GB2563444A

GB2563444A - Radar with stepped frequency complementary code sequences

Info

Publication number: GB2563444A
Application number: GB1709631.4A
Authority: GB
Inventors: Achir Mounir
Original assignee: Canon Inc
Current assignee: Canon Inc
Priority date: 2017-06-16
Filing date: 2017-06-16
Publication date: 2018-12-19
Anticipated expiration: 2037-06-16
Also published as: GB201709631D0; GB2563444B

Abstract

A radio frequency signal, the signal comprising at least first and second pulses encoded with complementary codes A & B, the first and second sets S1 & S2 forming a complementary sequence; wherein the sets forming the complementary sequence have at least one pulse each, are modulated at a minimum of two frequencies with each set being modulated at a distinct frequency, and do not have a same sequence of encoded pulses between them at the same frequency. Then generating a signal based on the generated sets. The plurality of pulses of a set may be modulated to the same frequency in each set and may further be encoded with a same complementary code per set. A further set may be transmitted at a same frequency of a previously transmitted set. Also disclosed is a method comprising receiving a reflected signal, applying cross correlations to obtain compressed signals, summing the compressed signals while applying phase corrections using a function of the modulation difference between the signals, and applying an Inverse Fourier Transform to obtain a rage profile signal.

Description

TITLE OF THE INVENTION

Radar with Stepped Frequency Complementary Code Sequences

FIELD OF THE INVENTION

The invention relates to the field of radar apparatuses, in particular the transmission and reception of stepped frequency complementary code sequences.

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 emit 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 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. Thanks to the property of the complementary codes, the amplitude of the main lobe is doubled while the side-lobes cancel each other out.

Stepped frequency complementary coded pulses may be used to detect targets that are close to each other with different RCS. Two or more types of pulses, for example a sequence of alternating pulses A, B, A, B..., (e.g., pulses encoded using alternating codes) are sent with a carrier frequency that is periodically shifted or stepped to a next carrier frequency. A specific processing known as “Synthetic Bandwidth Processing” is performed upon reception in order to build the range profile signal. The range profile signal may correspond to the power of the received signal coming from all objects present at a given range from the radar.

Figure 1 shows transmitted and received signals to illustrate the principle of stepped frequency with phase complementary coded pulse compression.

If S_n(t) is the amplitude of the pulse transmitted at time t by a stepped frequency radar, then:

S_n(t) = Z. exp(2. π. j(/o + n. Af). t) [equation 1] wherein Z is a code pulse (A or B), fO is the carrier frequency, n is the index of the frequency step, π is the mathematical constant Pi (^3.14159), Af (Greek letter delta) is the frequency step and the bandwidth of the transmitted pulse S_n(t), and j is equal to the square root of -1.

Let REF_n(t) be a reference signal generated by the Radar RF module, such as:

REF_n(t) = V . exp(—2.7t.j(/₀ + n.Af). t) [equation 2] wherein V is a voltage amplitude.

From equation 1, the signal expression received by the Radar and which is a combination of all the echoes coming from the targets present in the scene can be computed as follows:

[equation 3] wherein a, is the amplitude (Greek letter alpha) of the received echo i, and c is the speed of light.

An analogue demodulation is performed by the stepped frequency radar RF module by mixing the received echo R_n(t) with the reference signal REF_n(t).

A signal V_n(Ri) is obtained as follows:

Wi)=/?n(t)-^F_n (t) =^₌₁a_i.Z.V.exp(-2.n.j(f₀+n.^.²-^) [equation 4]

The signal V_n(Ri) is applied to an analog-to-digital ADC converter, and a cross-correlation between V_n(Ri) and the transmitted sequence (pulses A, B) is performed.

An Inverse Fast Fourier Transform IFFT is then performed for each range bin as shown in Figure 1, wherein N is the number of frequency steps [C. Fukushima, N. Hamada, “A Study on Stepped Frequency Radar by Using Intra-Pulse Phase Coded Modulation”, WCECS 2008, San Francisco, USA],

The output of the transforms is as follows:

W) = ^.Yn=oVn^t)-exp(2.n.j.k.^) [equation 5]

Replacing V_n(Ri) with its expression provides:

. exp

[equation 6]

The maxima of the |W(k)| equations are obtained when k/N-Af*(2*Ri)/c=0 and hence:

ki = NAf. [equation7]

From the above equation, the range resolution is as follows:

AR = —-— [equation8]

2.NAf ^1J

The range resolution AR is defined by the full bandwidth (N*Af) and the analog-to-digital converter must be able to sample a signal having a bandwidth equal to Af.

In summary, the radar transmitter transmits, at each frequency, an alternating sequence of S pulses A, B, A, B.... (S corresponding to a number of transmitted pulses) with pulse repetition intervals or PRI being the time between the start of two successive pulses. A frequency sweep (transmitting the same S pulses at each frequency) is performed as illustrated in Figure 1 over the full bandwidth (N*Af), with a range resolution AR for a given frequency being c/(2*Af). Upon reception, after performing the IFFT transforms, the range resolution AR is equal to c/(2*N*Af), thus with an improvement of N times (the denominator being larger, providing a smaller thus better range resolution).

Such a technique allows a high range resolution without requiring analog-todigital converters with high sampling rates, and side lobes are not problematic due to the complementary codes.

Nevertheless, such a stepped frequency technique may be improved.

SUMMARY OF THE INVENTION

Embodiments of the invention relate to a method of generating a signal, comprising the steps of:

generating at least first and second sets of pulses encoded with complementary codes, the at least first and second sets forming a complementary sequence, wherein the sets forming the complementary sequence:

have at least one pulse each, are modulated at at least two frequencies, each set being modulated at a distinct frequency, and do not have a same sequence of encoded pulses between them at the same frequency; and generating a signal based on the generated sets.

According to one embodiment, the method further comprises transmitting the first set, and then transmitting the second set.

According to one embodiment, the second set is transmitted consecutively to the first set.

According to one embodiment, a complementary sequence is a sequence of complementary codes wherein a sum of compressed signals resulting from each crosscorrelation computed for each code of the sequence provide a processed signal with reduced sidelobes and an increased mainlobe.

According to one embodiment, modulating each set at a distinct frequency comprises modulating each pulse of each set at the distinct frequency.

According to one embodiment, a set comprises a plurality of pulses modulated at a same frequency.

According to one embodiment, the plurality of pulses of a set are encoded with a same complementary code.

According to one embodiment, the method further comprises transmitting at least one further set comprising a same sequence of encoded pulses of a previouslytransmitted set and modulated at a same frequency of a previously-transmitted set or of the previously-transmitted set, wherein a set transmitted immediately before the at least one further set and the at least one further set form a complementary sequence.

According to one embodiment, the method further comprises a preliminary step of initializing an index k; and further steps of:

determining whether the index k is equal to a maximum value kmax, in order to determine whether a number of frequency steps has been achieved;

transmitting, if the response is yes, at least one further set comprising a same sequence of encoded pulses of a previously-transmitted set and modulated at a same frequency of a previously-transmitted set or of the previously-transmitted set, wherein a set transmitted immediately before the at least one further set and the at least one further set form a complementary sequence; otherwise, increasing the index k and repeating the steps of transmitting the first and second sets.

According to one embodiment, a pulse of one of the sets is determined according to one of the following equations:

Sn(t)=Z .exp(2.TT.j(f_0+(n-1).Af).t) if n=M.k+m; or

Sn(t)=Z .exp(2.TT.j(f_0+(N-1).Af).t) if n=N+m-1 wherein Z is a complementary code, fO is the carrier frequency, n is the index of the frequency step, π is the mathematical constant Pi, Af is the frequency step value and the bandwidth of the transmitted pulse S(t), j is equal to the square root of -1, M is equal to the total number of complementary codes, m is an index from 1 to M, incrementing by one for each sets of pulses, k is an index from 0 to kmax, kmax being equal to a number N of frequency steps and the variable M as kmax = (N-M)/M.

Embodiments of the invention also relate to a method of processing a signal, comprising the steps of:

receiving a reflected signal from at least one target reflecting a signal; and processing the received signal by:

applying cross correlations on the received signal to obtain compressed signals;

obtaining processed signals by summing the compressed signals, wherein a phase correction has been applied on at least one of the compressed signals, wherein the phase correction is a function of a frequency modulation difference between the summed compressed signals; and obtaining a range profile signal by applying an Inverse Fast Fourier Transform to the processed signals.

According to one embodiment, the phase correction is applied between two compressed signals related to at least two received sets of pulses encoded with complementary codes, wherein the at least two sets forming a complementary sequence:

have at least one pulse each, are modulated at at least two frequencies, each set being modulated at a distinct frequency, and do not have a same sequence of encoded pulses between them at the same frequency.

Embodiments of the invention also relate to a pulse radar device comprising a transmitter configured to generate a modulated signal according to an embodiment of the invention.

Embodiments of the invention also relate to a pulse radar device comprising a receiver configured to process a signal according to an embodiment of the invention.

Embodiments of the invention also relate to a pulse radar system comprising a transmitter according to an embodiment of the invention and a receiver according to an embodiment of the invention.

Embodiments of the invention also relate to a modulated signal comprising at least:

first and second sets of pulses encoded with complementary codes, the at least first and second sets forming a complementary sequence, wherein the sets forming the complementary sequence:

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:

Figure 1, previously described, shows transmitted and received signals to illustrate the principle of stepped frequency with phase complementary coded pulse compression,

Figure 2 shows transmitted and received signals according to a first embodiment of the invention,

Figure 3 is a flowchart showing steps of a method of generating and transmitting a signal according to the first embodiment of the invention,

Figure 4 is a flowchart of a method of receiving and processing a signal according to the first embodiment of the invention,

Figure 5 shows transmitted and received signals according to a second embodiment of the invention,

Figure 6 shows transmitted and received signals according to a third embodiment of the invention, and

Figure 7 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 a stepped frequency complementary code sequence. Such a radar allows an improved (decreased) sweep time 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 sweep time and a same number of averaging to provide an increased maximum range, or an increased number of averaging for a same sweep time and a same PRI to provide a better signal-to-noise ratio.

A “complementary sequence” is a particular sequence of complementary codes wherein when each cross-correlation is computed for each code of the sequence, thus providing compressed signals, the sum of the compressed signals may typically provide a processed signal with reduced sidelobes and an increased mainlobe. Ideally, the processed signal may be a Dirac function. (A, B); (A, B, B, A); (A, B, B, A, B, A, A, B); and (A, B, B, A, B, A, A, B, B, A, A, B, A, B, B, A) are four examples of complementary sequences of pulses encoded with two complementary codes A and B.

Figure 2 shows transmitted and received signals according to a first embodiment of the invention. A complementary sequence is transmitted with two complementary codes A and B over a plurality of frequency steps, and the echoes are received and processed.

In particular, a set of S consecutive A pulses (e.g., pulses encoded with code A) is sent at a first frequency step, followed by a set of S consecutive B pulses sent at a second frequency step, followed by a set of S consecutive A pulses sent at a third frequency step, and so forth. Thus, at each frequency step, pulses encoded with one code (A or B) belonging to the complementary sequence (A and B) of complementary codes are transmitted.

It may be noted that the number of pulses A or B sent in each set is not necessarily the same for each set, and that though in general a relatively high number of pulses are sent for each set, the number of pulses for each set could be equal to 1.

The expression of the transmitted signal is then n = 1 to N+1; where N is the number of frequency steps, with a set Sn (n from 1 to N+1) as follows:

(A . exp(2. n.j(f₀ + (n - 1). Δ/). t) if n = 2.k + 1 {Line 1} S_n(t) = < B . exp(2. n.j(f₀ + (n - 1). Δ/). t) if n = 2.k + 2 {Line 2}

U . exp(2. n.j(f₀ + (N - 1). Δ/). t) wherein k is an index from 0 to kmax, and j is equal to the square root of negative 1.

The variable kmax may be defined with respect to the number N of frequency steps, and more particularly with respect to a number M of codes in a complementary sequence as kmax = (N-M)/M. For example, in the above case, two codes A and B are sent, such that M = 2, and kmax = (N-2)/2. Furthermore, the number N of frequency steps has a minimum equal to the number M of codes, thus two in the above case, but may be larger, for example 16, 32, 64, and so forth.

if n = N + 1 [Line 3}

If for example N is equal to 4, M is equal to 2, k can be equal to 0 or 1, then as shown in Figure 2:

- a first set S1 of A pulses is sent at frequency fO (since n is equal to 2*0+1, which when substituted into Line 1 of the set of lines, negates the Af term) from Line 1;

- a second set S2 of B pulses is sent at frequency fO+1*Af (since (2*0+2)-1) from Line 2,

- a third set S3 of A pulses is sent at frequency fO+2*Af (since (2*1+1)-1) from

Line 1,

- a fourth set S4 of B pulses is sent at frequency fO+3*Af (since (2*1+2)-1) from Line 2, and

- a fifth set S5 of A pulses is sent at fO+3*Af (since (4-1)) from Line 3.

Figure 3 is a flowchart showing steps of a method 300 of generating and transmitting a signal according to the first embodiment of the invention.

The method 300 comprises steps 301 to 308 and relates to the transmitted signal TX as shown in relation with Figure 2, wherein two complementary codes A and B are sent and N is equal to 4. At step 301 the method starts.

At step 302, the index k is initialized, k = 0. At step 303, the radar transmitter transmits a first set of S pulses of code A with the carrier frequency fO+(n-1)*Af, n = 2k+1 (Line 1).

Step 302 comprises:

encoding a first set of pulses with the complementary code A;

modulating each pulse of the first set at a first frequency (e.g., fO+(n-1)*Af with n = 2k+1); and

- transmitting the modulated pulses.

Alternatively, the whole first set may be modulated, rather than modulating each pulse.

At step 304, the radar transmitter transmits a second set of S pulses of code B over the carrier frequency fO+(n-1)*Af, n = 2k+2 (Line 2).

Step 304 comprises:

encoding a second set of pulses with the complementary code B; modulating the pulses of the second set at a second frequency (e.g., fO+(n-1)*Af n = 2k+2); and

- transmitting the modulated pulses.

Alternatively, the whole second set may be modulated, rather than modulating each pulse.

At step 305, the radar transmitter determines whether the index k is equal to kmax, in order to determine whether the number N of frequency steps has been achieved. If the response is yes, at step 306, the radar transmitter transmits S pulses of code A over the carrier frequency fO+(N-1)*Af, n = N+1 (Line 3). At step 307, the method stops.

Otherwise, if the response at step 305 is no, at step 308 the index k is increased by one, k = k+1, and the method returns to step 303.

In summary, the method relates to generating a signal, wherein at least first and second sets of pulses encoded with complementary codes are generated, the at least first and second sets forming a complementary sequence. The sets forming the complementary sequence have at least one pulse each, are modulated at at least two frequencies, each set being modulated at a distinct frequency, and do not have a same sequence of encoded pulses between them at the same frequency. The method further comprises generating a signal based on the generated sets.

Returning to the description of Figure 2, the radar receiver performs synthetic bandwidth processing after performing a specific phase correction.

When the radar transmits the code pulse A at a frequency fO, the received echo, coming from T targets present at ranges Ri from the radar, can be written as follows:

Vo(^i=i...r) = Zl=i^ai-^A-exp [equation 9]

Likewise, when the radar transmits the code pulse B at a frequency step, the received echo coming from T targets present at ranges Ri from the radar can be written as follows:

^vi(^ri=i...t) = ΣΓ=1 «i B. exp (-2. n.j. (/₀ + Δ/). [equation 10]

For a cross-correlation (XC) of the two complementary received echoes xcorr(y₀(Ri), A) and xcorr(V₁(R_i),B'), a phase shift should be applied to either Vjffj) or to Vj^Ri).

If the phase shift is applied to V1(Ri), then the crosscorrelation: xcorrty^Ri). exp (+2nj.Af. B) is complementary with the crosscorrelation xcorr(V₀(Ri),A).

Thus, in order for xcorr(y_n(Ri),Z(n)) and xcorr(V_n+1(Ri),Z(n+ 1)) to be complementary, a phase shift is applied to V_n+1(Rt) for n = 1 to N-1, wherein Z(n) is the code (A or B) transmitted with the carrier frequency f₀ + (n- 1). Δ/.

After the phase correction, the sum of the two obtained cross-correlations is as follows:

/ 2Ra xcorr(y_n(Ri), C(n)~) + exp ( +2π). Δ/.---1. xcorr(V_n+1(R_i), Z(n + 1)) [equation 11]

For n = N, the sum of the two obtained cross-correlations is done without phase correction since the frequency used for transmitting the pulses at steps N and N+1 is the same (frequency fO + 3* Δί in the case of Figure 2):

xcorr(V_N(Ri), Z(Nf) + xcorr(V_N+1(Ri),Z(N + 1)) [equation 12]

The last step is the application of the multiple IFFT in order to perform the synthetic bandwidth processing as described in relation with Figure 1.

Consequently, in relation with Figure 2, a phase correction PC1

PCI = exp [equation is applied by means of a phase shifter PS2 to the cross-correlation XC(V1, B) relating to the set S2. An adder AD1 then receives on input the result of the shift and the cross-correlation XC(V0, A) and supplies on output the summed value to the transform IFFT.

Likewise, the phase correction PC1 is applied by means of a phase shifter PSn-i to the cross-correlation XC(V_N.!, A) relating to the set S3 (S_N-i); the result of the shift and the cross-correlation XC(V1, B) are then applied to an adder AD2 and then supplied to the transform IFFT. The phase correction PC1 is applied by means of a phase shifter PS_N to the cross-correlation XC(V_N, B) relating to the set S4 (S_N); the result of the shift and the cross-correlation XC(V_N+1, A) are then applied to an adder AD_n and then supplied to the transform IFFT. It is not necessary to apply a phase correction to the cross-correlation XC(V_N+i, A) as it is at the same frequency as the cross-correlation XC(V_N, B). A range profile signal is obtained on output of the IFFT.

In a general manner, the phase correction is applied between at least two received sets of pluses having different sequences of encoded pulses (e.g, they comprise pulses encoded in a different order, or they comprise a different number of pulses) and modulated at different frequencies.

Figure 4 is a flowchart of a method 400 of receiving and processing a signal according to the first embodiment of the invention. The method 400 comprises steps 401 to 411 and relates to the received signal RX as shown in relation with Figure 2, wherein two codes A and B are sent with N equal to 4. In particular, the method 400 relates to performing the phase correction before synthetic bandwidth processing can be performed.

At step 401 the method starts. At step 402, the index k is initialized, k = 0. At step 403, the radar receiver receives S echoes of code A with the carrier frequency fO+(n-1)*Af, n = 2k+1 (Line 1). At step 404, it is determined whether k is equal to 0. If the response is no, then at step 405, the phase correction PC1 is applied and then the method proceeds to step 406. Otherwise, if the response at step 404 is yes, then the method proceeds directly to step 406 as no phase correction needs to be applied (corresponding to set S1 of Figure 2).

At step 406, the radar receiver receives S echoes of code B with the carrier frequency fO+(n-1)*Af, n = 2k+2 (Line 2). At step 407, the phase correction PC1 is applied. At step 408, it is determined whether k is equal to kmax. If the response is yes, then the number of transmitted and received frequency steps is equal to N and at step 409, the radar receiver receives S echoes of code A with the carrier frequency fO+(N-1)*Af, n = N+1 (Line 3). It is then not necessary to apply a phase correction since the sets S4 and S5 were transmitted at the same frequency step, and at step 410 the method stops.

Otherwise, if the response at step 408 is no, then at step 411 the index k is incremented, k = k+1, and the method returns to step 403.

In summary, the method relates to receiving a reflected signal from at least one target reflecting a signal; and processing the received signal by applying cross correlations on the received signal to obtain compressed signals, and obtaining processed signals by summing the compressed signals. A phase correction has been applied on at least one of the compressed signals, wherein the phase correction is a function of a frequency modulation difference between the summed compressed signals. The method further comprises obtaining a range profile signal by applying an Inverse Fast Fourier Transform to the processed signals.

Returning to the description of Figure 2, more than two codes (A, B) can be generated and transmitted [“Sequences of Complementary Codes for the Optimum Decoding of Truncated Ranges and High Sidelobe Suppression Factors for ST/MST Radar Systems”, E. Spano and O. Ghebrebrhan, IEEE Trans. On Geoscience and Remote Sensing, 1996], For example, in the case where the complementary sequence contains four codes: A, B, C, D then the expression of the transmitted signal is n = 1 to N+3.

^rA . exp(2. n.j(f₀ + (n - 1). Δ/). t)

B . exp(2. n.j(f₀ + (n - 1). Δ/). t)

C . exp(2. n.j(f₀ + (n - 1). Δ/). t)

S_n(t) = \^D- exp(2. + (n- 1). Δ/). t) A . exp(2. n.j[f₀ + (A - 1). Δ/). t)

B. exp(2. n.j(f₀ + (A - 1). Δ/). t) < C. exp(2. n.j(f₀ + (TV - 1). Δ/). t) if n = 4. k + 1 [Line 1} if n = 4. k + 2 [Line 2} if n = 4. k + 3 [Line 3} if n = 4. k + 4 [Line 4} if n = N + 1 [Line 5} if n = N + 2 [Line 6} if n = N + 3 [Line 7} wherein k is an index from 0 to kmax (for example (N-4)/4 here), and j is equal to the square root of negative 1 as previously.

If N=8, then k = 0, 1, and the following set are sent: set A at fO, set B at fO+1*Af, set C at fO+2*Af, set D at fO+3*Af, set A at fO+4*Af, set B at fO+5*Af, set C at fO+6*Af, set D at fO+7*Af, set A at fO+7*Af, set B at fO+7*Af, and set C at fO+7*Af.

In the case where the complementary sequence contains eight codes: A, B, C,

D, E, F, G, H then the expression of the transmitted signal is n = 1 to N+7:

^rA . exp(2. n.j(f₀ + (n - 1). Δ/). t)

B . exp(2. n.j(f₀ + (n - 1). Δ/). t)

C . exp(2. n.j(f₀ + (n - 1). Δ/). t)

S_nW) =

D . exp(2. n.j(f₀ + (n - 1). Δ/). t) E . exp(2. n.j(f₀ + (n - 1). Δ/). t) F . exp(2. n.j(f₀ + (n - 1). Δ/). t) G . exp (2. π.;(/₀ + (n - 1). Δ/). t) H . exp(2. π.;(/₀ + (n - 1). Δ/). t)

A . exp(2. n.J(f₀ + (N - 1). Δ/). t)

B. exp(2.7i.j(fo + (N - 1). Δ/). t)

C. exp(2. n.j(f₀ + (N - 1). Δ/). t)

D. exp(2. n.j(f₀ + (A - 1). Δ/). t)

E. exp(2. n.j(f₀ + (A - 1). Δ/). t)

F. exp(2. n.j(f₀ + (A - 1). Δ/). t) <6. exp(2. n.j(f₀ + (/V - 1). Δ/). t) if n = 8.k + 1 [Line 1} if n = 8. k + 2 [Line 2} if n = 8. k + 3 [Line 3} if n = 8.k + 4 [Line 4} if n = 8. k + 5 [Line 5} if n = 8. k + 6 [Line 6} if n = 8.k + 7 [Line 7} if n = 8. k + 8 [Line 8} if n = N + 1 [Line 9} if n = N + 2 [Line 10} if n = N + 3 [Line 11} if n = N + 4 [Line 12} if n = N + 5 [Line 13} if n = N + 6 [Line 14} if n = N + 7 [Line 15} wherein k is an index from 0 to kmax (for example (N-8)/8 here), and j is equal to the square root of negative 1 as previously.

The above sets of lines may be generalized as follows:

5_n(t) = Z. exp(2.π.;(/₀ + (n — 1). Δ/). t) if n = M. k + m or

5_n(t) = Z. exp(2. + (N — 1). Δ/). t) if n = N + m — 1 wherein Z is a code pulse (i.e. complementary code A, B, C, D...), fO is the carrier frequency, n is the index of the frequency step, π is the Greek letter pi, Af (Greek letter delta) is the frequency step and the bandwidth of the transmitted pulse S(t), j is equal to the square root of -1, M is equal to the total number of codes (two in the case of codes A, B, four in the case of codes A, B, C, D, and so forth), m is an index from 1 to M, incrementing by one for each set of pulses, k is the index from 0 to kmax.

Furthermore, the total number of sets transmitted may be generalized as the sum of the number N of frequency steps and the number M of complementary codes minus 1, as N + (M-1).

In such a case, the methods 300 and 400 of Figures 3 and 4 respectively may be similarly adapted, adding steps of transmitting further sets of codes (C, D) or (C, D, E, F, G, H).

Figure 5 shows transmitted and received signals according to a second embodiment of the invention. As previously, a complementary sequence (A, B) is transmitted with two codes A and B over a plurality of frequency steps, and the echoes are received and processed.

At each frequency step, pulses encoded with one code belonging to the complementary sequence are transmitted. The expression of the transmitted signal is then (n=1 to N+1; where N is the number of frequency steps) as follows:

iA . exp(2. n.j(f₀ + (n - 1). Δ/). t) if n = 2.k + 1 {Line 1}

S_n(t) = < B . exp(2. n.j(f₀ + (n - 1). Δ/). t) if n = 2.k + 2 {Line 2} fA . exp{2.n.j{f_oft) if n = N + 1 {Line 3} wherein k is an index from 0 to kmax (here kmax = (N-2)/2), and j is equal to the square root of negative 1.

If for example N is equal to 4, k can be equal to 0 or 1, then the first four sets S1 to S4 correspond to those shown in Figure 2, in particular a first set S1 of A pulses is sent at frequency fO, a second set S2 of B pulses is sent at frequency fO+1*Af, a third set S3 of A pulses is sent at frequency fO+2*Af, and a fourth set S4 of B pulses is sent at frequency fO+3*Af. However, the last set S5 of A pulses is sent at frequency fO.

On the side of the receiver, the phase correction PC1 as above is applied for the values of n = 1 to N-1, providing the result of equation 11 above.

However, for the value of n = N, a second phase correction PC2 related to the frequency difference between sets S4 and S5 is applied, wherein:

PC2 = exp [-2π]. (N - 1). Δ/. [equation 14]

Consequently, the following result is obtained:

— 2nj. (N — 1). Δ/.—-). xcorr(V_N+1(R[),C (N + 1)) [equation 15]

With respect to the receiver shown in Figure 2, an additional phase shifter PS_N+1 is arranged to receive the phase correction PS2 and the cross-correlation of the last term, here (V_N+1(Ri), A), the result of which is then applied to the adder AD_N, as previously.

Figure 6 shows transmitted and received signals according to a third embodiment of the invention. As previously, a complementary sequence is transmitted with two codes A and B over a plurality of frequency steps, and the echoes are received and processed.

At each frequency step, pulses encoded with one code belonging to the complementary sequence are transmitted. The expression of the transmitted signal is then (n=1,... ,N+1; where N is the number of frequency steps):

(A . exp(2. n.j(f₀ + (n — 1). Δ/). t) if n = 2.k + 1 [Line 1}

S_n(t) = < B . exp(2. n.j(f₀ + (n — 1). Δ/). t) if n = 2. k + 2 [Line 2} ( A . exp(2. n.j(Jo + (N — 2). Δ/). t) if n = N + 1 [Line 3} wherein k is an index from 0 to kmax (here kmax = (N-2)/2), and j is equal to the square root of negative 1.

If for example N is equal to 4, k can be equal to 0 or 1, then the first four sets

S1 to S4 correspond to those shown in Figure 2. However, the last set S5 of A pulses is sent at frequency fO+2*Af.

On the side of the receiver, the phase correction PC1 is applied for the values of n = 1 to N-1, providing the result of equation 11 above.

However, for the value of n = N, a third phase correction PC3 is applied, wherein

PC3 = exp (—2nj. Af [equation 16]

Consequently, the following result is obtained:

I 2Ra xcorrtyffiRfLCfNf) + exp \—2nj. Af.---J. xcorr(V_N+1(Rf), C(N + 1)) [equation 17]

The various advantages provided by embodiments of the invention will now be discussed.

The sweep time ST needed to sweep the full band of frequency steps N*Af, the number of pulses S, the pulse repetition interval PRI, and the number N of frequency steps are related.

For a prior art sequence of alternating A and B pulses as shown in Figure 1, the following equation is provided:

STa = Sa*(2*PRIa*N) [equation 18a] wherein STa is the sweep time according to the prior art, Sa is the number of pulses sent during a set of the prior art, PRIa is the Pulse Repetition Interval (in seconds) of the prior art, and N is the number of frequency steps. The number 2 relates to the number of codes (A, B....) sent for each frequency.

In contrast, for the present invention as shown in Figure 2, the following equation is provided:

STb = Sb*PRIb*(N+1) [equation 18b] wherein STb is the sweep time according to the invention, Sb is the number of pulses during a set according to the invention, PRIb is the Pulse Repetition Interval (in seconds) according to the invention, and N is the number of frequency steps.

A first advantageous implementation allows a decreased sweep time with respect to a same PRI (pulse repetition interval) and a same number of averaging. If the number of pulses Sa, Sb are set equal to each other and the intervals PRIa, PRIb are set equal to each other, then the sweep time STb according to the invention is improved (decreased), as shown by the following numerical illustration:

Sa = Sb = 1000,

PRIa = PRIb = 0.2 ps (microseconds), and

N = 32

Specifically, the sweep time of the prior art STa is equal to 12.8 ms (milliseconds), while the sweep time STb of the present invention is equal to 6.6 ms. Consequently, the sweep time provided by the present invention is almost half that of the prior art for the same PRI and the same number of averaging, such that less transmission time is required, allowing the target range to be obtained more quickly.

A second advantageous implementation provides an improved (increased) PRI for a same sweep time and a same number of averaging.

Setting the sweep times STa, STb given in the equations 18a, 18b above equal to each other, STa = STb, provides:

Sa*(2*PRIa*N) = Sb*PRIb*(N+1) [equation 19]

As the values Sa, Sb are also equal to each other, they may be canceled out. Solving for the value PRIb provides:

(2*PRIa*N)/(N+1) = PRIb [equation 20]

As a numerical illustration, if PRIa is equal to 0.2 ps, and N is equal to 32, then PRIb is equal to 0.39 ps, almost twice that of PRIa of the prior art.

The maximum range Rmax according to the invention is twice the maximum range of that of the prior art since:

Rmax = c*PRI/2 [equation 21] wherein c is the speed of the light.

Finally, a third advantageous implementation provides an improved (increased) number of averaging for a same sweep time and a same PRI.

Again, setting the sweep times STa, STb given in the equations 18a, 18b above equal to each other, STa = STb, provides:

Sa*(2*PRIa*N) = Sb*PRIb*(N+1) [equation 22]

As the values PRIa, PRIb are also equal to each other, they may be canceled out. Solving for the value Sb provides:

Sa*(2*N) = Sb*(N+1)

Sa*(2*N)/(N+1) = Sb [equation 23]

As a numerical illustration, if the number of averaging Sa is equal to 1000, and N is equal to 32, then the number of averaging Sb is equal to 1939, almost twice that of Sa of the prior art.

It may be noted that if the number of averaging increases then the signal-tonoise ratio is increased.

In one alternative embodiment, instead of a set of S A pulses at a first frequency, a set of S B pulses at a second frequency and so forth, the transmitter sends a first set of S pulses encoded with several complementary codes at the first frequency, and then sends a second set of S pulses encoded at the second frequency.

In a first example, the first set may correspond to a sequence of two pulses (A, B), and the second set may correspond to another sequence of two pulses (B, A).

In a second example, the first set may correspond to a sequence of four pulses (A, B, B, A), and the second set may correspond to another sequence of four pulses (B, A, A, B).

In a third example, the first set may correspond to a sequence of eight pulses (A, B, B, A, B, A, A, B), and the second set may correspond to another sequence of eight pulses (B, A, A, B, A, B, B, A).

In another embodiment, the transmitter sends a first set of Si pulses at the first frequency, and then sends a second set of S₂ pulses encoded at the second frequency, wherein St and S₂ correspond to the number of transmitted pulses and are different from each other.

In a first example, the first set may correspond to a sequence of three pulses (A, B, B), and the second set may correspond to a sequence of one pulse (A).

In a second example, the first set (sent at the first frequency) may correspond to a sequence of four pulses (A, B, B, A), the second set (sent at the second frequency) may correspond to a sequence of three pulses (B, A, A), and a third set (sent at a third frequency) may correspond to a sequence of one pulse (B). In this example, the first and second sets (A, B, B, A - B, A, A) do not correspond to a complementary sequence. The complementary sequence is given by the three sets (A, B, B, A-B, A, A-B).

In another alternative embodiment, instead of performing the sum of consecutive set, for example XC(V0, A) and XC(V1, B) relating to set S1 and S2 as shown in Figure 2, the sum of non-consecutive sets, for example XC(V0, A) and XC(V_N, B) relating to sets S1 and S4 could be performed, with an adapted phase correction applied to one of the cross correlations.

Figure 7 is a schematic block diagram of a computing device 70 for implementing one or more embodiments of the invention. The computing device 70 may be a device such as a micro-computer, a workstation or a light portable device.

The computing device 70 comprises:

- a communication bus 71;

- a central processing unit 72 or CPU, such as a microprocessor;

- a random access memory 73 or RAM;

- a read only memory 74 or ROM;

- a network interface 75 or Nl;

- a user interface 76 or Ul;

- a hard disk 77 or HD; and

- an input/output module 78 or I/O.

The RAM 73 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 74 stores computer programs for implementing embodiments of the invention.

The network interface 75 is typically connected to a communication network over which digital data to be processed are transmitted or received. The network interface 75 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 72.

The user interface 76 may be used for receiving inputs from a user or to display information to a user, the a hard disk 77 may be provided as a mass storage device, and the I/O module 78 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 74, on the hard disk 77, on a removable digital medium such as a disk, or even received by means of a communication network, via the network interface 75, in order to be stored in one of the storage means of the communication device 70, such as the hard disk 77, before being executed.

The central processing unit 72 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 72 is capable of executing instructions from main RAM memory 73 relating to a software application after those instructions have been loaded from the program ROM 74 or the hard disc 77 for example. Such a software application, when executed by the CPU 72, causes the steps of the flowcharts shown in Figures 3 and/or 4 to be performed.

Any step of the algorithm shown in Figures 3 and/or 4 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”), 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 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 generating a signal, comprising the steps of:

2. The method according to claim 1, further comprising transmitting the first set, and then transmitting the second set.

3. The method according to claim 2, wherein the second set is transmitted consecutively to the first set.

4. The method according to one of claims 1 to 3, wherein a complementary sequence is a sequence of complementary codes wherein a sum of compressed signals resulting from each cross-correlation computed for each code of the sequence provide a processed signal with reduced sidelobes and an increased mainlobe.

5. The method according to one of claims 1 to 4, wherein modulating each set at a distinct frequency comprises modulating each pulse of each set at the distinct frequency.

6. The method according to one of claims 1 to 5, wherein a set comprises a plurality of pulses modulated at a same frequency.

7. The method according to claim 6, wherein the plurality of pulses of a set are encoded with a same complementary code.

8. The method according to claim 2, further comprising transmitting at least one further set comprising a same sequence of encoded pulses of a previouslytransmitted set and modulated at a same frequency of a previously-transmitted set or of the previously-transmitted set, wherein a set transmitted immediately before the at least one further set and the at least one further set form a complementary sequence.

9. The method according to claim 2, further comprising a preliminary step of initializing an index k; and further steps of:

10. The method according to one of claims 1 to 9, wherein a pulse of one of the sets is determined according to one of the following equations:

Sn(t)=Z ,exp(2.TT.j(f_0+(n-1).Af).t) if n=M.k+m; or

11. A method of processing a signal, comprising the steps of:

12. The method according to claim 11, wherein the phase correction is applied between two compressed signals related to at least two received sets of pulses encoded with complementary codes, wherein the at least two sets forming a complementary sequence:

13. A pulse radar device comprising a transmitter configured to generate a modulated signal according to one of claims 1 to 10.

14. A pulse radar device comprising a receiver configured to process a signal according to one of claims 11 or 12.

15. A pulse radar system comprising a transmitter according to claim 13 and a receiver according to claim 14.

16. A modulated signal comprising at least: