System and method for joint radar-sensing and communication waveform utilizing unique word OFDM (UW-OFDM)

Abstract

A system and method utilizing a novel waveform structure based on unique word (UW)—orthogonal frequency division multiplexing (OFDM) is proposed for the applications of joint radar-sensing and communication (JRC). A predetermined chirp sequence is used as the UW in the waveform. The predetermined chirp sequence is used to perform radar functionality, which also increases power efficiency of linear power amplifier that is critical for radar applications.

Claims

1. A method for assembling unique word (UW)— orthogonal frequency division multiplexing (OFDM) data symbols for use in joint radar-sensing and communication (JRC), the method comprising: generating OFDM time domain symbols having N.sub.u zeroes at an output of an N-point inverse fast Fourier transformation (IFFT) block of a transmitter, wherein N.sub.u is an integer greater than one; and adding a predetermined chirp sequence in the N.sub.u zeroes to assemble UW-OFDM symbols having a chirp sequence, wherein the UW is the predetermined chirp sequence for joint radar-sensing and communication (JRC).

2. The method of claim 1, wherein the predetermined chirp sequence forms a tail of each of the OFDM time domain symbols.

3. The method of claim 1, wherein generating the OFDM time domain symbols having N.sub.u zeroes at the output of the N-point inverse fast Fourier transformation (IFFT) block further comprises: providing OFDM frequency domain symbols to a code generator matrix to introduce redundancy into the OFDM frequency domain symbols; and modulating the OFDM frequency domain symbols having redundancy on a plurality of subcarriers using the IFFT block to generate the OFDM time domain symbols having N.sub.u zeroes.

4. The method of claim 3, wherein the redundancy introduced into the OFDM frequency domain by the code generator matrix is distributed over the plurality of subcarriers.

5. The method of claim 1, wherein the JRC is mono-static JRC.

6. The method of claim 1, wherein the JRC is bi-static JRC.

7. The method of claim 1, further comprising: transmitting, by the transmitter, the UW-OFDM symbols having a chirp sequence over a channel; receiving the UW-OFDM symbols having a chirp sequence at a receiver; and decoding the UW-OFDM symbols having a chirp sequence using a best linear unbiased estimator (BLUE) that is matched to the code generator matrix.

8. A method for assembling unique word (UW)— orthogonal frequency division multiplexing (OFDM) data symbols for use in joint radar-sensing and communication (JRC), the method comprising: providing OFDM frequency domain symbols to a code generator matrix of a transmitter to introduce redundancy into the OFDM frequency domain symbols; modulating the OFDM frequency domain symbols having redundancy on a plurality of subcarriers using the IFFT block to generate OFDM time domain symbols having N.sub.u zeroes, wherein N.sub.u is an integer greater than one; and adding a predetermined chirp sequence in the N.sub.u zeroes to assemble UW-OFDM symbols having a chirp sequence, wherein the UW is the predetermined chirp sequence for joint radar-sensing and communication (JRC).

9. The method of claim 8, further comprising: transmitting, by the transmitter, the UW-OFDM symbols having a chirp sequence over a channel; receiving the UW-OFDM symbols having a chirp sequence at a receiver; and decoding the UW-OFDM symbols having a chirp sequence using a best linear unbiased estimator (BLUE) at the receiver that is matched to the code generator matrix.

10. A transmitter for assembling unique word (UW)— orthogonal frequency division multiplexing (OFDM) data symbols for use in joint radar-sensing and communication (JRC), the transmitter comprising: an N-point inverse fast Fourier transformation (IFFT) block to generate OFDM time domain symbols having N.sub.u zeroes at an output, wherein N.sub.u is an integer greater than one; and the transmitter to add a predetermined chirp sequence in the N.sub.u zeroes to assemble UW-OFDM symbols having a chirp sequence, wherein the UW is the predetermined chirp sequence for joint radar-sensing and communication (JRC).

11. The transmitter of claim 10, wherein the predetermined chirp sequence forms a tail of each of the OFDM time domain symbols.

12. The transmitter of claim 10, wherein the N-point inverse fast Fourier transformation (IFFT) block further is further configured to: provide OFDM frequency domain symbols to a code generator matrix to introduce redundancy into the OFDM frequency domain symbols; and module the OFDM frequency domain symbols having redundancy on a plurality of subcarriers using the IFFT block to generate the OFDM time domain symbols having N.sub.u zeroes.

13. The transmitter of claim 12, wherein the redundancy introduced into the OFDM frequency domain by the code generator matrix is distributed over the plurality of subcarriers.

14. The transmitter of claim 10, wherein the JRC is mono-static JRC.

15. The transmitter of claim 10, wherein the JRC is bi-static JRC.

16. The transmitter of claim 10, further comprising: a receiver configured to receive the UW-OFDM symbols having a chirp sequence transmitted by the transmitter over a channel; and the receiver configured to decode the UW-OFDM symbols having a chirp sequence using a best linear unbiased estimator (BLUE) that is matched to the code generator matrix.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) Many aspects of the present disclosure can be better understood with reference to the following drawings. The components in the drawings are not necessarily to scale, emphasis instead being placed upon clearly illustrating the principles of the present disclosure. Moreover, in the drawings, like reference numerals designate corresponding parts throughout the several views.

(2) FIG. 1 illustrates an exemplary use case requiring both radar-sensing and communication functionality, in accordance with an embodiment of the present invention.

(3) FIG. 2A illustrates a transmit frame design of an exemplary CP-OFDM waveform.

(4) FIG. 2B illustrates a transmit frame design of an exemplary UW-OFDM waveform.

(5) FIG. 3 illustrates a time-frequency representation of an UW-OFDM with chirp, in accordance with an embodiment of the present invention.

(6) FIG. 4 illustrates a schematic of energy loss in linear power amplifier (PA), in accordance with an embodiment of the present invention.

(7) FIG. 5A illustrates the efficient use of PA for UW-OFDM time-power representation, in accordance with an embodiment of the present invention.

(8) FIG. 5B illustrates the efficient use of PA for CP-OFDM time-power representation.

(9) FIG. 6A illustrates the power spectral density of the UW-OFDM with chirp, a CP-OFDM and FMCW for the whole transmission band, in accordance with an embodiment of the present invention.

(10) FIG. 6B illustrates the power spectral density of the UW-OFDM with chirp, a CP-OFDM and FMCW for the guard bands, in accordance with an embodiment of the present invention.

(11) FIG. 7A illustrates radar-sensing performance evaluation of UW-OFDM with chirp waveform for a mono-static system, in accordance with an embodiment of the present invention.

(12) FIG. 7B illustrates radar-sensing performance evaluation of UW-OFDM with chirp waveform for a bi-static system, in accordance with an embodiment of the present invention.

DETAILED DESCRIPTION OF THE INVENTION

(13) Joint radar-communication (JRC) systems have been considered as enablers for 5G, 6G, and future technologies. Furthermore, JRC systems are vital in realizing other emerging technologies, such as vehicle-to-vehicle (V2V) communication and sensing for autonomous vehicles.

(14) In various embodiments, the present invention provides a novel waveform structure based on unique word (UW)—orthogonal frequency division multiplexing (OFDM) for the application of joint radar-sensing and communication (JRC). As a UW in the waveform, the chirp sequence is used to perform radar functionality, which also increases power efficiency of linear power amplifier. The proposed waveform has been shown to perform well in both mono and bi-static systems.

(15) In the following description, lower-case bold face variables (a, b, . . . ) indicate vectors and upper-case bold face variables (A, B, . . . ) indicate matrices. To distinguish between time and frequency domain variables, a tilde symbol is used to specify the frequency domain vectors and matrices (ã, Ã), respectively. Further, C is used to designate the set of complex numbers, - to denote ceil operation, I.sub.N to denote the N×N identity matrix, 0 to denote zero matrix with appropriate size, (.Math.).sup.T to denote transpose, (.Math.) to denote real part of the complex value, (.Math.).sup.H to denote conjugate transpose, E(.Math.) to denote expectation. The null space of A is defined as (A){N.sub.A ∈.sup.n×k:AN.sub.A=0}.

(16) The V2V scenario illustrated in FIG. 1 is considered in the following description, however, this is not intended to be limiting and the proposed scheme is also applicable to a variety of different use cases. The proposed waveform structure may perform both mono and bi-static radar function in addition to providing communication.

(17) As shown in FIG. 1, a transmitter 120, a receiver 125 and several targets 100, 105, 110, 115 are considered in this V2V scenario. As shown in FIG. 1, the transmitter 120 comprises an N-point inverse fast Fourier transformation (IFFT) block 122.

(18) Let c ∈ .sup.N.sup.u.sup.×1 be a predefined chirp sequence, which is also referred to as a “unique word”. It is defined as follows:

(19) $\begin{array}{cc}c={\left\{c_k\right\}}_{k=1}^{N_u}=\exp \left(\frac{j\pi \beta }{\tau }{\left(\frac{k}{F_s}\right)}^2\right)& \left(1\right)\end{array}$

(20) where F.sub.s, β, and τ denote the sample rate, the allocated bandwidth and the time duration of the chirp signal, respectively. As in conventional OFDM, the complex data symbols, modulated via quadrature amplitude modulation (QAM) drawn from a complex symbol alphabet , are denoted by the vector {tilde over (d)} ∈ .sup.N.sup.u.sup.×1.

(21) The UW-OFDM signal is constructed in two steps. In the first step, N.sub.u zeroes are generated in the time domain at the output of N-point inverse fast Fourier transformation (IFFT) block. The generator matrix G ∈.sup.(N.sup.d.sup.+N.sup.u.sup.)×N.sup.d is created to allocate N.sub.u redundant subcarriers to insert N.sub.u zeroes at the last N.sub.u samples of the one OFDM symbol. Compared to the systematic coded UW-OFDM implementation known in the art, the original data symbols {tilde over (d)}, do not appear directly on the subcarriers after being multiplied with the generator matrix G. To minimize the error covariance, the code generator matrix G is selected such that the error covariance of the best linear unbiased estimator (BLUE) at the receiver is minimized. This is satisfied when G.sup.HG=I. Moreover, to decrease OOB emission, the N.sub.u zero subcarriers are located at the band edges of the DC subcarrier. The final data vector {tilde over (x)} in the frequency domain is:
{tilde over (x)}=BG{tilde over (d)},  (2)

(22) where B ∈ .sup.N×(N.sup.d.sup.+N.sup.u.sup.) maps the usual zero subcarriers to reduce OOB emission. It is similar to identify matrix consisting of zero-rows at the positions of the zero subcarriers.

(23) The UW forms the tail of each OFDM time domain symbol vector using the redundant subcarriers. Hence, an OFDM time domain symbol vector consists of two parts and is of the form x=[x.sub.d.sup.Tx.sub.u.sup.T].sup.T ∈ .sup.N×1. Here, only x.sub.d ∈.sup.(N−N.sup.u.sup.)×1 is random and affected by the data. As a result of the first step, the OFDM symbol time-domain data vector x′ ∈ .sup.N×1 is constructed as:

(24) $\begin{array}{cc}{x}^{\prime }=F_N^H\mathrm{BG}\tilde{d}=\left[\begin{array}{c}{x}_d\\ 0\end{array}\right],& \left(3\right)\end{array}$

(25) where F.sub.N denotes the length-N-FFT matrix with elements

(26) ${\left[F_N\right]}_{kl}=e^{-j\frac{2\pi }{N}kl}\mathrm{for}k,l=0,1,.Math.,N-1.$
The problem of the high energy requirement on redundant subcarriers is solved by implementing non-systematic UW-OFDM. In this scheme, the energy on redundant subcarriers is spread over all subcarriers by exploiting the code generator matrix, G. Define Q ∈ .sup.N×(N.sup.d.sup.+N.sup.u.sup.) matrix as:

(27) $\begin{array}{cc}{F}_N^{H}B=Q=\left[\begin{array}{c}{Q}_1\\ Q_2\end{array}\right],& \left(4\right)\end{array}$

(28) where Q.sub.1 ∈ .sup.(N−N.sup.u.sup.)×(N.sup.u.sup.+N.sub.d) and Q.sub.2 ∈.sup.N.sup.u.sup.×(N.sup.u.sup.+N.sup.d.sup.). Then, the generator is decomposed into two different matrices:
G=N.sub.Q.sub.2C,  (5)

(29) where N.sub.Q.sub.2=(.sub.2) ∈ .sup.(N.sup.u.sup.+N.sup.d.sup.)×N.sup.d contains orthonormal null space vectors of Q.sub.2. The matrix C ∈ .sup.N.sup.d.sup.×N.sup.d is restricted to the case where C.sup.HC=I, as this corresponds to the minimization of the BLUE estimator. Similarly, the UW contribution to the time domain OFDM symbol can be written as vector x.sub.u′∈.sup.N×1, which is:

(30) $\begin{array}{cc}{x}_u^{\prime }=\left[\begin{array}{c}0\\ x_u\end{array}\right]=F_N^H\mathrm{BJ}{\tilde{x}}_u,& \left(6\right)\end{array}$

(31) where J is a matrix similar to generator matrix G, which should be selected to generate the zeroes in the first N−N.sub.u rows of the x at the output of the IFFT. The matrix J is selected as follows:
J=(Q.sub.1)  (7)

(32) Define the matrix T=[T.sub.1.sup.TT.sub.2.sup.T]=F.sub.N.sup.HBJ to map frequency domain vector {tilde over (x)}.sub.u into time domain vector x.sub.u′. The vector {tilde over (x)}.sub.u is selected as:
{tilde over (x)}.sub.u=T.sub.2.sup.H(T.sub.2T.sub.2.sup.H).sup.−1c=T.sub.2.sup.†c  (8)

(33) Even if pseudo-inverse operation affects the chirp signal generated in the time domain, as shown in seen in FIG. 5A, the linearly increased frequency pattern is not destroyed, which can be seen in FIG. 3. The energy of the UW is increased to use the linear PA efficiently. The power scale is arranged in a way that the power of the UW signal's sample does not pass the peak energy of the other part of the IFFT output, which depends on the data symbols. The power scale of the unique word can be represented as follows:
x.sub.u″=σx.sub.u′  (9a)

(34) and

(35) $\begin{array}{cc}\sigma =\sqrt{\frac{\max \left\{{.Math.x^{\prime }.Math.}^2\right\}}{\max \left\{{.Math.x_u^{\prime }.Math.}^2\right\}}}& \left(9b\right)\end{array}$

(36) The generated UW-OFDM signal is depicted in FIG. 5A with comparison of CP-OFDM under the same linear PA input supply level shown in FIG. 5B. Finally, the transmitted signal x=x′+x.sub.u″ is upconverted to the desired radio frequency (RF) band.

(37) The Doppler shift and flight time for the paths reflecting from the targets 100, 105, 110, 115 are as shown in FIG. 1 and are assumed to be fixed over a coherent transmission time. Under the linear time-varying channel, the received passband signal is represented as:

(38) $\begin{array}{cc}r\left(t\right)=\underset{p=1}{\overset{P}{.Math.}}{\alpha }_p\mathrm{.Math.}\left\{x\left(t-{\tau }_p\right)e^{j2\pi \left(f_c+{\psi }_p\right)\left(t-{\tau }_p\right)+j\overline{\theta }+j{\vartheta }_p}\right\}+n\left(t\right)& \left(10\right)\end{array}$

(39) where α.sub.p, τ.sub.p and ϑ.sub.p are the attenuation factor depending on nonfluctuating radar cross section (RCS), time delay related with the distance between the transmitter 120 to target plus target to the receiver 125 or two-way propagation distance (mono or bi-static range) and phase error, respectively. The notation ψ.sub.p is the Doppler frequency associated with the pth path depending on relative speed v.sub.p. The number P indicates the number of radar targets; in other words, the number of specular scatterers in the environment. Also, n(t)˜(0, σ.sup.2) denotes the additive white Gaussian noise (AWGN). The attenuation factor α.sub.p is proportional to the large-scale path-loss. Having the path distance d as propagation distance, the path-loss G is:

(40) $\begin{array}{cc}G=\frac{G_{TX}{G}_{RX}{\lambda }^2}{{\left(4\pi \right)}^2{d}^{PL}}& \left(11\right)\end{array}$

(41) where PL is the path-loss exponent, λ is the wavelength, G.sub.TX and G.sub.RX are the transmit and receive antenna gain, respectively.

(42) The doubly dispersive channel effect in the receiver after sampling at the rate F.sub.s, can be represented as finite impulse response (FIR) filter:

(43) $\begin{array}{cc}r\left[n\right]=\underset{p=1}{\overset{P}{.Math.}}h\left[n,.Math.{\tau }_p/F_s.Math.\right]x\left[n-.Math.{\tau }_p/F_s.Math.\right]+w\left[n\right]& \left(12\right)\end{array}$

(44) where h[n,τ.sub.p/F.sub.s] denotes the channel response of τ.sub.p/F.sub.s samples delayed path at the nth time instant and w[n] is the sampled noise. Based on FIR property of the channel, the received signal can be written in the matrix block representation as:
r=Hx+w  (13)

(45) H is the (N×N) channel matrix representing the convolute operation. For all p channel paths, the matrix H is defined as:

(46) 0$\begin{array}{cc}{H}_{nm}=\{\begin{array}{cc}h\left[n,.Math.{\tau }_p/F_s.Math.\right]& \mathrm{if}n-m=.Math.{\tau }_p/F_s.Math.\\ 0& \mathrm{if}n-m\ne .Math.{\tau }_p/F_s.Math.\end{array}& \left(14\right)\end{array}$

(47) The following discussion explains the radar-sensing processing for both mono-static and bi-static system architecture using the novel UW-OFDM with chirp sequence, in accordance with the present invention.

(48) Since the transmitted symbols and frame design are known and synchronized in mono-static radar operation, the whole OFDM symbol can be used to estimate range and Doppler shift. In conventional CP-OFDM, periodogram based estimation is used by removing the CP parts of the whole received OFDM signal. Periodogram based estimation is also used in the proposed UW-OFDM with chirp sequence without removing any part of it. The matrix

(49) $\begin{array}{cc}{K}_{\mathrm{TX}}=\left(\begin{array}{cccc}{k}_{1,1}& k_{1,2}& .Math.& k_{1,N_d+N_u}\\ k_{2,1}& k_{2,2}& .Math.& k_{2,N_d+N_u}\\ .Math.& .Math.& \ddots & .Math.\\ k_{M,1}& k_{M,2}& .Math.& k_{M,N_d+N_u}\end{array}\right)& \left(15\right)\end{array}$

(50) where k.sub.m,n denotes the complex quantity located on the nth OFDM subcarrier of mth UW-OFDM symbols. After receiving the signal affected by the channel, the matrix K.sub.RX denotes the values of complex symbols located on the same indices with K.sub.TX. K.sub.RX contains the effects of delays and Doppler shifts due to speed and range of objects in the environment. Let N.sub.k be the total filled subcarriers N.sub.k=N.sub.d+N.sub.u. The modulated complex symbol determined at the transmitter are removed by element-wise division as follows:

(51) $\begin{array}{cc}{K}_{m,n}=\frac{{\left(K_{RX}\right)}_{m,n}}{{\left(K_{TX}\right)}_{m,n}}& \left(16\right)\end{array}$

(52) Then, this matrix is utilized to perform periodogram based radar processing. The output power of the periodogram at the mth Doppler and the nth bin is:

(53) $\begin{array}{cc}P\left(m,n\right)=\frac{1}{M{N}_k}{.Math.\underset{k=1}{\overset{N_k-1}{.Math.}}\left(\overbrace{\underset{l=1}{\overset{M-1}{.Math.}}{\left(K\right)}_{m,n}{e}^{-j2\pi \frac{lm}{M}}}\right)e^{-j2\pi \frac{kn}{N_k}}.Math.}^2& \left(17\right)\end{array}$

(54) Sinusoids in K related to object's distance and velocity lead to peaks in P(m,n). Then, certain distance and velocity values can be found from related range and Doppler bin value of peaks.

(55) In bi-static radar processing, the radar processing is done with the chirp sequence in the time domain. Down-converting the received passband signal r(t) into baseband and sampling with the frequency of F.sub.s=NΔf, the discrete-time signal becomes:

(56) $\begin{array}{cc}y\left[n\right]=\underset{p=1}{\overset{P}{.Math.}}{h}_{p}x\left(n/F_s-{\tau }_p\right)e^{j2\pi n{\psi }_p/F_s}+w\left[n\right],n\in {\mathbb{N}}^{+}& \left(18a\right)\end{array}$

(57) and
h.sub.p=α.sub.pe.sup.−j2π(f.sup.c.sup.+ψ.sup.p.sup.)τ.sup.p.sup.+jθ+j+ϑ.sup.p  (18b)

(58) where h.sub.p is the complex channel gain of target p. Then, the stretch processing is employed in the discrete domain for the superimposed signal to get delays and Doppler shifts estimations. The processed signal in one chirp time interval can be written as:
y[n′]=y[n′]×e.sup.−jπ(n′/F.sup.s.sup.2.sup./τ,n′=1,2, . . . ,τF.sub.s  (19)

(59) and the de-chirping process is repeated for each chirp time interval. Fast-time/slow-time coherent processing interval (CPI) matrix is formed as previously known. However, it is done with the time domain samples. Fast time samples (range bins) are obtained at the rate of F.sub.s from the points on each chirp. Slow-time samples (Doppler bins) are taken from the points on every chirp at the same range bins. Then, periodogram-based estimation method is utilized, yielding peaks at the intersection of τ.sub.p and ψ.sub.p for each pth target. The threshold to find peak values is determined after several Monte-Carlo simulations.

(60) Estimation of the complex attenuation factor h.sub.p for every pth scatterer (target) can be done in the chirp with the least-square estimation. Besides the estimation of delays τ.sub.p and Doppler shifts ψ.sub.p, estimation of the matrix h.sub.p completes the process to recreate the channel matrix H with some estimation errors. This channel estimation in bi-static radar can be used to demodulate the communication symbols, which is well known in the art.

(61) In the following discussion, the receiver scheme of the proposed transmit frame for communication operations is investigated. Since the receiver can perform radar-sensing functions, the knowledge obtained from the radar process can be leveraged for the data estimation process to improve the performance. After the FFT and subcarrier de-mapping process of the signal, the received signal can be written as:
{tilde over (y)}=B.sup.TF.sub.NHF.sub.N.sup.HB(G{tilde over (d)}+σJ{tilde over (x)}.sub.u)+B.sup.TF.sub.Nw  (20)

(62) If there is no Doppler shift, the matrix F.sub.NHF.sub.N.sup.−1 is diagonal and contains the sample channel frequency response on its main diagonal. Let the matrix {tilde over (H)}=B.sup.TF.sub.NHF.sub.N.sup.−1B with {tilde over (H)} ∈ .sup.(N.sup.d.sup.+N.sup.u.sup.)×(N.sup.d.sup.+N.sup.u.sup.) be a down-sized version of the latter removing the indices corresponding to the guard bands.

(63) Here, the communication symbols can be decoded using the estimated channel in the case of bi-static radar scenario. Firstly, the chirp sequence is removed from the total received signal in the frequency domain by using estimate channel matrix Ĥ as follows:
{tilde over (y)}′={tilde over (y)}−σĤJ{tilde over (x)}.sub.u={tilde over (H)}G{tilde over (d)}+{tilde over (v)}  (21)

(64) where {tilde over (v)} includes both residual error due to successive interference cancellation (SIC) under imperfect channel estimation and noise vector B.sup.TF.sub.Nw.

(65) The data estimation is obtained by BLUE estimator using Gauss-Markov theorem as follows. The estimated data symbols {tilde over (d)}′ are evaluated as follows:
{tilde over (d)}′=(G.sup.HH.sup.HC.sup.−1HG).sup.−1G.sup.HH.sup.HC.sup.−1{tilde over (y)}  (22)

(66) where the matrix C denotes the covariance matrix E[{tilde over (v)}{tilde over (v)}.sup.H]. In the case of perfect channel estimation, the covariance matrix is C=(N.sub.d+N.sub.u)σ.sub.n.sup.2I, then the estimated data symbols are denoted as follows:
{tilde over (d)}′=E.sub.BLUE=(G.sup.HH.sup.HHG).sup.−1G.sup.HH.sup.H{tilde over (y)}  (23)

(67) where the equalizer matrix E.sub.BLUE is the pseudo-inverse of the matrix HG.

(68) The BER performance of the non-systematic UW-OFDM is numerically analyzed under the assumption of imperfect channel estimation. Here, it is shown that BER performance of UW-OFDM depends on the generator matrix G and outperforms the conventional CP-OFDM due to frequency diversity introduced by spreading of data symbols with the generator matrix G.

(69) In the following discussion, the proposed scheme of the present invention is analyzed regarding its radar performance in the case of both mono-static and bi-static scenarios, OOB emission and efficient power distribution in the time-domain, considering high peak-to-average power ratio (PAPR) of the OFDM signal. Simulation parameters depending on radar and communication requirements are shown in Table I. It is assumed that the maximum delay caused by targets is smaller than the UW length of each OFDM symbol, where UW length is ⅛ of the whole OFDM symbol. This UW to OFDM ratio is in accordance with the conventional CP-OFDM.

(70) TABLE-US-00001 TABLE I Simulation Parameters Parameter Value Carrier frequency (f.sub.c) 60 GHz Bandwidth (β) 100 MHz Sample Rate (F.sub.s) 122.88 MHz Chirp duration (τ) 2.08 μs Subcarrier spacing (Δf) 60 kHz Number of FFT (N) 2048 Number of allocated subcarriers 1691 Number of guard subcarriers  101 CP ratio 1/8

(71) As shown in FIG. 6A, the proposed UW-OFDM with chirp waveform 600 has around 1 dB less OOBs emissions than CP-OFDM 605 and has much lower OOB emissions than the FMCW waveform 610. The energy in the redundant subcarriers is distributed with non-systematic UW generation, showing a smoother profile. FIG. 6A illustrates the entire transmission band, which FIG. 6B illustrates the guard bands.

(72) As shown in FIG. 1, the channel includes 4 targets 100, 105, 110, 115 for mono-static operation, with one of the targets 115 blocking the communication signal. The power delay profile (PDP) of the channel is determined as an exponentially decaying function and the amplitude of each tap follows the Raleigh distribution.

(73) FIG. 7A and FIG. 7B illustrate the radar-sensing performance when the noise power is fixed. FIG. 7A illustrates the radar-sensing performance evaluation of the UW-OFDM with chirp waveform under mono-static conditions. FIG. 7A illustrates the radar-sensing performance evaluation of the UW-OFDM with chirp waveform under bi-static conditions.

(74) The signal power changes accordingly by assuming the usage of constant power supply linear PA, as visualized in FIG. 4. Additionally, as shown in a comparison of FIG. 5A and FIG. 5B, which illustrate the efficient use of linear PA, it can be seen that with the proposed UW-OFDM with chirp waveform (FIG. 5A) less energy is dissipated as heat, as compared to the CP-OFDM waveform (FIG. 5B). Velocity and range of targets for both mono-static and bi-static systems can be estimated with a proper threshold level. In the bi-static radar case, after evaluating the complex attenuation factor h.sub.p denoted in (18b), the estimation of channel matrix Ĥ can be created by using the obtained values of Doppler shifts and delays, which is done previously via chirp waveform in the UW part. Using Ĥ, the communication symbols can be demodulated.

(75) The advantages of using UW-OFDM in JRC systems over CP-OFDW can be itemized as follows: (1) No need for CP removal in periodogram based radar processing, which increases maximum resolvable velocity; (2) Less OOBs emission; (3) Improved power efficiency by using chirp as UW; (4) Feasible for both mono-static and bi-static radar.

(76) Accordingly, the present invention provides a novel joint radar-sensing and communication (JRC) transmission-reception frame using UW-OFDM with chirp sequence. In various embodiments, the chirp sequence is used as UW to perform radar functionality in mono-static and bi-static radar cases. The proposed structure is compared with the conventional CP-OFDM in terms of power characteristics and radar-sensing functionality and shown to perform better. Moreover, since it provides inherent diversity that enhances BER performance, the proposed scheme is promising for future applications.

(77) The present invention may be embodied on various computing platforms that perform actions responsive to software-based instructions and most particularly on touchscreen portable devices. The following provides an antecedent basis for the information technology that may be utilized to enable the invention.

(78) The computer readable medium described in the claims below may be a computer readable signal medium or a computer readable storage medium. A computer readable storage medium may be, for example, but not limited to, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any suitable combination of the foregoing. More specific examples (a non-exhaustive list) of the computer readable storage medium would include the following: an electrical connection having one or more wires, a portable computer diskette, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or Flash memory), an optical fiber, a portable compact disc read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the foregoing. In the context of this document, a computer readable storage medium may be any non-transitory, tangible medium that can contain, or store a program for use by or in connection with an instruction execution system, apparatus, or device.

(79) A computer readable signal medium may include a propagated data signal with computer readable program code embodied therein, for example, in baseband or as part of a carrier wave. Such a propagated signal may take any of a variety of forms, including, but not limited to, electro-magnetic, optical, or any suitable combination thereof. A computer readable signal medium may be any computer readable medium that is not a computer readable storage medium and that can communicate, propagate, or transport a program for use by or in connection with an instruction execution system, apparatus, or device.

(80) However, as indicated above, due to circuit statutory subject matter restrictions, claims to this invention as a software product are those embodied in a non-transitory software medium such as a computer hard drive, flash-RAM, optical disk or the like.

(81) Program code embodied on a computer readable medium may be transmitted using any appropriate medium, including but not limited to wireless, wire-line, optical fiber cable, radio frequency, etc., or any suitable combination of the foregoing. Computer program code for carrying out operations for aspects of the present invention may be written in any combination of one or more programming languages, including an object-oriented programming language such as Java, C#, C++, Visual Basic or the like and conventional procedural programming languages, such as the “C” programming language or similar programming languages.

(82) It should be emphasized that the above-described embodiments of the present disclosure are merely possible examples of implementations set forth for a clear understanding of the principles of the disclosure. Many variations and modifications can be made to the above-described embodiment(s) without departing substantially from the spirit and principles of the disclosure. All such modifications and variations are intended to be included herein within the scope of this disclosure and protected by the following claims.