NL2022643B1 - Phase coded frequency modulated continuous wave radar system - Google Patents

Abstract

21 Abstract: The invention is related to a method of detecting an object, the method comprising: (a) generating an initial signal in a signal generator; 5 (b) generating a coded signal by modulating the initial signal; (c) generating a transmission signal by modulating a carrier signal and the coded signal; (d) transmitting the transmission signal; (e) receiving a reflected signal, the reflected signal having been reflected from the 10 object; (f) generating a received signal by demodulating the reflected signal with the carrier signal and the initial signal; (g) generating a corrected received signal by filtering the received signal with a group delay filter; 15 (h) generating a decoded signal by modulating the corrected received signal with a decoding signal; (i) determining a range of the object from the decoded signal. The invention is furthermore related to a PC-FMCW radar system for detecting distance and relative velocity of a target, comprising a group delay filter. 20

Description

PHASE CODED FREQUENCY MODULATED CONTINUOUS WAVE RADAR SYSTEM Field of the Invention The present invention relates to a method for detecting objects, by using radar systems and, more particularly, by using Phase Coded Frequency-Modulated-Continuous- Wave (PC-FMCW) radar systems. It furthermore relates to radar systems, and more particular to PC-FMCW radar systems. Background of the Invention Radio frequency interference (RFI) is a serious issue for radar applications (such as in automotive radars) due to the crowded electromagnetic spectrum and may be observed as synchronous or asynchronous interference. it has been reported by R.M. Davis et al (IEEE Transactions on Aerospace and Electronic Systems, vol. 43, no.1, pp. 401-408, January 2007) that phase coding can also be used to reduce RF] between radars in the same vicinity. The growth in MIMO applications to exploit the spatial diversity in radar systems has increased the research for alternative codes for radar waveform design. For radar applications, many code families have been explored in the past. Different classes of codes can be distinguished, ranging from binary sequences (Barker, M-sequence, Gold, Kasami, etc. }, to complementary pairs (Golay) and poly-phase codes such as Frank code, P1, P2, P3 and P4.

Performance of a code usually measured by its ambiguity function which jointly demonstrates the propagation delay and Doppler relationship. The Doppler resilient - longer codes are preferred in radar applications due to their range sidelobes provided by the code’s autocorrelation, as described by Z. Dunn et al (2016 IEEE Radar Conference, May 2016, pp 1-4).

Matched filtering (pulse compression technique), that increases the range resolution, is currently used processing the PC waveforms to reach the optimal Signal-to- Noise ratio (SNR). In literature, mismatched filters are also introduced to lower range sidelobes in PC waveforms by R.M. Davis et al (IEEE Transactions on Aerospace and Electronic Systems, vol. 43, no.1, pp. 401-408, January 2007). In both, using longer codes or using mismatched filters, the computational complexity usually increases {especially for the longer codes). Moreover, for wideband applications, a high-end analog-to-digital converter

(ADC) with large bandwidth is needed to digitize the received signal which makes the applicability of PC waveforms into radar transceivers challenging such as an FMCW automobile radar.

Linear frequency modulated (LFM}) waveform has been used as the primary waveform at most of the operational radar systems for several decades. However, there is a growing interest in the use of phase coded (PC) waveforms since phase coding makes possible the sensing and communication functions on a single waveform. In other words, PC waveforms can perform joint sensing and communications which brings multi-functionality to the traditional radar systems.

Conventional radar systems transmit modulated or pulsed signals to determine properties of an object, such as range to the object or speed of the object. For example, in frequency modulated continuous wave (FMCW) radar the frequency of a radar signal is modulated, yielding information about range to an object when the radar signal is reflected from the object.

Frequency Modulated Continuous Wave (FMCW) radar systems use stretch processing to process large bandwidth waveforms, which reduces the bandwidth requirement of analog to digital converters since stretch processing typically occurs in the analog domain in FMCW radar. However, unlike the matched filtering, any delay between transmitted and received PC waveform creates discrepancies and results undesired beat signals.

There are multiple approaches to phase-coded continuous wave (PC-CW) radar systems described in the prior art. Such a system uses for example multiple decoders for each range gate (range channels) which decodes the signal with a shifted version of the code signal, EP-A-3 428 679 describes a modulated radar system for detecting objects. it further describes a Phase Coded Continuous wave radar and uses correlators (matched filtering) in the receiver to extract range information. A disadvantage of the process described is that for matched filtering in the digital domain a wide bandwidth for analogue to digital converters {ADC) is required and a good digital signal processor (DSP).

Hence there remains a need for a frequency modulated continuous wave (FCMW) radar that takes the advantage of stretch processing to reduce the sampling requirements of radar systems. Preservation of this benefit when applying phase modulation {phase coding) into FMCW radar systems for interference mitigation or joint communication is not possible due to the nature of stretch processing. The current invention proposes a new system and processing strategy to address these issues.

Summary of the Invention It is an object of the present invention to provide a new hardware architecture for FMCW Radar. lt is a further object of the invention to provide a new hybrid architecture (both hardware and software) for FMCW radar. it is a further object of the invention to make stretch processing possible even different time delays present between transmitted and received phase coded waveform. It is an even further object to solve the issue of radio frequency interference (RFI. It is an even further object of the present invention to take the advantages of both LFM and coded waveforms jointly, such as a phasecode LFM waveform for the radar system.

These and other objects are addressed by the method and apparatus of the present invention.

Accordingly, the present invention relates to a method of detecting an object, the method comprising: (a) generating an initial signal in a signal generator; (b) generating a coded signal by modulating the initial signal; {c) generating a transmission signal by modulating a carrier signal and the coded signal; (d) transmitting the transmission signal; (e) receiving a reflected signal, the reflected signal having been reflected from the object; {f) generating a received signal by demodulating the reflected signal with the carrier signal and the initial signal; (g) generating a corrected received signal by filtering the received signal with a group delay filter; (h) generating a decoded signal by modulating the corrected received signal with a decoding signal; (i) determining a range of the object from the decoded signal.

In a further aspect, the present invention relates to a Phase Coded Frequency-Modulated-Continuous-Wave (PC-FMCW) radar system for detecting a distance and a relative velocity of a target, the radar system comprising: (a) a signal generator; (b) a phase coder; {c} a modulator; {d} a transmitter; {e} a receiver; (f) a demodulator; {g) a group delay filter; (h} a phase decoder; {i) an analog to digital converter; and (j) a processor.

Detailed Description of the Invention Embodiments of the invention are described hereinafter with reference to the accompanying drawings, wherein like letters and numerals refer to like parts, wherein the figures are approximately to scale, and wherein: Fig. 1 illustrates a simplified block diagram of a traditional FMCW radar system; Fig. 2 illustrates a typical transmit and received signal with their envelopes wherein a) is an instantaneous frequency of transmit signal; b} an envelope of transmit signal as bipolar binary coding; c) an instantaneous frequency of received signal; and d} an envelope of received signal as bipolar binary coding.

Fig. 3 illustrates a simplified block diagram according to the invention of a Phase- Coded FMCW radar system (radar transceivers part with phase coding capabilities is highlighted by a dashed line); Fig. 4 illustrates in a) beat frequencies without any processing; in b) traditional decoding signal; in c) beat frequencies after group delay filter; and in d) delayed bipolar binary decoding signal.

Fig. 5 illustrates a coding matrix for a range-Doppler processing frame whose rows consist of randomly shifted codes.

Fig. 6 illustrates a small part of a) input signal (beat frequency), b} filter output, and ¢) decoded signal.

Fig. 7 illustrates a Bode plot of the designed filter with a) magnitude response, b) phase response. 5 Fig. 8 illustrates a Group delay of the designed filter, Fig. 9 illustrates a Range-Doppler plot of the simulated single target with a speed of 10m/s at range 10m.

Fig. 10 illustrates a range cut of the simulated single target.

Comparison of tradition FMCW output, unprocessed signal output, and processed (filtered and decoded) signal output.

Fig. 11 illustrates a Range-Doppler plot of multiple targets.

Two targets are at the same range and two targets are at the same Doppler.

Fig. 12 illustrates an experiment. a) Collected (beat frequency) signal, b) filter output, and c) decoded signal.

Fig. 13 illustrates a Range Doppler plot of the experimental data after proposed processing.

Fig. 14 illustrates a Range Doppler plot of the experimental data without decoding.

Fig. 15 illustrates a simplified block diagram of a Phase-Coded FMCW radar system architecture according to the invention.

Envelop alignment and decoding are moved from digital domain to hardware domain.

In the figures the following abbreviations have been used, which represent the following: Tx = transmitter (antenna) Rx = Receiver (antenna) HPA = High Power Amplifier ADC = Analogue to Digital Converter LO = Linear Oscillator LNA = Low Noise Amplifier LPF = Low Pass Filter Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs.

The terminology used in the description of the invention herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention.

The terms "radar" as used herein, includes a detection system that uses radio waves to determine the range, angle, or velocity of objects.

It can be used to detect for example aircraft, ships, spacecraft, guided missiles, motor vehicles, weather formations, and terrain, A radar system generally consists of a transmitter producing electromagnetic waves in the radio or microwaves domain, a transmitting antenna, a receiving antenna (often the same antenna is used for transmitting and receiving) and a receiver and processor to determine properties of the object(s). Radio waves {pulsed or continuous) from the transmitter reflect off the object and return to the receiver, giving information about the object's location and speed.

The term “Continuous-Wave (CW) radar systems” as used herein, includes a type of radar system where a known stable frequency continuous wave radio energy is transmitted and then received from any reflecting objects.

Continuous-wave (CW) radar uses Doppler, which renders the radar immune to interference from large stationary objects and slow- moving clutter.

The term “Frequency-modulated continuous-wave radar (FMCW)” — also called continuous-wave frequency-modulated (CWFM) radar as used herein, includes a range measuring radar set capable of determining distance.

This increases reliability by providing distance measurement along with speed measurement, which is essential when there is more than one source of reflection arriving at the radar antenna, The term “MIMO” or “MIMO radar” as used herein, includes an advanced type of phased array radar employing digital receivers and waveform generators distributed across the aperture.

MIMO radar signals propagate in a fashion similar to Multistatic radar.

However, instead of distributing the radar elements throughout the surveillance area, antennas are closely located to obtain better spatial resolution, Doppler resolution, and dynamic range.

MIMO radar systems transmit mutually orthogonal signals from multiple transmit antennas.

The term “dechirping” as used herein, is an alternative for stretch processing or deramping. These three terms are all used for reducing the sampling requirements of radar systems.

The term “uncoded” signal as used herein, includes a signal that has not been coded.

The term “signal generator” as used herein, includes means for generating frequency modulated continuous wave (FMCW) signal.

The term “phase coder” as used herein, includes means for generating phase coded signal by changing the phase of FMCW signal in accordance with the elements of a code sequence.

The term “modulator” as used herein, includes means of mixing phase coded signal with a carrier signal.

The term “transmitter” as used herein, includes means for transmitting modulated signals.

The term “receiver” as used herein includes means for receiving the return signal reflected target in every detection cycle.

The term “demodulator” as used herein, includes means of extracting a beat component signal from the uncoded modulated signal and a received return signal.

The term “group delay filter” as used herein, includes means of delaying all frequency components of an input signal independently in accordance with the delay of return signal.

The term “phase decoder” as used herein, includes means of generating decoder signal by changing the phase of filtered signal in accordance with a decoding signal.

The term “analog to digital converter” as used herein, includes means of digitizing analog signals.

The term “processor” as used herein, includes means of processing digital signal to extract range and velocity information of target.

The term “range” as used herein, includes referring to the object that is detected by the radar and the range is preferably related to the distance and the relative velocity of the object as calculated from the decoded signal. The relative velocity is a term generally used in radar technology, and is advantageously the velocity in relation to the transmitter and / or receiver of the signals and / or reflected signals.

In frequency modulated continuous wave (FMCW) radar, the frequency of the transmit signal changes over time, usually in the form of a linear sweep over a predetermined bandwidth.

The frequency difference between transmitted and received signals is determined by mixing these two signals (also known as stretch processing or dechirping) and can be used to measure the distance and velocity of the objects.

A simplified block diagram of a traditional FMCW radar is illustrated in Figure 1. To explain it in more detail, a generator, preferably a signal generator, more preferably an arbitrary waveform generator (AWG), a voltage controlled oscillator (VCO) or a direct digital synthesizers (DDS), creates a waveform whose instantaneous frequency is shown in Figure 2 a) and where the duration of different possible events are marked as follows: Tawen is the dwell time; Tsette is the settling time of the waveform generator; Tapc is the analog-to-digital converter (ADC) sampling time; and Treset is the reset time of the waveform generator.

The instantaneous frequency of the waveform is set by fit) = kt where the slope of the waveform k = B/T is equal to the ratio of bandwidth B and the duration T = Tsettlet Tanc of the waveform.

Then, the instantaneous phase of the waveform with an initial phase co is defined as, t HO) =27 | f()dt ’ (1) = ol fue ue +d, A transmit waveform with an envelope A(t) can be written as x, (1) = A(t) cos ((1)), (2} and the received waveform which might be reflected from a target at a distance Ro with a line of sight velocity v can be written as a delayed copy of transmitted signal, x, (1) = B() cos (p(t — 7) (3) where B(t) is the envelope of received signal which is usually approximated as B(t) ~ A{t - 1) {assuming no loss), and the round-trip time delay is e= 2(% rr) (4) Cc

The received and transmitted signals can be mixed in order to reduce the required sampling rate.

The mixing generates the intermediate frequency {which is also known as beat, dechirped or deramped) signal is x, (1) = x, (2) x, (7) (5) = A(DB(t) cos (g(r) cos (g(t —1)) which can be also written as,

50 = OPO cos (50) - gta - 0) + A sg). (0

The beat signal is then low-pass filtered to eliminate the high frequency {sum) components before digitized by an analog-to-digital converter (ADC) at a rate of at least twice the maximum beat frequency f+max.

Only the difference frequencies pass out of the low-pass filter which yields a beat signal

50 = XP cos (pity gti). 7)

Now going into more detail with respect to phase coding, phase coded waveforms usually divide the pulse into L- time segments.

Each time segment, also known as chip, may have a different phase than the others.

Chip phase can be 0 or for n binary phase codes,

while polyphase codes may support more phase changes.

A single period of a phase-coded waveform for a binary sequence au, 02, ..., Ot for Le bits a, € {-1, +1}, can mathematically be represented as,

i 4 t—ni C= 2 e’” ee] n=l2 LZ, (8) where ó(n) € {-0, nt} denotes the phase corresponding to the n bit of the sequence.

The phase is kept constant for a chip duration Te = T/L.. As the concurrent chip value changes from -1 to +1, or vice versa, then a phase discontinuity will take place as the phase is shifted 180°. If the transmit waveform is coded with a bipolar phase code C(t) € {-1,1}, then the envelope of transmit and received signal become A(t) = C(t) and, B(t) = C{t - 1), respectively.

The beat signal for the phase-coded FMCW radar after dechirping and low-pass filtering can be written as,

550 = OD ogg) gir). (9 As illustrated in figure 2 b) and figure 2 d), the transmitted A(t) = C(t) and the received

B(t) = C(t -t) signal envelopes do not match with each other due to the roundtrip time delay. In that case, it is not possible to successfully decode the received signal. Thus, stretch processing does not give expected range profiles after spectral analysis.

The phase coded FMCW radar system according to the invention, which is illustrated in figure 3, has the received signal mixed with uncoded transmit signal which preserves original phase coding for each beat frequencies after dechirping. The radar transceivers part with phase coding capabilities is highlighted by a dashed line. This phase coded FMCW radar system has two distinctive futures as compared to the system represented in figure 1. Firstly, the received signal is preferably mixed with uncoded transmit signal which preserves original phase coding for each beat frequencies after dechirping. Secondly and more importantly, the system according to the invention uses a time domain group delay filter to align the envelope of each beat frequency which allows to successfully decode received signal even though each beat frequency is delayed differently in time.

The group delay filter according to the invention can be used to align the envelopes.

figure 4 a) illustrates the beat frequencies in the time-frequency domain without any processing. The beat frequencies belonging to the far range targets are delayed more than the beat frequencies belonging to the closer range targets. Thus, each beat frequency is shifted differently from each other.

The exact time delay of a beat frequency for an arbitrary range R is written as 7, = ELS (10) Cc whereas a beat frequency is written as 2RB 1 = Of (11) Alternatively, combining (10) and (11), we find that a beat frequency fb was delayed by 7, ——f, (12) Note that, the maximum beat frequency fumax = fs/2 is delayed with the maximum delay Tmax due to the nature of the round trip delay from maximum range Rmax. To align the envelope of all beat frequencies, each beat frequency needs to be delayed to the same time instance with fo;max. Thus, all beat frequencies with 0 < fb < fo,;max need to be delayed with

Tp = Tax == Ty 1 (13) = & (ones - te ) *

The above describes the theory behind envelope alignment and the group delay filter.

In reality it seems more complex, as a received signal x(t} consists of multiple beat frequencies as echoes are received simultaneously from multiple targets.

For P targets at arbitrary ranges, the overall received signal can be written as Pp x)= x,(1,7,), (14) p= where 1, is the time delay for p™ target.

Note that for the proposed system in figure 3, the received signal is dechirped with the uncoded waveform A(t) = 1. Thus, the beat signal for the method according to the current invention is written as, Clt-T x(t, 7) =D cos (pga). (15)

To process the shifted received signal envelopes, we use in our invention a time- domain group delay filter which delays all frequency components of the input signal independently.

A group-delay filter is an all-pass filter that passes all signals but the delay for signal components will be different for the various frequencies.

The group delay of a filter is defined as the negative derivative of the phase.

For a filter with a magnitude response IH (f)| and a phase response /H( f), explicitly H(N=|HC|ZH(f), (16) its group delay is defined as 1d T. =———ZH(/). 17 an(f) 27 df (f (17) For an arbitrary signal in the form of v(t) = E(t) cos(g(1)) where E(t) is the slow varying envelope, the output of the group delay filter h(t) is defined as =S) zE(-7(f)eos(g(1-7,(f))). (18) Here, the envelope function is delayed by the group delay, whereas the carrier (in our case beat signal) is delayed by the phase delay which is 1 ZH(f) Wz fe (19)

According to the invention, we advantageously define a filter hsp with a constant magnitude response IH (f)| = 1 and a group-delay tep = Tp which yields a phase response Hf) ==27 [Tan ( Adf = 2] (fra 1d, (20) Hf) = BEL fo) k 2 As a result of applying this filter according to the invention, the envelope of the received signal is delayed as desired for each frequency components (beat frequencies). Note that, there will be a phase delay for each beat frequencies, as seen from the second part of (18), explicitly cos(ó{t- to(f))). We furthermore advantageously use spectral estimation methods {such as fast Fourier transform (FFT)) to exploit the range information after stretch processing.

Since the frequency component is exploited by spectral analysis, a phase delay (change) in beat signal does not affect the range estimates.

The time-domain output signal after group delay filtering can be written as X(H=x()Bh,, (1) _ y en) Gas) cos (4c -7,)-@(t—7, — 7,)) 21) EE 2 Even though a single group delay filter hep is preferably applied in the time domain, the output of the filter X{s}is illustrated in time-frequency domain to demonstrate the influence of the filter on beat frequencies.

Figure 2 c} shows the beat frequencies after the proposed group-delay filter.

As illustrated in the figure, all beat frequencies are aligned with the fomax at the same time instance Tmax.

Also decoding can advantageously be applied in the method and apparatus of the invention, to preserve phase codes in time-domain received signal.

Decoding can preferably be applied just before the spectral estimation.

The range information is then more accurate, as without decoding, spectral estimation techies cannot exploit the frequency content due to the abrupt phase changes in the beat signal.

The range of the object comprises advantageously a distance and a relative velocity of the object determined from the decoded signal.

The relative velocity is a term generally used in radar technology, and is advantageously the velocity in relation to the location of the transmitter and / or receiver of the signals.

it should be noted that, after the group-delay filtering, all beat frequencies are aligned at the maximum delay as seen in figure 2 c). A proper decoding signal should correct the phase changes initiated by the coding signal C{t} so the decoding signal should be the complex conjugate of the coding signal (in the current case the negative envelope due to the binary coding, see (8)). Moreover, the decoding signal should preferably be perfectly aligned with the received signal. Under these preferred circumstances, a proper decoding signal can be defined as CO)y=C"(t-7,,)=-Clt-7,,) (22) which is illustrated in Figure 2 d) for this specific example. Finally, the decoded beat signal is given by s(t) = C(x (1) go) cos(gir—7,)— g(r 7, -7,)). (23) since C(t —7,,)(-C(t—1,,))=u(t—1,,.) where u(t—t,)= f <i, (24) 1 t>1, is preferably applied as the step function.

Figure 15 represents a simplified block diagram of a Phase-Coded FMCW radar system architecture. Envelop alignment and decoding are moved from the digital domain to the hardware domain. A group delay filter that satisfies the requirement is in this example implemented into the hardware architecture. The inverse of the coded signal (for BPSK) might be delayed and mixed with filtered signal, to decode the beat frequencies before analogue to digital conversion. The proposed hardware implementation is suitable for interference mitigation without any extra signal processing, which can yield a Lc times signal to interference ratio (SIR) improvement SIR=20log10{L.), if advantageously different codes are used in coding and decoding. After this process, a microcontroller {MCU) might be used to directly compute the 2D-FFT of digitized signal for range Doppler processing.

Advantageously, the system according to the invention, uses a time domain group delay filter to align the envelope of each beat frequency which allows to successfully decode received signal even though each beat frequency is delayed differently in time.

Advantageously, the group delay filter is a time domain group delay filter or a frequency domain group delay filter.

Advantageously, the system according to the invention, preserves phase codes in time-domain received signal.

Advantageously, decoding might be applied before the spectral estimation. The result of this is that the range information is more precise. Without decoding, spectral estimation techies cannot exploit the frequency content due to the abrupt phase changes in the beat signal and thus range information is less accurate. it should be noted that, after the group-delay filtering, all beat frequencies are aligned at the maximum delay.

Advantageously, decoding is applied before determining the range.

With the current method and apparatus of the invention, traditional FMCW processing techniques might be used to process decoded signal s(t). Preferably, each burst (pulse) (that filtered by same group-delay filter) has the same amount of phase delay as shown in (19). With this approach, the Doppler processing is preferably not affected by the proposed algorithm. One may apply 2D-FFT to a series of decoded signals to achieve the range-Doppler information of the targets.

The following, non-limiting examples are provided to illustrate the invention.

The success of the proposed phase-coded FMCW radar is first demonstrated by simulations. Following, the appropriate signal processing approach is verified by controlled laboratory experiments.

Example 1: Simulations Even though the proposed method is more general and applicable to different systems, for the purpose of simulation, the radar design parameters are selected similar to a shortrange automotive radar (SRR) systems as summarized in Table |.

1) The Coding Matrix: As a coding signal, we choose 16-bit Kasami sequence with a generator polynomial g{z) = [z%+ z + 1]. This is preferred, since Kasami sequence is known to be a set of sequences that have good cross-correlation properties. Then, a selected code signal is randomly shifted for each pulse (burst). In a coherent processing interval (CPt), 512 bursts (pulses or chips) are transmitted. Thus, in this example a range-Doppler processing frame consists of 512 bursts {slow time samples) and 1024 ADC samples {fast-time samples).

Figure 5 illustrates a coding matrix for a range-Doppler processing frame whose rows consist of randomly shifted Kasami codes.

Table 1: Radar system design parameters for simulation | ADC Sampling Ts Tape 2560 ps | | Dwell Time Poell LOO jes | | Settle Time ette 3.53 us | | ADC Sampling Treguency Fa $1 MHz | | Bandwidth B ZOZ | | Number of Chirps STE | Number of Bits (Chips) per Chirp LR | Duration of Chips Tal us| First, a single target at a range of 10m with a velocity of 10m/s is simulated. Figure 6 a) shows a part (155 samples over 1024) of an input signal (unprocessed beat frequency) for the group delay filter together with the coding signal. As seen from figure 6 a), due to the round-trip delay, received beat frequency is shifted and its phase change does not coincide with the transmitted code signal. This misalignment is preferably corrected by a single time- domain group delay filter for all beat frequencies.

2) The design of the Group Delay Filter: A real, stable, infinite impulse response {IIR} group-delay filter is designed {as described above} due to its speed (comparing to the finite impulse response filters) and easy implementations to the radar processors such as a microcontroller (MC). Filter order is set 30 which yields a direct-form H filter structure (can be implemented 60 multipliers and 60 adders) and a frequency response as illustrated in Figure 7. As seen from figure 7, even though the requirement for magnitude response | H{f}| = 1 is quite satisfied after optimization, there is still a small ripple in magnitude response as expected.

Figure 8 shows the ideal and optimized group delay of the designed IIR filter. It should be noted that filter itself has a constant delay which is 24,13 samples as seen from figure 8. The comparison of group delay of the optimized filter and the ideal group delay is illustrated Figure 8. Note that the ideal group delay is shifted by 24,13 samples for easy comparison. Figure 8 also shows that the simulated target's beat frequency and delay (34,45 samples). In this example case, the maximum delay is 35,78 samples. Whereas, the delay due to the round trip is 35,78 — 34,45 = 1,33 samples which can be observed easily from Figure 6 a) since the frequency change occurs roughly 2 samples later than the phase change of the coding signal.

The output of this filter is illustrated in Figure 6 b) together with the transmitted code signal. It is obvious that the group delay filter is managed to align the shifted beat frequency. Bearing in mind that the filtered signal must be aligned with the maximum delay Tmax as explained above, for illustration purpose, the signal was manually shifted back to its original position for easy comparison {phase codes are used as reference points). Note that, in realtime processing, this alignment is not needed. Finally, the decoded signal is illustrated in Figure 6 c) together with the overlaid decoder signal as well as a beat signal from a traditional FMCW radar as a reference. The processed signal has a smoother phase comparing to the input signal and has been well aligned with the decoder signal. Comparing to the reference signal, a phase shift observed in the processed signal which is expected due tothe equation as represented in (18).

3) Range Doppler Processing: After filtering and decoding, the beat signals can be processed traditionally. Range-Doppler processing can efficiently be executed by 2D-FFT. During range-Doppler processing, a Hamming window in both range and Doppler dimension is used for sidelobes suppression. Figure 9 shows the final range-Doppler image of the system where the simulated target forms a peak at correct range and velocity. To further investigate the system response a range cut illustrated in Figure 10. As seen from figure 10, waveform slightly affected due to a Doppler shift (movement of the target).

Example 2 Multiple target The simulation was extended to a multiple target scenario to demonstrate the success of the proposed approach even there are multiple targets in the same range and/or same velocity (Doppler frequency). Radar path-loss model is included to simulate different signal-to-noise ratio (SNR) levels. Location of five different targets together with their velocities, radar cross sections (RCS) and SNR values are summarized in Table 2.

Table 2: Target's parameters for multi target simulation HN EY Hd i BD 2 3 SRT Figure 11 shows the result of the aforementioned multi-target scenario. As seen from figure 11, all five targets are focused by range-Doppler processing, after group-delay filtering and decoding. it should be noted that a single group delay filter is managed to align all targets beat frequencies so that encoding is successful which yields a well-focused range- Doppler output.

Example 3 Experiments To validate results obtained from the simulation model, experiments are set up in an intermediate frequency (IF). Due to unavailability of a phase-coded FMCW radar, controlled experiments are performed using an arbitrary waveform generator (AWG) and an oscilloscope, Signal generation for the phase coded-LFM waveform is done in the digital domain using MATLAB environment. Like simulations, 16-bits Kasami sequence is used for phase coding. The sampling frequency for waveform generation is equal to the maximum sampling rate of the AWG (Tektronix AWG5014B), which equals 1.2 GSa/s. Since the maximum allowable bandwidth is 0.5 GHz, the bandwidth of the waveform is selected as 0.4 GHz which yields a range resolution 0.37 cm. Other parameters are selected as in Table I. AWG is programmed to create a set of delayed signal to mimic target returns which are collected by an oscilloscope {Agilent DSOX-91604A} with a speed of 1 GSa/s. Collected waveforms are dechirped and downsampled to 40 MHz to create the beat signals as similar to simulations.

One of the collected signals is illustrated in Figure 12.a together with the 16 bits coding signal, Unlike the simulation, it is hard to observe the phase changes since there are two targets in collected data and the amplitude of the collected signal is decreasing towards the high frequencies due to the internal low-pass filter of the AWG.

The output of the {IR group delay filter of a length 46, is illustrated in Figure 12.b together with the transmitted code signal. A new group delay filter is designed according to (13) to process the experimental data since the bandwidth of the signal used in experiments is different than the simulation. The filtered signal is then decoded and illustrated in Figure 12 c) together with the overlaid decoder signal. Bearing in mind that, Figure 12 c} is shifted back to its original position for easy comparison. After filtering for envelope alighment and decoding, range-Doppler processing is applied to a frame which consists of 512 slow-time and 1024 fast-time samples. Hamming window is applied for both range and Doppler dimension to control the excessive sidelobes. The result of the range-Doppler processing is shown in Figure 13 where two stationary targets are clearly focused. To see the qualitative improvement, a range-Doppler plot of the experimental data without any decoding is illustrated in Figure 14. As seen from the figure, results for experimental data without any processing spreads through range dimension which is due to the spread spectrum nature of the phase codes.

As shown above, the LFM waveform coded prior to transmission are successfully decoded in the FMCW radar receiver. Decoded waveforms are used to achieve range and velocity information of the targets. The success of the proposed PC-FMCW system according to the invention is illustrated by simulations and verified by experiments.

Claims (11)

CONCLUSIONS A method for detecting an object, the method comprising: a. Generating an initial signal with the aid of a signal generator; b. generating an encoded signal by modulating the initial signal; c. generating a transmission signal by modulating a carrier signal and the encoded signal; d. sending the transmission signal; e. receiving a reflected signal, the reflected signal being reflected from the object; f generating a receiving signal by demodulating the reflected signal with the carrier signal and the initial signal; g. generating a corrected received signal by filtering the received signal using a group delay filter; h. generating a decoded signal by modulating the corrected received signal with a decoding signal; i. determining a range of the object of the decoded signal. The method of claim 1, wherein the range of the object includes a distance and a relative speed of the object determined from the decoded signal. The method of claim 1 or 2, wherein the group delay filter is a time domain or frequency domain group delay filter. A method according to any preceding claim, wherein phase codes are stored in the time domain received signal. A method according to any one of the preceding claims, wherein the decoding is performed before determining the range. 6. Phase Coded Frequency Modulated Continuous Wave (PC-FMCW) radar system for detecting a distance and relative speed of a target, the radar system comprising: a. A signal generator; b. a phase encoder; c. a modulator; d. a transmitter; e. a recipient; f. a demodulator; g. a group delay filter; h. a phase decoder; i. an analog-to-digital converter; and J. a processor. The system of claim 6, wherein the signal generator is an arbitrary waveform generator (AWG), a voltage controlled oscillator (VCO), or a direct digital synthesis (DDS). . The system of claim 6 or 7, wherein the signal generator, the phase encoder, and the modulator are configured in a single component. The system of claims 6 to 8, wherein the frequency modulated continuous wave signal (FMCW) is configured as a linear frequency modulated continuous wave signal. The system of claims 6 to 9, wherein the coded signal comprises multiple phase changes in accordance with the elements of the code sequence. The system of claims 6 to 10, wherein the group delay filter and the phase encoder are configured to be implemented in the processor by means of a time domain or a frequency domain processing.