adapted to control and direct the execution of the instructions or portions of software code of the program or programs according to embodiments of the invention, the instructions of which are stored in one of the aforementioned storage means. After powering on, the CPU 720 is capable of executing instructions from main RAM memory 730 relating to a software application after those instructions have been loaded from the program ROM 740 or the hard disc

770 for example. Such a software application, when executed by the CPU 720, causes the steps of the flowcharts shown in Figures 3 and/or 4 to be performed.

Any step of the algorithm shown in Figures 5 and/or 6 may be implemented in software by execution of a set of instructions or program by a programmable 5 computing machine, such as a PC (“Personal Computer”), a DSP (“Digital Signal Processor”), 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 which lie within the scope of the present invention will be apparent to a person skilled in the art. In particular different features from different embodiments may be interchanged, where appropriate. Many further modifications and variations will suggest themselves to those versed in the art upon making reference to 15 the foregoing illustrative embodiments, which are given by way of example only and which are not intended to limit the scope of the invention as determined by the appended claims.

Claims

1. A method of receiving echoes by means of a radar receiving device comprising receiving antenna elements, the receiving antenna elements being configured to receive echoes of transmitted pulses, wherein the transmitted pulses are encoded by mutually orthogonal complementary sets of codes, each set comprising at least a first code and a second code; and wherein pulses encoded with the first codes are transmitted in a first timeslot, and pulses encoded with the second codes are transmitted in a second timeslot;

the receiving method comprising the steps of:

receiving, by each of the receiving antenna elements, a second echo resulting from the reflection off of the at least one target of the pulses transmitted in the second timeslot;

2. The method according to claim 1, wherein the filter is determined by: calculating the cross-correlations of each first code with the first echo; calculating the cross-correlations of each second code with the second echo; summing the calculated cross-correlations corresponding to a same set of codes to obtain a summed correlation signal for each set of codes; and summing at least two summed correlation signals to obtain the filter.

3. The method according to claim 2, wherein all the summed correlation signals are summed to obtain the filter.

4. The method according to claim 2, wherein only two of the summed correlation signals are summed to obtain the filter, the summed correlation signals relating to mutually orthogonal pairs.

5. The method according to one of claims 2 to 4, wherein the filter is applied to each summed correlation signal.

6. The method according to one of claims 1 to 5, further comprising a step of applying an angle of arrival algorithm on the obtained separated signals.

7. The method according to one of claims 1 to 6, wherein the number of receiving antennas is greater than two.

8. The method according to one of claims 1 to 7, wherein the number of receiving antennas is a power of two.

9. The method according to one of claims 1 to 7, wherein the total number of receiving antennas is an uneven number, and a Golay matrix for determining the pulses to transmit is obtained by determining the next higher power of two greater than the number of receiving antennas.

10. The method according to claim 9, wherein a sub-matrix of the obtained Golay matrix is determined to encode pulses.

11. A method of transmitting pulses by means of a radar transmitting device comprising transmitting antenna elements;

wherein the transmitted pulses are encoded by mutually orthogonal complementary sets of codes, each set comprising at least a first code and a second code;

the transmitting method comprising the steps of:

12. A radar receiving device comprising receiving antenna elements configured to receive echoes of transmitted pulses, wherein the transmitted pulses are encoded by mutually orthogonal complementary sets of codes, each set comprising at least a first code and a second code; and wherein pulses encoded with the first codes are transmitted in a first timeslot, and pulses encoded with the second codes are transmitted in a second timeslot;

the radar receiving device configured to:

13. The device according to claim 12, wherein the filter is determined by: calculating the cross-correlations of each first code with the first echo; calculating the cross-correlations of the each second code with the second echo;

14. The device according to claim 13, wherein all the summed correlation signals are summed to obtain the filter.

15. The device according to claim 13, wherein only two of the summed correlation signals are summed to obtain the filter, the summed correlation signals relating to mutually orthogonal pairs.

16. The device according to one of claims 13 to 15, wherein the filter is applied to each summed correlation signal.

17. The device according to one of claims 12 to 16, further configured to apply an angle of arrival algorithm on the obtained separated signals.

18. The device according to one of claims 12 to 17, wherein the number of receiving antennas is greater than two.

19. The device according to one of claims 12 to 18, wherein the number of receiving antennas is a power of two.

20. The device according to one of claims 12 to 18, wherein the total number of receiving antennas is an uneven number, and a Golay matrix for determining the pulses to transmit is obtained by determining the next higher power of two greater than the number of receiving antennas.

21. A radar transmitting device comprising transmitting antenna elements configured to transmit pulses;

the transmitting device configured to:

22. A radar apparatus comprising a radar receiving device according to one of claims 12 to 20, and a radar transmitting device according to claim 21.