Direction of arrival estimation for automotive spread radar systems

Abstract

A method of direction of arrival estimation with an automotive spread radar system. The automotive spread radar system includes a plurality of at least two transceiver antenna units, which are configured to work in a MIMO configuration, wherein the transceiver antenna units are arranged at a priori known positions. The automotive spread radar system is configured to determine, for each transceiver unit antenna unit of the plurality of transceiver antenna units, a range of a target reflecting radar waves that have been transmitted by at least the specific transceiver antenna unit by reading out a plurality of range gates assigned to a specific transceiver antenna unit. The method and radar system are capable of estimating a direction of arrival without the need of ensuring a synchronization of antennas on the scale of a radar carrier frequency.

Claims

1. A method of direction of arrival estimation with an automotive spread radar system, the automotive spread radar system comprising a plurality of at least two transceiver antenna units, which are configured to work in a multiple-input and multiple-output configuration, wherein the transceiver antenna units are arranged at a priori known positions, and the automotive spread radar system is configured to determine, for each specific transceiver antenna unit of the plurality of transceiver antenna units, a range of a target reflecting radar waves that have been transmitted by at least the specific transceiver antenna unit by reading out a plurality of range gates that are assigned to the specific transceiver antenna unit, the method comprising steps of: for each specific one of the plurality of transceiver antenna units, determining a range of a target occurring in one of separated angular directions lying within an angular range that is arranged about a common direction at least from radar waves that have been transmitted by the specific transceiver antenna unit and have been reflected by the target, by reading out range gates out of the plurality of range gates of the specific transceiver antenna unit, determining a pattern of occupied range gates from the read-out range gates of the plurality of transceiver antenna units, wherein the pattern of occupied range gates are created by mutually shifted range gate allocations of the plurality of transceiver antenna units, and estimating a direction of arrival based on relating the determined pattern of occupied range gates to a plurality of expected patterns of occupied range gates for targets occurring in the separated angular directions, the plurality of expected patterns of occupied range gates being predetermined from the a priori known positions of the plurality of transceiver antenna units, and wherein the direction of arrival is estimated without using phase information from reflected radar waves.

2. The method as claimed in claim 1, wherein the step of determining, for each specific one of the plurality of transceiver antenna units, a range of a target includes determining a range of a target from radar waves that have been transmitted by the specific transceiver antenna unit and at least another one of the plurality of transceiver antenna units and have been reflected by the target, by reading out range gates out of the plurality of range gates of the specific transceiver antenna unit and of the at least one another transceiver antenna units.

3. The method as claimed in claim 1, wherein prior to the step of determining a range of the target occurring in one of separated angular directions, a step of merging consecutive range gates of each plurality of range gates into packages of a predetermined number of range gates is executed for all transceiver antenna units.

4. The method as claimed in claim 1, wherein the step of estimating a direction of arrival includes solving the linear equation system
R.sub.m=A.Math.t wherein t denotes a vector that represents occurring targets detected in the separated angular directions, R.sub.m represents a vector comprising results from reading out the plurality of range gates and A is a matrix that is calculated from the a priori known positions and the separated angular directions, wherein A represents a linear mapping, by which vector t is transformed into vector R.sub.m.

5. A non-transitory computer-readable medium for controlling automatic execution of steps of the method as claimed in claim 1, wherein the method steps are stored on the computer-readable medium as a program code, wherein the computer-readable medium comprises a part of the automotive spread radar system or a separate control unit and the program code is executable by a processor unit of the automotive spread radar system or a separate control unit.

6. An automotive spread radar system for direction of arrival estimation, comprising: a plurality of at least two transceiver antenna units, which are configured to work in a multiple-input and multiple-output configuration, wherein the transceiver antenna units are arranged at a priori known positions, for each specific transceiver antenna unit of the plurality of transceiver antenna units, a plurality of range gates that are configured to indicate a range of a target reflecting radar waves that have been transmitted by at least the specific transceiver antenna unit, an evaluation and control unit that is configured to: read out the plurality of range gates for all transceiver antenna units, determine a pattern of occupied range gates from the read-out range gates of the plurality of transceiver antenna units, wherein the pattern of occupied range gates are created by mutually shifted range gate allocations of the plurality of transceiver antenna units, and estimate a direction of arrival based on relating the determined pattern of occupied range gates to a plurality of expected patterns of occupied range gates for targets occurring in the separated angular directions, the plurality of expected patterns of occupied range gates being predetermined from the a priori known positions of the plurality of transceiver antenna units, and wherein the direction of arrival is estimated without using phase information from reflected radar waves.

7. The automotive spread radar system as claimed in claim 6, wherein the plurality of transceiver antenna units is arranged at the a priori known positions to form a one-dimensional linear array.

8. The automotive spread radar system as claimed in claim 6, wherein the a priori known positions of the plurality of transceiver antenna units are arranged at a front region of a vehicle.

9. The automotive spread radar system as claimed in claim 6, wherein the evaluation and control unit comprises a processor unit and a digital data memory unit to which the processor unit has data access.

10. The automotive spread radar system as claimed in claim 6, further comprising modulation means to operate the plurality of at least two transceiver antenna units in a phase-modulated continuous wave mode.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) Further details and advantages of the present invention will be apparent from the following detailed description of not limiting embodiments with reference to the attached drawing, wherein:

(2) FIG. 1 illustrates a possible embodiment of the automotive spread radar system in accordance with the invention in a state of being installed in a vehicle,

(3) FIG. 2 schematically shows the plurality of transceiver antenna units of the automotive spread radar system pursuant to FIG. 1,

(4) FIG. 3 shows a phase-modulated continuous wave for operating the transceiver antenna units pursuant to FIG. 2,

(5) FIG. 4 shows a sequence to be transmitted by the transceiver antenna units, coded by a Hadamard matrix,

(6) FIG. 5 illustrates separated directions of arrival arranged within an angular range of about a common angular direction ,

(7) FIG. 6 shows an example of contents of the plurality range gates of the plurality of transceiver antenna units pursuant to FIG. 2 with targets occurring within the angular range ,

(8) FIG. 7 illustrates a determined pattern of occupied range gates for a fixed direction of arrival,

(9) FIG. 8 shows the plurality of range gates of the plurality of transceiver antenna units after merging consecutive range gates of each plurality of range gates into packages of a predetermined number of range gates,

(10) FIG. 9 schematically illustrates a situation of determining the range of the occurring target in different ones of separated angular directions of arrival,

(11) FIG. 10 schematically shows the occurring target in relation to range cells of two transceiver antenna units,

(12) FIG. 11 schematically shows a situation of two transceiver antenna units detecting a two-target configuration,

(13) FIG. 12 schematically shows a discrimination of the two possible two-target configurations by range-based decoded information derived from cross talk between transceiver antenna units,

(14) FIG. 13 illustrates a plurality of range gates of transceiver antenna units decoding their own radar signal as well as the radar signals transmitted by the other transceiver antenna units reflected by a target,

(15) FIG. 14 is a schematic layout of a signal processing unit of the automotive spread radar system, and

(16) FIG. 15 schematically shows multiplication of a signal with each row of a Hadamard matrix after correlation.

DESCRIPTION OF THE ILLUSTRATED EMBODIMENTS

(17) FIG. 1 shows a possible embodiment of an automotive spread radar system 10 for direction of arrival estimation of radar waves reflected by a target 28 in accordance with the invention. The automotive spread radar system 10 is installed in a vehicle 26 formed by a passenger car to provide information that is to be used as an input for a collision avoidance system of the vehicle 26. The automotive spread radar system 10 comprises a plurality of N=4 transceiver antenna units TRx.sub.k, k=1N, that are arranged at a priori known positions at a front region of the vehicle 26.

(18) FIG. 2 schematically illustrates the plurality of N=4 transceiver antenna units TRx.sub.k, k=1N, of the automotive spread radar system 10 pursuant to FIG. 1. In FIG. 2, the transceiver antenna units TRx.sub.k are shown to be arranged at a priori known positions to form a one-dimensioned linear array 24, wherein the transceiver antenna units TRx.sub.k are evenly spaced by a distance d, for example 0.5 m. For reasons of simplicity of the considerations to follow, this arrangement differs from the arrangement shown in FIG. 1. However, those skilled in the art will appreciate that similar geometrical considerations apply.

(19) In this specific embodiment, the transceiver antenna units TRx.sub.k are identically designed. Each transceiver antenna unit TRx.sub.k includes a plurality of n=4 patches. In other embodiments, the number of patches may be different for some or for all of the transceiver antenna units TRx.sub.k.

(20) The plurality of transceiver antenna units TRx.sub.k is configured to work in a multiple-input and multiple-output (MIMO) configuration. The individual transceiver antenna units TRx.sub.k transmit orthogonal codes, i.e. each transceiver antenna unit TRx.sub.k can decode its own echo and the echoes generated by other transceiver antenna units TRx.sub.k without cross talk disturbances. To this end, the automotive spread radar system 10 comprises modulation means to operate the plurality of transceiver antenna units TRx.sub.k in a phase-modulated continuous wave (PMCW) mode.

(21) In this embodiment, PMCW is based on bi-phase modulation, which means (t)=0 or (t)=180 for an emitted signal u(t)=A cos(ft+(t)). The phase code c=(c.sub.k) {1,1}.sup.L.sup.c, which is meant to be sent out could be properly chosen, for example as an Almost Perfect Auto-Correlation Sequence (APAS) or a Maximum Length-Sequence (m-sequence), depending on the requirements. The phase can then be modelled via

(22) ${}_c\left(t\right):=\{\begin{array}{cc}0& \mathrm{if}{c}_{.Math.\frac{t}{T_c}.Math.\mathrm{mod}{L}_c}=1\\ 180& \mathrm{if}{c}_{.Math.\frac{t}{T_c}.Math.\mathrm{mod}{L}_c}=-1\end{array}$
with chirp duration T.sub.c T.sub.c and code length L.sub.c. A potential phase-modulated radar waveform is illustrated in FIG. 3.

(23) For the PMCW automotive spread radar system 10 the MIMO concept can be realized via Hadamard coding to provide orthogonal signals. This per se known technique is called Outer Code MIMO Concept. For that purpose one has to take a matrix from the Walsh-Hadamard family (exists for all lengths multiple of 2 from 4 to 664) in which all rows are orthogonal. The length of needed outer code is equal to the number of transceiver antenna units TRx.sub.k. For this specific embodiment with four transceiver antenna units TRx.sub.k, one Hadamard matrix is given by

(24) $H=\left[\begin{array}{cccc}1& 1& 1& 1\\ 1& -1& 1& -1\\ 1& 1& -1& -1\\ 1& -1& -1& 1\end{array}\right]$

(25) Then the sequence S, which is sent out will be coded (multiplied) by such Hadamard matrices as shown in FIG. 4.

(26) For each specific transceiver antenna unit TRx.sub.k of the plurality of transceiver antenna units TRx.sub.k, the automotive spread radar system 10 includes a plurality of range gates 12 that are configured to indicate a range of a target 28 reflecting radar waves that have been transmitted by the specific transceiver antenna unit TRX.sub.m as well as radar waves that have been transmitted by all other transceiver antenna unit TRX.sub.k, k=1N, km, of the plurality of transceiver antenna unit TRX.sub.k. The number of range gates is L.

(27) The approach to obtain additional information for DoA is based on an allocation of the different range gates 12 of the transceiver antenna units TRx.sub.k.

(28) In the following, an embodiment of a method of direction of arrival estimation with an automotive spread radar system in accordance with the invention will be described.

(29) Each of the transceiver antenna units TRx.sub.k determines a range of an occurring target 28 in one of separated angular directions of arrival d.sub.k lying within an angular range of that is arranged about a common direction (uniqueness bin ). The separated angular directions of arrival d.sub.k correspond to angles .sub.k of value (FIG. 5):

(30) ${}_k=-+k.Math.\frac{2}{N+1}+,k=1,\mathrm{.Math.},N$

(31) For each one of the plurality of transceiver antenna units TRx.sub.k, the received signal is decoded in a first step for the received radar wave that has been transmitted by itself, and the plurality of range gates 12 is read out (FIG. 6).

(32) For a fixed angular direction of arrival d.sub.k ad.sub.knd a fixed target 28 located in this angular direction of arrival d.sub.k, the occupied range gates 12 of the individual transceiver antenna units TRx.sub.k are mutually shifted (FIG. 7):

(33) Left side delay l.sub.k (if .sub.k) in terms of range resolution units (denoted by r) of transceiver antenna units TRx.sub.j to TRx.sub.j+1:

(34) $l_k=-\frac{d\sin \left({}_k\right)}{r}\mathrm{for}j=1,\mathrm{.Math.},\frac{N}{2}$

(35) Right side delay r.sub.k (if .sub.k) in terms of range resolution units r of transceiver antenna units TRx.sub.j to TRx.sub.j+i:

(36) $r_k=\frac{d\sin \left({}_k\right)}{r}\mathrm{for}j=\frac{N}{2}+1,\mathrm{.Math.},N.$

(37) Thus, the maximum delay between adjacent transceiver antenna units TRx.sub.k is

(38) $m=\frac{-d\sin \left({}_1\right)}{r}=\frac{d\sin \left({}_N\right)}{r}$
range gates 12.

(39) In another step of the method, a pattern of occupied range gates 12 from the read-out range gates of the plurality of transceiver unit antenna units TRx.sub.k is determined. As illustrated in FIG. 7, the pattern shows as a mutual shifting of occupied range gates 12 among the plurality of transceiver unit antenna units TRx.sub.k.

(40) A direction of arrival d.sub.k is estimated based on relating the determined pattern of occupied range gates 12 to a plurality of expected patterns of occupied range gates 12 for targets occurring in the separated angular directions .sub.k. The plurality of expected patterns of occupied range gates 12 has been predetermined from the a priori known positions of the plurality of transceiver unit antenna units TRx.sub.k.

(41) For obtaining unambiguity, prior to the step of determining a range of the occurring target 28, a step of merging consecutive range gates 12 of each plurality of range gates 12 into packages of a predetermined number of range gates 12 is executed for all transceiver antenna units TRx.sub.k. The merging is illustrated in FIG. 8.

(42) Then, for transceiver antenna unit TRx.sub.1 a target 28 which is detected in angular direction corresponding to an angle

(43) ${}_k,k\frac{N}{2}$
and a distance d[j.Math.m, (j+1).Math.m]=:R.sub.m(1,l), j{0, . . . , {tilde over (L)}N} is detected as a target 28 in range

(44) $.Math.\frac{l-1}{k}.Math..Math.m+\left[j.Math.m,\left(j+1\right).Math.m\right]\text{=:}{R}_m\left(j,l\right)$
for the other transceiver antenna units TRx.sub.l, l>1, as illustrated in FIG. 8.

(45) Accordingly, the range gates 12 are occupied for targets 28 in the direction corresponding to angle .sub.k,

(46) $k>\frac{N}{2}.$

(47) The former range resolution decreases from r to sin(.sub.1) d on the finer angular grid. The finer angle resolution requires additional computational effort of (n(N{tilde over (L)}).sup.2), wherein denotes the Landau symbol.

(48) An important observation can be made at this point: A higher angular resolution by transceiver antenna units TRx.sub.k will reduce the loss in range resolution in the refined angular grid, but at the same time will increase the computational costs.

(49) For example, the considered PMCW automotive spread radar system 10 with parameters n=4, N=4, d=0.5 m, R=0.01 m, L=1000 will increase the separation in 16 angular directions (from 4 directions). The range resolution on the finer angular grid is reduced to 0.1 m and the finer angle resolution requires an additional computational effort of (4.Math.400.sup.2)=(640 000) operations, which is in the range of standard processing.

(50) The step of relating the determined pattern of occupied range gates 12 to a plurality of expected patterns of occupied range gates 12 for targets occurring in the separated angular directions .sub.k can formally be described as a linear mapping. The linear mapping takes place from the space of all possible target configurations to the resulting range gate occupations for the different transceiver antenna units TRx.sub.k and can be described by the following equation:

(51) 0$\left(\begin{array}{c}{R}_m\left(1,1\right)\\ R_m\left(1,2\right)\\ \mathrm{.Math.}\\ R_m\left(1,N\right)\\ \mathrm{.Math.}\\ R_m\left(\tilde{L},1\right)\\ R_m\left(\tilde{L},2\right)\\ \mathrm{.Math.}\\ R_m\left(\tilde{L},N\right)\end{array}\right)=A.Math.\left(\begin{array}{c}t\left(1,1\right)\\ t\left(1,2\right)\\ \mathrm{.Math.}\\ t\left(1,N\right)\\ \mathrm{.Math.}\\ t\left(\tilde{L},1\right)\\ t\left(\tilde{L},2\right)\\ \mathrm{.Math.}\\ t\left(\tilde{L},N\right)\end{array}\right)=A.Math.t$
wherein t denotes a vector that represents occurring targets detected in the separated angular directions .sub.k, and t(j, k) has a value of 1 if there is a target 28 occurring in angular direction .sub.k and distance in [j.Math.m, (j+1).Math.m] from transceiver antenna unit TRx.sub.1, and a value of 0 else. R.sub.m represents a vector comprising results from reading out the plurality of range gates 12, and A is a matrix that is calculated from the a priori known positions and that represents a linear mapping, by which vector t is transformed to vector Ram. The step of estimating a direction of arrival d.sub.k is then carried out by solving the above linear equation system.

(52) In many cases, the matrix A is a sparse matrix, i.e. the number of non-zero matrix elements is small compared to the total number of matrix elements, and the well-known methods of numerically solving linear equations systems with sparse matrices can beneficially be applied.

(53) In general, the matrix A is not a square matrix. Well-known methods for solving linear equation systems represented by such matrices may be applied, such as compressed sensing, provided that known method-specific prerequisites are met.

(54) Depending on actual parameters, for instance a range value, of a scenario of detecting a target and estimating a direction of arrival of radar waves reflected by the target, different matrices A may be employed for relating the determined pattern of occupied range gates 12 to a plurality of expected patterns of occupied range gates 12.

(55) With reference to FIG. 1, the automotive spread radar system 10 comprises an evaluation and control unit 16 that is configured for reading out the plurality of range gates 12 for all transceiver antenna units TRx.sub.k, determining a pattern of occupied range gates 12 from the read-out range gates of the plurality of transceiver unit antenna units (TRx.sub.k), and estimating a direction of arrival d.sub.k based on relating the determined pattern of occupied range gates 12 to a plurality of expected patterns of occupied range gates 12 for targets occurring in the separated angular directions .sub.k, the plurality of expected patterns of occupied range gates 12 being predetermined from the a priori known positions of the plurality of transceiver unit antenna units TRx.sub.k.

(56) In particular, the evaluation and control unit 16 is configured for relating the determined pattern of occupied range gates 12 to the plurality of expected patterns by solving the above-described linear equation system R.sub.m=A.Math.t.

(57) The evaluation and control unit 16 can be located at any place within the vehicle 26 that appears suitable to those skilled in the art.

(58) In order to be able to execute these steps, the evaluation and control unit 16 is equipped with a processor unit and a digital data memory unit to which the processor unit has data access, and a signal processing unit 18 (FIG. 14) whose function will be described later on. The digital data memory unit comprises a non-transitory computer-readable medium. Values of elements of matrix A reside in the digital data memory unit. The evaluation and control unit 16 is furnished with a software module. Method steps to be conducted are converted into a program code of the software module. The program code is implemented in the digital data memory unit of the evaluation and control unit and is executable by the processor unit of the evaluation and control unit.

(59) In the cases of targets 28 occurring in the far field of the transceiver antenna units TRx.sub.k considered up to now, a range of the occurring target 28 is determined by each one of the plurality of transceiver antenna units TRx.sub.k in the same one of separated angular directions corresponding to angle .sub.k lying within the angular range .

(60) In case of targets 28 occurring in the near field of the transceiver antenna units TRx.sub.k, a range of the occurring target 28 can be determined by each one of the plurality of transceiver antenna units TRx.sub.k in different ones of separated angular directions corresponding to angles .sub.k lying within the angular range . The situation is illustrated in FIG. 9, for the sake of clarity only for two transceiver antenna units TRx.sub.1, TRx.sub.2.

(61) When at transceiver antenna units TRx.sub.1 and TRx.sub.2 range gate 2r.sub.1, and range gate 2r.sub.2 show a peak, respectively, then the target 28 is located at

(62) $x=\cos \left(\right)r_1,y=\sin \left(\right)r_1\mathrm{wherein}=\mathrm{arcos}\left(\frac{-r_2^2+r_1^2+d^2}{2r_{1}d}\right)$

(63) and coordinates are as shown in FIG. 9.

(64) For these cases, the mapping matrix A has to be adjusted accordingly.

(65) A target 28 located at
(x,y)=(cos()r.sub.1,sin()r.sub.1)
will generate range gate peaks in
r.sub.1={square root over (x.sup.2+y.sup.2)},r.sub.2={square root over ((dx).sup.2+y.sup.2)}
at transceiver antenna units TRx.sub.1, TRx.sub.2, respectively.

(66) The number of cells 14 to decode is immediately linked with the coarseness of the grid (the size of the cells 14, compare FIG. 10). To reduce the complexity of the problem and achieve unambiguity one can increase the size of the cells 14 by merging range gates as described before. As in all angular decoding techniques, there is a trade-off between resolution and unambiguity which needs to be decided on.

(67) As presented before, an incoherent processing is unable to distinguish between target configurations like those illustrated in FIG. 11 (triangles A.sub.1, A.sub.2 versus crosses B.sub.1, B.sub.2). However, a coherent processing regarding range resolution yields uniqueness of the target configuration.

(68) To achieve this, for each one of the plurality of transceiver antenna units TRx.sub.k, a received signal from radar waves reflected by the targets is decoded not only for the received radar wave that has been transmitted by a specific transceiver antenna unit TRx.sub.m, but also for the radar waves that have been transmitted by the balance of the plurality of transceiver antenna units TRX.sub.k, k=1N, km, and the plurality of range gates 12 is read out.

(69) A plurality of range gates of the transceiver antenna units TRx.sub.k after decoding their own radar signal as well as the radar signals that have been transmitted by the other transceiver antenna units TRX.sub.k, k=1N, km, and have been reflected by a target is illustrated in FIG. 13. Herein, an occupied range gate R(i,j,k) symbolizes a radar wave that has been transmitted by transceiver antenna units TRx.sub.k, has been decoded by transceiver antenna units TRx.sub.j, and has been received in a time slot corresponding to a distance of i times the range resolution r.

(70) The range information one can get out of a complete MIMO concept is given in the table below.

(71) TABLE-US-00001 A.sub.1 A.sub.2 B.sub.1 B.sub.2 Tx1 to Rx1 2r.sub.2 2r.sub.1 2r.sub.1 2r.sub.2 Tx1 to Rx2 r.sub.2 + s.sub.2 r.sub.1 + s.sub.1 r.sub.1 + s.sub.2 r.sub.2 + s.sub.1 Tx2 to Rx1 s.sub.2 + r.sub.2 s.sub.1 + r.sub.1 s.sub.2 + r.sub.1 s.sub.1 + r.sub.2 Tx2 to Rx2 2s.sub.2 2s.sub.1 2s.sub.2 2s.sub.1

(72) The cross talks of the transceiver antenna units TRx.sub.k deliver further information (rows 2 and 3 of table), which can be used to discriminate the different target configurations. Again, it is emphasized that this information is solely range-based, and not phase-based.

(73) The additional information gained from decoding the mutual signals corresponds to distance separations by ellipses (here specified by constants c.sub.1, c.sub.2), as is illustrated in FIG. 12.

(74) Signals received by the transceiver antenna units TRx.sub.k are processed by the signal processing unit 18 that forms part of the automotive spread radar system 10. The signal processing unit 18 is known per se and described herein for the sake of completeness.

(75) The layout of the signal processing unit 18 is illustrated in FIG. 14. Correlators 20 will perform ranging, similar as in a global positioning system (GPS). The number of parallel correlators 20 is equal to sequence length L.sub.c to provide the range processing in one step. The coherent accumulator 22 will increase the signal-to-noise ratio (SNR) via M accumulations, and at least a Fast Fourier Transform (FFT) to extract the Doppler information will be performed.

(76) At the receiver side a multiplication of a signal v with each row of the Hadamard matrix H..sub.i is necessary to distinguish between each transmitter (after correlation, see for example, FIG. 15).

(77) Design parameters of the automotive spread radar system 10 are:

(78) Total Dwell time
T.sub.d=T.sub.c.Math.L.sub.c.Math.M.Math.N
Range resolution

(79) $R_{\mathrm{res}}=\frac{{\mathrm{cT}}_c}{2}$
Unambiguous range

(80) $R_{\max }=\frac{{\mathrm{cL}}_c}{2R_c}$
Velocity resolution

(81) $v_{\mathrm{res}}=\frac{{}_c}{2T_d}$

(82) with wavelength .sub.c of the carrier frequency

(83) Processing gain
G.sub.preFFT=10 log.sub.10(L.sub.cM)
G.sub.FFT=10 log.sub.10(N)

(84) While the invention has been illustrated and described in detail in the drawings and foregoing description, such illustration and description are to be considered illustrative or exemplary and not restrictive; the invention is not limited to the disclosed embodiments.

(85) Other variations to be disclosed embodiments can be understood and effected by those skilled in the art in practicing the claimed invention, from a study of the drawings, the disclosure, and the appended claims. In the claims, the word comprising does not exclude other elements or steps, and the indefinite article a or an does not exclude a plurality, which is meant to express a quantity of at least two. The mere fact that certain measures are recited in mutually different dependent claims does not indicate that a combination of these measures cannot be used to advantage. Any reference signs in the claims should not be construed as limiting scope.