2012 IEEE 7th Sensor Array and Multichannel Signal Processing Workshop (SAM)
Random Switch Antenna Array FMCW Radar and Its Signal Processing Method Chenxi Hu∗† , Huadong Meng∗ , Wei Wang† , Gang Li∗ and Xiqin Wang∗ ∗ Department
of Electronic Engineering Tsinghua University, Beijing, P. R. China Email:
[email protected] † Xi’an Electronic Engineering Research Institute, Xi’an, P. R. China
Abstract—In this paper, random switch antenna array (RSAA) is proposed to apply to the switch antenna array (SAA) frequency-modulated continuous-wave (FMCW) radar system. Firstly, the signal model and signal processing method of RSAA is analyzed and it shows that RSAA can successfully solve azimuthvelocity coupling problem. Then we suppose a method by using RSAA to reduce the switching frequency and sampling rate based on sparse signal representation with multiple measurement vectors (MMV). It is shown in simulations that the proposed algorithms yield better performance in terms of azimuth-velocity decoupling and can obtain high image accuracy with less observation data. Keywords—FMCW Radar; Time-division multiplexing antenna array; RSAA; Azimuth-velocity coupling; M-FOCUSS
I. I NTRODUCTION Antenna array FMCW radar systems have been used in automotive applications in recent years [1][2]. The FMCW wave-form approach enables simpler hardware, lower peak power output and cost than the pulse-waveform implementation. FMCW radars can provide information on the range and relative velocity of multiple targets while the angle of targets can be obtained by using an array of receiving antennas. In conventional multiple-channel antenna array systems, each antenna element need an independent receiver so that the hardware expense and power consumption of such a system is considerably high. A novel scheme, switch antenna array (SAA) in which all sensors share one transceiver but in different time slots appointed was proposed in [3]. Compared with multi-channel antenna array (MAA) where every sensor uses its own transceiver simultaneously, SAA can greatly reduce system cost and radar size. Now only sequential switch antenna array (SSAA) is used in SAA. In static applications, the same signal processing method with that in MAA can be utilized. However, in moving objects applications, SSAA will encounter a azimuth-velocity coupling problem which is caused by the fact that the phase difference between adjacent array units not only depends upon target azimuth, but also the target movement within switch periods. This problem may result in wrong target azimuth estimation. A 2-dimension method using MUSIC is proposed in [4] to overcome this problem. However, the method needs multiple cycles of observation data and high sweep frequency. [1][5] supposed RX channels switch as fast as the sampling frequency to minimize the time difference, but in this case the
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system would call for high switching frequency and receiver circuit with wide frequency response range. In this paper, a new method is proposed, which successfully solves azimuth-velocity coupling problem by using RSAA. In RSAA, the receiving antennas are switched to the single receiving channel in a pseudorandom order. [6] has shown that a random switching could be used in channel sounding to eliminate the ambiguity between doppler frequency and directions. What is more, RSAA can be used to realize the sparse sampling of the signal. By seeming the observation data as a multiple measurement sparse solution problem, we use the sparse reconstruction algorithm to obtain precise measurement of targets with low switching frequency and sampling rate. II. S YSTEM AND S IGNAL M ODEL In the FMCW system (shown in Fig. 1), the frequency modulation period is T , the sweeping bandwidth is B, the number of sensors is M , the wavelength is λ, and the sensor spacing is d. In SAA, the system works continuously for N cycles, in each of which sensors are turned on in turn from 1 to M . Next we would introduce two common time-division multiplexing (TDM) modes of SAA: multi-cycle TDM mode and single-cycle TDM mode. The signal models of SSAA and RSAA in the two modes are given and compared, too. x0 (t )
x1 (t )
xm (t )
FMCW Switch
A/D
Signal Processing Unit
xM (t ) Sync. Pulse
Fig. 1.
Block diagram of the switch-antenna array FMCW radar.
A. Multi-Cycle Time-Division Multiplexing Mode In multi-cycle TDM mode, the switching interval Tsw equals the frequency modulation period T as shown in Fig. 2. The mode can estimate the azimuth, range and velocity of targets simultaneously, and received signal bandwidth equals that in MAA. However, the processing time is as long as N M T , which restricts the movement of targets and reaction time of a driver.
297
Sampling Time n = 1 (1st Cycle)
Sampling Time
n = N (Nth Cycle)
n = 1 (1st Cycle) Ts … …
1
2
…
M
……
1
2
…
n = N (Nth Cycle)
M
Pulse
Fig. 2. The multiple-cycle time-division multiplexing mode of SAA. During each pulse, the fast time sampling is produced with the sampling period Ts . 1
1) Sequential Switch Antenna Array: Suppose L is number of targets with their radial velocity vi , angle θi and distance ri . For the kth period within the nth cycle, the received signal can be expressed as an equation (1):
2
…
M
……
1
2
…
M
Ts Pulse
Fig. 3. The single-cycle time-division multiplexing mode of SAA. Only one sample is obtained in each switch.
1) Sequential Switch Antenna Array: The corresponding xi (t) exp {−j (2π (d sin θi + 2vi T ) (k − 1) /λ)} signal model is as follow. Note that the range and velocity is i=1 coupled here and this problem can be solved with transmitting · exp {−j (2π · 2M vi T (n − 1) /λ)} + nk (t) (1) FMCW radar waveform with triangle shape. where xi (t) ¡= ai exp {j (2πf t + φ )}, f = 2αr /c + i i i ¢ i L © ¡ ¡ ¢ ¢ª P 2vi /λ, φi = 2π f0 τi − ατi2 /2 and n(t) is noise. 2vi i yn,k = ai exp j 2π 2αr (n − 1) M Ts c + λ Let fai = (2d sin θi + vi T ) /λ, fbi = (M vi T ) /λ, then © i=1¡ ¡ ¢ ¢ ¢ª ¡ 2αr θi 2vi i equation (1) can be written as: · exp n−j³ 2π d sin + ´o Ts (k − 1) λ c + λ ¡ ¢2 · exp j 2rλi − 12 α 2rc i + nn,k L P (5) ynk (t) = xi (t) exp {−j (2π (k − 1) fai )} (2) i=1 In this case, high switching frequency and sampling rate are · exp {−j (2π (n − 1) fbi )} + nk (t) needed by the Nyquist sampling theorem: It can be seen from (2) that, if system only works in one fs = fsw ≥ M · bw (6) cycle (N = 1), only fai which corresponds to more than one pairs of θi and vi can be obtained. [4] supposed a method where bw = 2 ((B/T ) (2Rmax /c) + f0 (2vmax /c)) is the to overcome this problem by using recurrent sampling to bandwidth of down-converted signal correspond to one changenerate another variable fbi independent with fai . However, nel in MAA. the maximum unambiguous azimuth and velocity are still 2) Random Switch Antenna Array: In RSAA, the received limited by the following conditions: signal can be given by: ynk (t) =
L P
λ λ 2vmax , sin θmax < − T (3) 4M T 2d d 2) Random Switch Antenna Array: Here we use the RSAA to solve azimuth-velocity coupling problem. In every work cycle of RSAA, the receiving antennas are switched to the single receiving channel in a pseudorandom order. Then the received signal of RSAA can be given by: vmax
