APPLYING PORT DIVERSITY OF VIRTUAL ARRAY FOR IMPROVING SENSING CAPABILITY WITH JOINT COMMUNICATION LINKS

Abstract

A method of joint communication and sensing of a target obstacle (object or human) is disclosed. The method comprises deploying a joint communication and sensing transceiver, comprising a transmitter (TX) having at least two transmitting antennas and a receiver (RX) having at least one receiving antenna; transmitting at least two radio frequency (RF) signals carrying data to a communication receiver by the at least two transmitting antennas; and receiving at least one reflected radio frequency (RF) signal reflected by the target obstacle by the at least one receiving antenna; wherein the at least two RF signals transmitted by the at least two transmitting antennas are applied with cyclic shift diversity; and wherein the at least two RF signals transmitted by the at least two transmitting antennas contain TX-varying phase rotations.

Claims

1. A method of joint communication and sensing of a target obstacle, comprising: deploying a joint communication and sensing transceiver, comprising a transmitter (TX) having at least two transmitting antennas and a receiver (RX) having at least one receiving antenna; transmitting at least two radio frequency (RF) signals carrying data to a communication receiver by the at least two transmitting antennas; and receiving at least one reflected radio frequency (RF) signal reflected by the target obstacle by the at least one receiving antenna; wherein the at least two RF signals transmitted by the at least two transmitting antennas are applied with cyclic shift diversity; and wherein the at least two RF signals transmitted by the at least two transmitting antennas contain TX-varying phase rotations.

2. The method of claim 1, wherein the at least two RF signals are cyclic shifted in time domain.

3. The method of claim 1, wherein a virtual receiving array is generated by the at least two transmitting antennas and the at least one receiving antenna.

4. The method of claim 3, wherein the at least two transmitting antennas form at least one transmitting array.

5. The method of claim 1, wherein the at least two radio frequency (RF) signals are orthogonal frequency domain multiplexing (OFDM) signals.

6. The method of claim 5, wherein the at least two radio frequency (RF) signals form virtually orthogonal transmitter (TX) ports that are distinguishable at each of the at least one receiving antenna of the joint communication and sensing transceiver.

7. The method of claim 1, wherein the TX-varying phase rotations are determined based on spatial domain information of the communication receiver.

8. The method of claim 7, wherein the spatial domain information is a transmit precoder matrix indicator (TPMI) adopted by the communication receiver and sent from the communication receiver.

9. The method of claim 8, the at least two transmitting antennas form at least one transmitting array and wherein the cyclic shift diversity and the TX-varying phase rotation for each of the at least two transmitting antennas are chosen for the at least one transmitting array to generate a beam pattern of an Angle of Departure (AoD) whose angular frequency-domain flatness mainlobe direction aligns with that of a phase vector of the TPMI.

10. A method of joint communication and sensing a target obstacle, comprising: deploying a joint communication and sensing transceiver, comprising a transmitter (TX) having at least two transmitting antennas and a receiver (RX) having at least one receiving antenna; transmitting at least two radio frequency (RF) signals carrying data to a communication receiver by the at least two transmitting antennas; and receiving at least one reflected radio frequency (RF) signal reflected by the target obstacle by the at least one receiving antenna; wherein the at least two RF signals transmitted by the at least two transmitting antennas are applied with cyclic shift diversity.

11. The method of claim 10, wherein the at least two RF signals are cyclic shifted in time domain.

12. The method of claim 10, wherein a virtual receiving array is generated by the at least two transmitting antennas and the at least one receiving antenna.

13. The method of claim 12, wherein the at least two transmitting antennas form at least one transmitting array.

14. The method of claim 10, wherein the at least two radio frequency (RF) signals are orthogonal frequency domain multiplexing (OFDM) signals.

15. The method of claim 14, wherein the at least two radio frequency (RF) signals form virtually orthogonal transmitter (TX) ports that are distinguishable at each of the at least one receiving antenna of the joint communication and sensing transceiver.

16. The method of claim 10, wherein an azimuth angle and an elevation angle of the target obstacle is obtained.

17. A device capable of joint communication and sensing of a target obstacle, comprising: a joint communication and sensing transceiver, comprising a transmitter (TX) having at least two transmitting antennas and a receiver (RX) having at least one receiving antenna; wherein the at least two transmitting antennas transmit data on at least two cyclic shifted radio frequency (RF) signals to a communication receiver; and wherein the at least one receiving antenna receives at least one reflected cyclic shifted radio frequency (RF) signal reflected by the target obstacle; and wherein at least two cyclic shifted radio frequency (RF) signals contain TX-varying phase rotations.

18. The device of claim 17, wherein the at least two cyclic shifted radio frequency (RF) signals form virtually orthogonal transmitter (TX) ports that are distinguishable at each of the at least one receiving antenna of the joint communication and sensing transceiver.

19. The device of claim 17, wherein the TX-varying phase rotations are determined based on spatial domain information of the communication receiver.

20. The device of claim 19, wherein the spatial domain information is a transmit precoder matrix indicator (TPMI) adopted by the communication receiver and sent from the communication receiver.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0026] In order to sufficiently understand the essence, advantages and the preferred embodiments, the following detailed description will be more clearly understood by referring to the accompanying drawings.

[0027] FIG. 1 illustrates a geometry model of a collocated MIMO array.

[0028] FIG. 2(a) illustrates an array configuration used for joint communication and sensing in accordance with a first embodiment of the present disclosure.

[0029] FIG. 2(b) illustrates a virtual aperture of the array configuration in accordance with the first embodiment of the present disclosure.

[0030] FIG. 3(a) illustrates an array configuration used for joint communication and sensing in accordance with a second embodiment of the present disclosure.

[0031] FIG. 3(b) illustrates a virtual aperture of the array configuration in accordance with the second embodiment of the present disclosure.

[0032] FIG. 4(a) illustrates an array configuration used for joint communication and sensing in accordance with a third embodiment of the present disclosure.

[0033] FIG. 4(b) illustrates a virtual aperture of the array configuration in accordance with the third embodiment of the present disclosure.

[0034] FIG. 5(a) illustrates an array configuration used for joint communication and sensing in accordance with a fourth embodiment of the present disclosure.

[0035] FIG. 5(b) illustrates a virtual aperture of the array configuration in accordance with the fourth embodiment of the present disclosure.

[0036] FIG. 6 illustrates the beam patterns of Case 1.

[0037] FIG. 7 illustrates the beam patterns, angle of departure and bit error rate of Case 2.

[0038] FIG. 8 illustrates the beam patterns, angle of departure and bit error rate of Case 3.

[0039] FIG. 9 illustrates the beam patterns, angle of departure and bit error rate of Case 4.

[0040] FIG. 10 illustrates the beam patterns, angle of departure and bit error rate of Case 5.

[0041] FIG. 11 illustrates the beam patterns, angle of departure and bit error rate of Case 6.

[0042] FIG. 12 illustrates the beam patterns, angle of departure and bit error rate of Case 7.

[0043] FIG. 13 illustrates the beam patterns of Case 8.

[0044] FIG. 14 illustrates the beam patterns of Case 9.

[0045] FIG. 15 illustrates a method of joint communication and sensing of a target obstacle (object or human) in accordance with a fifth embodiment of the present disclosure.

DETAILED DESCRIPTION OF THE DRAWINGS

[0046] The following description discloses the preferred embodiments. The present disclosure is described below by referring to the embodiments and the figures. Thus, the present disclosure is not intended to be limited to the embodiments shown, but is to be accorded the principles disclosed herein. Furthermore, that various modifications or changes in light thereof will be suggested to a person having ordinary skill in the art and are to be included within the spirit and purview of this application and scope of the appended claims.

[0047] First of all, sensing surrounding target obstacles (objects or humans) through signal delay measurement and Doppler shift detection is commonly known and used in radar engineering. In a radar sensing system, it usually transmits several radio waves by transmitters and then receives reflected radio waves by receivers to determine one or more characteristics of the surrounding target obstacles, such as distances, azimuth angles, elevation angles, and/or velocities of the target obstacles.

[0048] The transmitters and receivers in the radar system may or may not be co-located. If transmitters and receivers are located at the same location, it is known as a monostatic sensing system. If transmitters and receivers are located at different locations, it is known as bistatic sensing system.

[0049] In 5G NR, MIMO (Multiple Input Multiple Output) technology deploys multiple antennas at both the transmitter and receiver (UE and gNB) to improve data throughput and reliability based on spatial multiplexing and spatial.

[0050] In 5G NR, sensing and communication are performed separately because constant-envelope sequences with zero autocorrelation properties are designed to use for sensing purpose only. Transmitting antenna ports are merely used for communication or gNB sounding. However, transmitted radio frequency (RF) signals intended for communication in essence have similar radio characteristics with those intended for sensing. Accordingly, transmitted RF signals intended for communication could be reused to provide sensing ability.

[0051] Now refer to FIG. 1 which illustrates a geometry model of a collocated MIMO array (100).

[0052] The collocated MIMO array (100) has M.sub.T transmitting (TX) antennas and L.sub.R receiving (RX) antennas. Let (x.sub.m.sup.T,y.sub.m.sup.T,z.sub.m.sup.T) be the location of the m.sup.th TX and (x.sub.l.sup.R,y.sub.l.sup.R,z.sub.l.sup.R) be the location of the l.sup.th RX. The geometric center of the collocated MIMO array (100) is chosen as the origin of the coordinate O=(0,0,0) for simplicity. Let (R,,) or (x,y,z) denote the location parameters of a target (200), where R is the distance from the origin of the collocated MIMO array (100) to the target (200), is the azimuth angle, and is the elevation angle, and the transformation from Polar coordinate system to Cartesian coordinate system is as follows.

[00001]$\{\begin{array}{cc}x& =R\cos \cos \\ y& =R\cos \sin \\ z& =R\sin \end{array}$

[0053] The distance from the m.sup.th TX to the target (200) is

[00002]$R_m=\sqrt{{\left(x_m^T-x\right)}^2+{\left(y_m^T-y\right)}^2+{\left(z_m^T-z\right)}^2},$

and the distance from the target (200) to the l.sup.th RX is

[00003]$R_l=\sqrt{{\left(x_l^R-x\right)}^2+{\left(y_l^R-y\right)}^2+{\left(z_l^R-z\right)}^2}.$

[0054] Under the far-field assumption

[00004]$\left(\frac{2D^2}{}R\right),$

where D is the size of the collocated MIMO array (100) and is the wavelength corresponding to the carrier frequency, R.sub.m and R.sub.l can be approximated as follows.

[00005]$\begin{array}{c}{R}_m=R-x_m^T\cos \cos -y_m^T\cos \sin -z_m^T\sin \\ R_l=R-x_l^R\cos \cos -y_l^R\cos \sin -z_l^R\sin \end{array}$

[0055] Then, the round-trip distance between the target (200) and TX/RX is as follows.

[00006]$R_m+R_l=2R-\left(x_m^T+x_l^R\right)\cos \cos -\left(y_m^T+y_l^R\right)\cos \sin -\left(z_m^T+z_l^R\right)\sin$

[0056] Upon the condition that each TX can be identified and separated at the receiver, the array response of the collocated MIMO array (100) is equivalent to that of the SIMO array with a virtual receiving array, which can be defined as follows.

[00007]$\left\{\left(x_m^T+x_l^R,y_m^T+y_l^R,z_m^T+z_l^R\right),m=0,1,.Math.,M_T-1,l=0,1,.Math.,L_R-1\right\}$

[0057] This virtual receiving array, also referred to as virtual aperture, has M.sub.TL.sub.R elements that are obtained via the spatial convolution of the TX and RX of the collocated MIMO array (100). Due to the enlarged virtual receiving array, the collocated MIMO array (100) has many advantages such as higher spatial resolution, improved parameter identifiability and enhanced system performance.

[0058] Now refer to FIG. 2(a), illustrating an array configuration used for joint communication and sensing in accordance with a first embodiment of the present disclosure.

[0059] The array configuration in accordance with the first embodiment of the present disclosure has 4 TX (i.e. M.sub.T=4) and 8 RX (i.e. L.sub.R=8), where a uniform filled (i.e., 0.5 inter-element spacing) linear receiving (RX) array with 8 elements is nested between the 4 TX, which forms a transmitting (TX) array. The virtual aperture of the array configuration in accordance with the first embodiment of the present disclosure is shown in FIG. 2(b).

[0060] Specifically, the location of the l.sup.th RX is given as follows:

[00008]$x_l^R=0,y_l^R=-\frac{}{4}\left(L_R-1\right)+\frac{l}{2},z_l^R=0\mathrm{for}l=0,1,.Math.,L_R-1.$

[0061] Specifically, the locations of the 4 TX are given as follows.

[00009]$\{\begin{array}{c}{x}_0^T=0,y_0^T=-\frac{}{4}{L}_R,z_0^T=\frac{d_z}{2}\\ x_1^T=0,y_1^T=-\frac{}{4}{L}_R,z_1^T=-\frac{d_z}{2}\\ x_2^T=0,y_2^T=\frac{}{4}{L}_R,z_2^T=\frac{d_z}{2}\\ x_3^T=0,y_3^T=\frac{}{4}{L}_R,z_3^T=-\frac{d_z}{2}\end{array}$

[0062] In the first embodiment of the present disclosure, d.sub.z is set as for simplicity. To obtain the maximized uniform virtual array along the y axis, the inter-element spacing of the transmitting (TX) array is set as

[00010]$\frac{}{2}{L}_R$

in the y direction. To extract the target information along the z axis, the vertical inter-element spacing of the transmitting (TX) array is set as d.sub.z. As shown in FIG. 2(b), the array configuration in accordance with the first embodiment of the present disclosure forms two parallel uniform linear virtual apertures with vertical offset d.sub.z. The location of the virtual array, for n.sub.1=0, 1, . . . , n.sub.2=0, 1, . . . , 2L.sub.R is given as follows.

[00011]$x_{\left\{n_1,n_2\right\}}^V=0,y_{\left\{n_1,n_2\right\}}^V=-\frac{}{4}\left(2L_R-1\right)+\frac{n_2}{2},z_{\left\{n_1,n_2\right\}}^V=-\frac{d_z}{2}+n_1{d}_z$

[0063] For sensing usage, the range-azimuth angle resolution cell obtained by the array configuration in accordance with the first embodiment of the present disclosure depends on the bandwidth of transmitted signal as well as the horizontal length of the virtual array. The height information of the target can be obtained by the interferometry between the two vertically displaced virtual apertures.

[0064] Assume that the bandwidth of the transmitted signal is B. The slant range resolution is

[00012]${}_R=\frac{c}{2B}.$

The horizontal length of the virtual aperture is resolution is

[00013]$L=\frac{2L_R}{2}=L_R.$

The azimuth resolution is

[00014]${}_{\cos \sin }=\frac{}{L}=\frac{1}{L_R}.$

[0065] To extract the 3-D target information for sensing usage, (R, cos sin ) is estimated by using the 2-D spectral estimation algorithm, such as 2D FFT, 2D CLEAN, etc. Then, the height z of the target at the range-azimuth cell (R, cos sin ) can be determined by using the estimated range and azimuth information as well as the phase difference between two horizontal virtual apertures at this resolution cell. The relationship between the phase difference and height is as follows.

[00015]$\frac{2d_{z}z}{R}=$

[0066] Since the phase difference is a modulo of 2, the maximum unambiguous height is as follows.

[00016]$.Math.\frac{2d_z\left(z_{\max }-z_{\min }\right)}{R}.Math.<2$

[0067] The smaller d.sub.z is, the larger the maximum unambiguous height is. In addition, the array configuration in accordance with the first embodiment of the present disclosure cannot distinguish scatters located at the same range-azimuth cell with different heights. In other words, when there are two scatters located at (R, cos sin ) with different heights, i.e. z.sub.1z.sub.2, the phase difference will be a hybrid result. Accordingly, it is assumed that no scatters located at the same range-azimuth cell with different heights in accordance with the first embodiment of the present disclosure (e.g., used for terrain estimation).

[0068] Now refer to FIG. 3(a), illustrating an array configuration used for joint communication and sensing in accordance with a second embodiment of the present disclosure.

[0069] The array configuration in accordance with the second embodiment of the present disclosure has 4 TX (i.e. M.sub.T=4) and 8 RX (i.e. L.sub.R=8), where two vertically displaced and sparsely separated receiving (RX) arrays with L.sub.R/2 (L.sub.R should be even) elements and inter-element spacing for each receiving (RX) array and two groups of 2-element TX with inter-element spacing /2 are deployed above the two ends of the two receiving (RX) arrays. The virtual aperture of the array configuration in accordance with the second embodiment of the present disclosure is shown in FIG. 3(b).

[0070] Specifically, the location of the l.sup.th RX antenna is given as follows.

[00017]$x_l^R=0,y_l^R=-\frac{}{4}\left(L_R-2\right)+\mathrm{mod}\left(l,\frac{L_R}{2}\right),z_l^R=z_0+\mathrm{mod}\left(l,\frac{L_R}{2}\right)d_z\mathrm{for}l=0,1,.Math.,L_R-1.$

[0071] Specifically, the locations of the 4 TX are given as follows.

[00018]$\{\begin{array}{c}{x}_0^T=0,y_0^T=-\frac{9}{4}{L}_R,z_0^T=-\frac{}{2}-z_0\\ x_1^T=0,y_1^T=-\frac{7}{4}{L}_R,z_1^T=-\frac{}{2}-z_0\\ x_2^T=0,y_2^T=\frac{7}{4}{L}_R,z_2^T=-\frac{}{2}-z_0\\ x_3^T=0,y_3^T=\frac{9}{4}{L}_R,z_3^T=-\frac{}{2}-z_0\end{array}$

[0072] For simplicity, Z.sub.0 is set as and d.sub.z is set as in accordance with the second embodiment of the present disclosure. The array configuration in accordance with the second embodiment of the present disclosure and that in accordance with the first embodiment of the present disclosure have a similar physical size and thus form the same virtual aperture, which means they have the same sensing capability and performance. The main difference between them is that the array configuration in accordance with the second embodiment of the present disclosure could provide a height estimation with data from only one TX.

[0073] Now refer to FIG. 4(a), illustrating an array configuration used for joint communication and sensing in accordance with a third embodiment of the present disclosure.

[0074] The array configuration in accordance with the third embodiment of the present disclosure has 4 TX (i.e. M.sub.T=4) and 8 RX (i.e. L.sub.R=8), where a vertical uniform filled transmitting (TX) array having 4 TX and a horizontal uniform filled receiving (RX) array having L.sub.R RX are deployed. The virtual aperture of the array configuration in accordance with the third embodiment of the present disclosure is shown in FIG. 4(b).

[0075] Specifically, the location of the l.sup.th RX is given as follows.

[00019]$x_l^R=0,y_l^R=y_0+\frac{l}{2},z_l^R=z_0\mathrm{for}l=0,1,.Math.,L_R-1.$

[0076] Specifically, the location of the m.sup.th TX is given as follows.

[00020]$x_m^T=0,y_m^T=-\frac{}{4}\left(L_R-1\right)-y_0,z_m^T=-\frac{3}{4}+\frac{m}{2}-z_0$$\mathrm{for}m=0,1,.Math.,M_T-1.$

[0077] An M.sub.TL.sub.R 2-D uniform virtual receiving array (FIG. 4(b)) could be obtained via the spatial convolution of the transmitting (TX) array and the receiving (RX) array. The location of the (m,l).sup.th virtual element of virtual receiving array for l=0, 1, . . . , L.sub.R1, and m=0, 1, . . . , M.sub.T1 is given as follows.

[00021]$x_{m,l}^V=0,y_{m,l}^V=-\frac{}{4}\left(L_R-1\right)+\frac{l}{2},z_{m,l}^V=-\frac{3}{4}+\frac{m}{2}$

[0078] Assume that the bandwidth of the transmitted signal is B. The slant range resolution is

[00022]${}_R=\frac{c}{2B}.$

The horizontal length of the virtual aperture is

[00023]$L_h=\frac{L_R}{2}.$

The azimuth resolution is

[00024]${}_{\cos \sin }=\frac{}{L_h}=\frac{2}{L_R}.$

The vertical length of the virtual aperture is

[00025]$L_v=\frac{M_T}{2}.$

The resolution in elevation is

[00026]${}_{\sin }=\frac{}{L_v}=\frac{2}{M_T}.$

For sensing usage, we could estimate (R, cos sin , sin q) of a potential target by using the 3-D spectral estimation algorithm, such as 3D FFT, 3D CLEAN, etc. Then, the Polar coordinate system can be transformed into the Cartesian coordinate system by using the aforementioned relationship.

[0079] It should be noted that, in order to avoid grating lobes in the y direction, inter-element spacing of each horizontal virtual arrays is set to /2 for the array configurations in accordance with the first and second embodiment of the present disclosure. In addition, in order to avoid grating lobes in both y and z directions, inter-element spacing of virtual arrays is set to /2 in the two directions for the array configuration in accordance with the third embodiment of the present disclosure.

[0080] Now refer to FIG. 5(a), illustrating an array configuration used for joint communication and sensing in accordance with a fourth embodiment of the present disclosure.

[0081] The array configuration in accordance with the fourth embodiment of the present disclosure has 4 TX (i.e. M.sub.T=4) and 8 RX (i.e. L.sub.R=8), where two vertically displaced and sparsely separated receiving (RX) arrays with L.sub.R/2 (L.sub.R should be even) elements and inter-element spacing for each receiving (RX) array and a vertical uniform filled transmitting (TX) array having 4 TX with inter-element spacing /2 are deployed. The transmitting (TX) array is located beside one end of each receiving (RX) array. The virtual aperture of the array configuration in accordance with the third embodiment of the present disclosure is shown in FIG. 5(b).

[0082] Specifically, the location of the l.sup.th RX is given as follows.

[00027]$x_l^R=0,y_l^R=y_0+\frac{\mathrm{mod}\left(l,\frac{L_R}{2}\right)}{2},z_l^R=z_0+2\mathrm{floor}\left(\frac{l}{\frac{L_R}{2}}\right)$$\mathrm{for}l=0,1,.Math.,L_R-1.$

[0083] Specifically, the location of the m.sup.th TX is given as follows.

[00028]$x_m^T=0,y_m^T=-\frac{}{4}\left(\frac{L_R}{2}-1\right)-y_0,z_m^T=-\frac{7}{4}+\frac{m}{2}-z_0$$\mathrm{for}m=0,1,.Math.,M_T-1.$

[0084] A

[00029]$2M_{T}x\frac{L_R}{2}$

2-D uniform virtual receiving array (FIG. 5(b)) could be obtained via the spatial convolution of the transmitting (TX) array and the receiving (RX) array.

[0085] The location of the (m,l).sup.th virtual element for l=0, 1, . . . ,

[00030]$\frac{L_R}{2}-1,$

and m=0, 1, . . . , 2M.sub.T1 is given as follows.

[00031]$x_{m,l}^V=0,y_{m,l}^V=-\frac{}{4}\left(\frac{L_R}{2}-1\right)+\frac{l}{2},z_{m,l}^V=-\frac{7}{4}+\frac{m}{2}$

[0086] Assume that the bandwidth of the transmitted signal is B. The slant range resolution is

[00032]${}_R=\frac{c}{2B}.$

The horizontal length of the virtual aperture is

[00033]$L_h=\frac{L_R}{4}.$

The azimuth resolution is

[00034]${}_{\cos \sin }=\frac{}{L_h}=\frac{4}{L_R}.$

The vertical length of the virtual aperture is L.sub.v=M.sub.T. The resolution in elevation is

[00035]${}_{\sin }=\frac{}{L_v}=\frac{1}{M_T}.$

For sensing usage through, we could estimate (R, cos sin , sin q) of a potential target by using the 3-D spectral estimation algorithm, such as 3D FFT, 3D CLEAN, 3D MUSIC etc. Then, the Polar coordinate system can be transformed into Cartesian coordinate system by using the aforementioned relationship.

[0087] Given the above, the Azimuth and Elevation resolution of the resolution cell in accordance with the first, second, third and fourth embodiment of the present disclosure is collectively listed in Cartesian coordinate system as follows. The 2-D virtual receiving array can be used to provide 3-D sensing information.

TABLE-US-00001 Azimuth resolution Elevation resolution Embodiment (.sub.cossin) (.sub.sin) 1.sup.st [00036]$\frac{1}{L_R}$ the height information is obtained by using interferometry between 2.sup.nd [00037]$\frac{1}{L_R}$ two vertically displaced virtual apertures 3.sup.rd [00038]$\frac{2}{L_R}$ [00039]$\frac{1}{2}$ 4.sup.th [00040]$\frac{4}{L_R}$ [00041]$\frac{1}{4}$

[0088] In the first, second, third and fourth embodiment of the present disclosure, the transmitting (TX) antennas may be used to transmit orthogonal frequency-domain multiplexing (OFDM) signals. The transmitted OFDM signal at the m.sup.th TX is given as follows.

[00042]$s_T\left(t\right)=s_m\left(t\right)e^{j2f_{c}t}=\frac{1}{N}\underset{k=0}{\overset{N-1}{.Math.}}{S}_m\left(k\right)e^{j\left(2f_{c}f+k\right)t},$$m=0,1,.Math.,M_T-1\mathrm{and}-T_{\mathrm{cp}}t<T,$

where N is the number of subcarriers, f is the spacing between the subcarriers, S.sub.m(k) is the data at the k.sup.th subcarrier,

[00043]$s_m\left(t\right)=\frac{1}{N}{.Math.}_{k=0}^{N-1}{S}_m\left(k\right)e^{\mathrm{jk}\mathrm{ft}},$

f.sub.c is the carrier frequency,

[00044]$T=\frac{1}{f}$

is the effective duration of the OFDM symbol, T.sub.cp is the length of cyclic prefix (CP), and T+T.sub.cp is the total length of each OFDM symbol.

[0089] Property of s.sub.m(t) is given as follows.

[00045]$s_m\left(t\right)=s_m\left(t+T\right),\mathrm{for}-T_{\mathrm{cp}}t<0.$

[0090] The echo signal received by the l.sup.th RX can be expressed as follows.

[00046]$r_l\left(t\right)={.Math.}_{m=0}^{M_T-1}{\mathrm{as}}_T\left(t-{}_{\mathrm{ml}}\right)+v\left(t\right),$

where a is the reflection coefficient of the target and

[00047]${}_{\mathrm{ml}}=\frac{R_{\mathrm{ml}}}{c}$

is the time delay.

[0091] It is assumed that T.sub.ml<T.sub.cp and that the sampling rate is

[00048]$T_s=\frac{1}{Nf}.$

After demodulating the received echo signal to baseband, sampling and removing the CP for 0t<T, the preprocessed received echo signal is given as follows.

[00049]$z_l\left(n\right)={.Math.}_{m=0}^{M_T-1}{\mathrm{as}}_m\left({\mathrm{nT}}_s-{}_{\mathrm{ml}}\right)e^{-j2f_c{}_{\mathrm{ml}}}+v\left(n\right),n=0,1,.Math.,N-1.$

[0092] Then, taking the N-Point DFT to z.sub.l(n), it is given as follows.

[00050]$Z_l\left(k\right)=\underset{m=0}{\overset{M_T-1}{.Math.}}{\mathrm{aS}}_m\left(k\right)e^{-j2\mathrm{fk}{}_{\mathrm{ml}}}{e}^{-j2f_c{}_{\mathrm{ml}}}+V\left(k\right)$

[0093] In short, applying a phase rotation in the frequency domain is equivalent to applying a cyclic shift in the time domain. The frequency-domain phase rotation to TX is given as follows.

[00051]$S_{m^{}}^{*}\left(k\right)Z_l\left(k\right)=\underset{m=0}{\overset{M_T-1}{.Math.}}{\mathrm{aS}}_{m^{}}^{*}\left(k\right)S_m\left(k\right)e^{-j2\mathrm{fk}{}_{\mathrm{ml}}}{e}^{-j2f_c{}_{\mathrm{ml}}}+S_{m^{}}^{*}\left(k\right)V\left(k\right)={\mathrm{aS}}_{m^{}}^{*}\left(k\right)S_{m^{}}\left(k\right)e^{-j2\mathrm{fk}{}_{m^{}l}}{e}^{-j2f_c{}_{m^{}l}}+\underset{m=0,m{m}^{}}{\overset{M_T-1}{.Math.}}{\mathrm{aS}}_{m^{}}^{*}\left(k\right)S_m\left(k\right)e^{-j2\mathrm{fk}{}_{\mathrm{ml}}}{e}^{-j2f_c{}_{\mathrm{ml}}}+S_{m^{}}^{*}\left(k\right)V\left(k\right)$

where S*.sub.m(k) is the conjugate transpose of S.sub.m(k).

[0094] Let

[00052]$S_m=e^{j\frac{I_{m}2k}{M_T}+j{}_m}S\left(k\right),$

where I={I.sub.0, I.sub.1, I.sub.2, . . . , I.sub.M.sub.T-1} is a permutation of a set {0, 1, 2, . . . , M.sub.T1}, and .sub.m is a nominal phase at TX element m. For example, in the case of 4 TX, I={0, 1, 2, 3} can be {0, /2, , 3/2}. The TX-varying phase .sub.m can be used as a design variable to achieve desired frequency response at the specified communication direction. In the first, second, third and fourth embodiment of the present disclosure, M.sub.T=4, so the frequency-domain phase rotation to each TX is given as follows.

[00053]$S_0^{*}\left(k\right)Z_l\left(k\right)=\mathrm{aS}*\left(k\right)S\left(k\right)\left(e^{-j2f_c{}_{0l}}{e}^{-j2{\mathrm{fk}}_{0l}}+e^{-j2f_c{}_{1l}+j\left({}_1-{}_0\right)}{e}^{-j2k\left(f{}_{1l}+\frac{I_0-I_1}{4}\right)}+e^{-j2f_c{}_{2l}+j\left({}_2-{}_0\right)}{e}^{-j2k\left(f_{2l}+\frac{I_0-I_2}{4}\right)}+e^{-j2f_c{}_{3l}+j\left({}_3-{}_0\right)}{e}^{-j2k\left(f{}_{3l}+\frac{I_0-I_3}{4}\right)}\right)+e^{-j\frac{I_{0}2k}{M_T}-j{}_0}S*\left(k\right)V\left(k\right)$$S_1^{*}\left(k\right)Z_l\left(k\right)=\mathrm{aS}*\left(k\right)S\left(k\right)\left(e^{-j2f_c{}_{1l}}{e}^{-j2\mathrm{fk}{}_{1l}}+e^{-j2f_c{}_{0l}+j\left({}_0-{}_1\right)}{e}^{-j2k\left(f{}_{0l}+\frac{I_1-I_0}{4}\right)}+e^{-j2f_c{}_{2l}+j\left({}_2-{}_1\right)}{e}^{-j2k\left(f{}_{2l}+\frac{I_1-I_2}{4}\right)}+e^{-j2f_c{}_{3l}+j\left({}_3-{}_1\right)}{e}^{-j2k\left(f{}_{3l}+\frac{I_1-I_3}{4}\right)}\right)+e^{-j\frac{I_{1}2k}{M_T}-j{}_1}S*\left(k\right)V\left(k\right)$$S_2^{*}\left(k\right)Z_l\left(k\right)=\mathrm{aS}*\left(k\right)S\left(k\right)\left(e^{-j2f_c{}_{2l}}{e}^{-j2\mathrm{fk}{}_{2l}}+e^{-j2f_c{}_{0l}+j\left({}_0-{}_2\right)}{e}^{-j2k\left(f{}_{0l}+\frac{I_2-I_0}{4}\right)}+e^{-j2f_c{}_{1l}+j\left({}_1-{}_2\right)}{e}^{-j2k\left(f{}_{1l}+\frac{I_2-I_1}{4}\right)}+e^{-j2f_c{}_{3l}+j\left({}_3-{}_2\right)}{e}^{-j2k\left(f{}_{3l}+\frac{I_2-I_3}{4}\right)}\right)+e^{-j\frac{I_{2}2k}{M_T}-j{}_2}S*\left(k\right)V\left(k\right)$$S_3^{*}\left(k\right)Z_l\left(k\right)=\mathrm{aS}*\left(k\right)S\left(k\right)\left(e^{-j2f_c{}_{3l}}{e}^{-j2\mathrm{fk}{}_{3l}}+e^{-j2f_c{}_{0l}+j\left({}_0-{}_3\right)}{e}^{-j2k\left(f{}_{0l}+\frac{I_3-I_0}{4}\right)}+e^{-j2f_c{}_{1l}+j\left({}_1-{}_3\right)}{e}^{-j2k\left(f{}_{1l}+\frac{I_3-I_1}{4}\right)}+e^{-j2f_c{}_{2l}+j\left({}_2-{}_3\right)}{e}^{-j2k\left(f{}_{3l}+\frac{I_3-I_2}{4}\right)}\right)+e^{-j\frac{I_{3}2k}{M_T}-j{}_3}S*\left(k\right)V\left(k\right)$

[0095] For constant amplitude waveform (|S.sub.m(k)|=1), the frequency-domain phase rotation to each TX is given as follows.

[00054]$S_0^{*}\left(k\right)Z_l\left(k\right)=a\left(e^{-j2f_c{}_{0l}}{e}^{-j2\mathrm{fk}{}_{0l}}+e^{-j2f_c{}_{1l}+j\left({}_1-{}_0\right)}{e}^{-j2k\left(f{}_{1l}+\frac{I_0-I_1}{4}\right)}+e^{-j2f_c{}_{2l}+j\left({}_2-{}_0\right)}{e}^{-j2k\left(f{}_{2l}+\frac{I_0-I_2}{4}\right)}+e^{-j2f_c{}_{3l}+j\left({}_3-{}_0\right)}{e}^{-j2k\left(f{}_{3l}+\frac{I_o-I_3}{4}\right)}\right)+e^{-j\frac{I_{0}2k}{M_T}-j{}_0}S*\left(k\right)V\left(k\right)$$S_1^{*}\left(k\right)Z_l\left(k\right)=a\left(e^{-j2f_c{}_{1l}}{e}^{-j2\mathrm{fk}{}_{1l}}+e^{-j2f_c{}_{0l}+j\left({}_0-{}_1\right)}{e}^{-j2k\left(f{}_{0l}+\frac{I_1-I_0}{4}\right)}+e^{-j2f_c{}_{2l}+j\left({}_2-{}_1\right)}{e}^{-j2k\left(f{}_{2l}+\frac{I_1-I_2}{4}\right)}+e^{-j2f_c{}_{3l}+j\left({}_3-{}_1\right)}{e}^{-j2k\left(f{}_{3l}+\frac{I_1-I_3}{4}\right)}\right)+e^{-j\frac{I_{1}2k}{M_T}-j{}_1}S*\left(k\right)V\left(k\right)$

[00055]$S_2^{*}\left(k\right)Z_l\left(k\right)=a\left(e^{-j2f_c{}_{2l}}{e}^{-j2\mathrm{fk}{}_{2l}}+e^{-j2f_c{}_{0l}+j\left({}_0-{}_2\right)}{e}^{-j2k\left(f{}_{0l}+\frac{I_2-I_0}{4}\right)}+e^{-j2f_c{}_{1l}+j\left({}_1-{}_2\right)}{e}^{-j2k\left(f^{{}_{1l}}+\frac{I_2-I_1}{4}\right)}+e^{-j2f_c{}_{3l}+j\left({}_3-{}_2\right)}{e}^{-j2k\left(f{}_{3l}+\frac{I_2-I_3}{4}\right)}\right)+e^{-j\frac{I_{2}2k}{M_T}-j{}_2}S*\left(k\right)V\left(k\right)$$S_3^{*}\left(k\right)Z_l\left(k\right)=a\left(e^{-j2f_c{}_{3l}}{e}^{-j2\mathrm{fk}{}_{3l}}+e^{-j2f_c{}_{0l}+j\left({}_0-{}_3\right)}{e}^{-j2k\left(f{}_{0l}+\frac{I_3-I_0}{4}\right)}+e^{-j2f_c{}_{1l}+j\left({}_1-{}_3\right)}{e}^{-j2k\left(f{}_{1l}+\frac{I_3-I_1}{4}\right)}+e^{-j2f_c{}_{2l}+j\left({}_2-{}_3\right)}{e}^{-j2k\left(f{}_{3l}+\frac{I_3-I_2}{4}\right)}\right)+e^{-j\frac{I_{3}2k}{M_T}-j{}_3}S*\left(k\right)V\left(k\right)$

[0096] At the IFFT spectrum of S*.sub.0(k)Z.sub.l(k), i.e., {tilde over ()}.sub.0(t)=IFFT(S*.sub.0(k)Z.sub.l(k)), there are four peaks in the time domain. The peak locations are .sub.0l,

[00056]${}_{1l}+\frac{T}{4}\left(I_0-I_1\right),{}_{2l}+\frac{T}{4}\left(l_0-I_2\right),{}_{3l}+\frac{T}{4}\left(I_0-I_3\right).$

[0097] At the IFFT spectrum of S*.sub.1(k)Z.sub.l(k), i.e., {tilde over ()}.sub.1(t)=IFFT(S*.sub.1(k)Z.sub.l(k)), there are four peaks in the time domain. The peak locations are .sub.1l,

[00057]${}_{0l}+\frac{T}{4}\left(I_1-I_0\right),{}_{2l}+\frac{T}{4}\left(I_1-I_2\right),{}_{3l}+\frac{T}{4}\left(I_1-I_3\right).$

[0098] At the IFFT spectrum of S*.sub.2(k)Z.sub.l(k), i.e., {tilde over ()}.sub.2(t)=IFFT(S*.sub.2(k)Z.sub.l(k)), there are four peaks in the time domain. The peak locations are .sub.2l,

[00058]${}_{0l}+\frac{T}{4}\left(I_2-I_0\right),{}_{1l}+\frac{T}{4}\left(I_2-I_1\right),{}_{3l}+\frac{T}{4}\left(I_2-I_3\right).$

[0099] At the IFFT spectrum of S*.sub.3(k)Z.sub.l(k), i.e., {tilde over ()}.sub.3(t)=IFFT(S*.sub.3(k)Z.sub.l(k)), there are four peaks in the time domain. The peak locations are .sub.3l,

[00059]${}_{0l}+\frac{T}{4}\left(I_3-I_0\right),{}_{1l}+\frac{T}{4}\left(I_3-I_1\right),{}_{2l}+\frac{T}{4}\left(I_3-I_2\right).$

[0100] Let

[00060]${\stackrel{}{s}}_m\left(t\right)=\{\begin{array}{c}{\stackrel{}{\stackrel{}{s}}}_m\left(t\right),t\left[0,\frac{T}{4}\right]\\ 0,t\left[\frac{T}{4},T\right]\end{array}.$

The echo signals from different TXs could be separated at the receiver. .sub.m(t) could be used for further azimuth compression in radar imaging.

[0101] In addition, the payload of the frequency-domain phase rotation to each TX is given as follows.

[00061]$\frac{S_0^{*}\left(k\right)Z_l\left(k\right)}{{.Math.S_0\left(k\right).Math.}^2}=a\left(e^{-j2f_c{}_{0l}}{e}^{-j2fk{}_{0l}}+e^{-j2f_c{}_{1l}+j\left({}_1-{}_0\right)}{e}^{-j2k\left(f{}_{1l}+\frac{I_0-I_1}{4}\right)}+e^{-j2f_c{}_{2l}+j\left({}_2-{}_0\right)}{e}^{-j2k\left(f{}_{2l}+\frac{I_0-I_2}{4}\right)}+e^{-j2f_c{}_{3l}+j\left({}_3-{}_0\right)}{e}^{-j2k\left(f{}_{3l}+\frac{I_0-I_3}{4}\right)}\right)+\frac{e^{-j\frac{I_{0}2k}{M_T}-j{}_0}S*\left(k\right)V\left(k\right)}{{.Math.S_1\left(k\right).Math.}^2}$$\frac{S_1^{*}\left(k\right)Z_l\left(k\right)}{{.Math.S_1\left(k\right).Math.}^2}=a\left(e^{-j2f_c{}_{1l}}{e}^{-j2fk{}_{1l}}+e^{-j2f_c{}_{0l}+j\left({}_0-{}_1\right)}{e}^{-j2k\left(f{}_{ol}+\frac{I_1-I_0}{4}\right)}+e^{-j2f_c{}_{2l}+j\left({}_2-{}_1\right)}{e}^{-j2k\left(f{}_{2l}+\frac{I_1-I_2}{4}\right)}+e^{-j2f_c{}_{3l}+j\left({}_3-{}_1\right)}{e}^{-j2k\left(f{}_{3l}+\frac{I_1-I_3}{4}\right)}\right)+\frac{e^{-j\frac{I_{1}2k}{M_T}-j{}_1}S*\left(k\right)V\left(k\right)}{{.Math.S_2\left(k\right).Math.}^2}$$\frac{S_2^{*}\left(k\right)Z_l\left(k\right)}{{.Math.S_2\left(k\right).Math.}^2}=a\left(e^{-j2f_c{}_{2l}}{e}^{-j2fk{}_{2l}}+e^{-j2f_c{}_{0l}+j\left({}_0-{}_2\right)}{e}^{-j2k\left(f{}_{0l}+\frac{I_2-I_0}{4}\right)}+e^{-j2f_c{}_{1l}+j\left({}_1-{}_2\right)}{e}^{-j2k\left(f{}_{1l}+\frac{I_2-I_1}{4}\right)}+e^{-j2f_c{}_{3l}+j\left({}_3-{}_2\right)}{e}^{-j2k\left(f{}_{3l}+\frac{I_2-I_3}{4}\right)}\right)+\frac{e^{-j\frac{I_{2}2k}{M_T}-j{}_2}S*\left(k\right)V\left(k\right)}{{.Math.S_3\left(k\right).Math.}^2}$$\frac{S_3^{*}\left(k\right)Z_l\left(k\right)}{{.Math.S_3\left(k\right).Math.}^2}=a\left(e^{-j2f_c{}_{3l}}{e}^{-j2fk{}_{3l}}+e^{-j2f_c{}_{0l}+j\left({}_0-{}_3\right)}{e}^{-j2k\left(f{}_{ol}+\frac{I_3-I_0}{4}\right)}+e^{-j2f_c{}_{1l}+j\left({}_1-{}_3\right)}{e}^{-j2k\left(f{}_{1l}+\frac{I_3-I_1}{4}\right)}+e^{-j2f_c{}_{2l}+j\left({}_2-{}_3\right)}{e}^{-j2k\left(f{}_{3l}+\frac{I_3-I_2}{4}\right)}\right)+\frac{e^{-j\frac{I_{3}2k}{M_T}-j{}_3}S*\left(k\right)V\left(k\right)}{{.Math.S_4\left(k\right).Math.}^2}$

[0102] At the IFFT spectrum of S*.sub.0(k)Z.sub.l(k)/|S.sub.0(k)|.sup.2, i.e., {tilde over ()}.sub.0(t)=IFFT(S*.sub.0(k)Z.sub.l(k)/|S.sub.0(k)|.sup.2), there are four peaks in the time domain. The peak locations are .sub.0l,

[00062]${}_{1l}+\frac{T}{4}\left(I_0-I_1\right),{}_{2l}+\frac{T}{4}\left(I_0-I_2\right),{}_{3l}+\frac{T}{4}\left(I_0-I_3\right).$

[0103] At the IFFT spectrum of S*.sub.1(k)Z.sub.l(k)/|S.sub.1(k)|.sup.2, i.e., {tilde over ()}.sub.1(t)=IFFT(S*.sub.1(k)Z.sub.l(k)/|S.sub.1(k)|.sup.2), there are four peaks in the time domain. The peak locations are .sub.1l,

[00063]${}_{0l}+\frac{T}{4}\left(I_1-I_0\right),{}_{2l}+\frac{T}{4}\left(I_1-I_2\right),{}_{3l}+\frac{T}{4}\left(I_1-I_3\right).$