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MIMO Radar

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摘要

MIMO雷达是提升mmwave雷达角度分辨率（空间分辨率）的关键技术。本文介绍了MIMO雷达的基本原则以及不同设计的可能性。本应用报告也简短地讨论了提升TI毫米波产品线上MIMO雷达的方式。

1 介绍

术语多入单出(multiple-input-single-output , SIMO)雷达是指有一个发送端(TX)以及多个接收端(RX)天线的雷达设备。一个MISO雷达的分辨率取决于RX天线的数量。例如，一个有四个RX天线的设备的角分辨率大约是30°，一个有8个RX天线的雷达的角分辨率大约是15°。因此，一个能够提升角度分辨率的直接方法要求提升RX天线的数量。这个方法有一定局限性，因为每一个新增的RX天线都要求设备商的一个独立的RX处理链(RX processing chain)(each with an LNA, mixer, IF filter, and ADC)。

多入多出(Multiple-input-multiple-output, MIMO)是指拥有多个TX以及多个RX天线的雷达。正如随后会讨论到的，一个有$ N_{TX}$个TX天线以及$N_{RX}$个天线的MIMO雷达的分辨率与一个有$N_{TX}\times N_{RX}$个RX天线的SIMO雷达是一致的。因此MIMO雷达提供了一个经济有效的提升雷达角度分辨率的方式。

本篇应用指南介绍了 MIMO 雷达，并为工程师提供了足够的信息来使用 TI 的毫米波产品线设计 MIMO 雷达应用。第二节是角度估计知识的快速概览。第三届列出了MIMO雷达的基本原理。本节说明跨TX天线的多路复用传输如何提高角度分辨率。第4节讨论了多路复用 TX 天线的不同策略。第5节讨论了使用 TI 雷达产品线实施MIMO雷达。

2 角度估计基础

估计一个物体的到达角度需要至少两个RX天线。图一展示了一个有一个TX天线以及两个间隔d的RX天线的雷达。

图一

来自TX天线的信号被一个物体反射(关于雷达的角度为𝞱)，信号被两个RX天线接收。为了到达第二个RX天线，来自物体的信号必须额外通过$dsin(\theta)$的距离。这对应了在两个RX天线之间接收的信号之间有$\omega =(2\pi /\lambda)dsin(\theta)$的相位差。因此，当相位差，$\omega$，被估计了，到达角，𝞱，可以使用公式一计算：
$$
\theta = sin^{-1}(\frac{\omega \lambda}{2\pi d}) \tag1
$$
由于相位差，$\omega$，只有在$(-\pi, \pi)$的范围能够被唯一估计，所以将$\omega = \pi$代入方程1，由此雷达的不模糊视场(unambiguous field of view, FOV)如下：
$$
\theta_{FOV}=\pm(\frac{\lambda}{2d})\tag2
$$
因此，使用$d=\lambda/2$可以达到公式3中的最大的FOV
$$
\theta_{FOV}=\pm90°\tag3
$$
总的来说，一个拥有$N_{RX}>$ two RX天线的雷达，例如图二展示了$N_{RX}=4$的情况。每个紧接着的天线的信号有一个额外的$\omega $的相移相对于前一个天线。因此，在N个天线之前有一个线性的相位(例如，$[0\ \omega\ 2\omega\ 3\omega]$)增加(相对于第一个RX天线)。因此，$\omega $可以通过在$N_{RX}$个天线之间采样信号并在这个信号序列上进行FFT（常被叫做angle-FFT），来进行可靠地估计。

增加天线的个数能够造成一个有更尖锐顶峰的FFT，接着，提升角度估计的准确度并且提升角度分辨率。图三展示了一个有4个以及8个天线的雷达（内部天线的距离为$\lambda /2$），有两个物体点分别在$\theta=-10° $以及$\theta=10° $。有四个天线的雷达设备无法分辨两个物体；然而，有8个天线的雷达可以。

附录A讨论了有N个相等间隔的天线（$\lambda /2$间隔）的RX阵列，角度分辨率通过公式4给出
$$
\theta_{RES}=\frac{2}{N} \tag4
$$

3 MIMO雷达基本原理

建立在第二节的讨论上，如果我们想要加倍图二中的雷达的角度分辨($\theta _{res}$减半)能力，一种方法是加倍RX天线的数量（从四个到8个），如图4所示。

使用MIMO的观点，相同的结果可以使用一个额外的TX天线被实现，在下面参照图五进行讨论。

图5中的雷达有两个发射天线，TX1和TX2。TX1的一次发射导致四个RX天线的$[0\ \omega\ 2\omega\ 3\omega]$的相位(以第一个RX天线为参考)。因为第二个TX天线（TX2）在距离TX1 4d的位置放置，相比TX1，从TX2散发的任何信号都穿过了一段额外的$4dsin(\theta)$的距离。相应的，在每一个RX天线的信号都有一个额外的$4\omega$的相移(相对TX1的发射)。四个RX天线的相位，由于TX2的发射，是$[4\omega\ 5\omega\ 6\omega\ 7\omega]$。连接4个RX天线相位序列，由于是来自TX1与TX2的发射，得到序列$[0\ \omega\ 2\omega\ 3\omega\ 4\omega\ 5\omega\ 6\omega\ 7\omega]$，这与图4中一个TX以及8个RX天线得到的序列是相同的。可以说图5的2TX – 4RX天线配置合成了8个RX天线的虚拟阵列(隐含一个TX天线)。

为了概括之前的讨论，有$N_{TX}$以及$N_{RX}$个天线，使用者能够生成（有合适的天线摆放位置）一个$N_{TX}\times N_{RX}$虚拟天线阵列。因此，部署MIMO雷达技术，导致了（虚拟）天线数量的成倍增加，并造成了角度分辨率的增加。

如果$p_m$表示$m^{th}$TX天线(m=0，1…NTX)的坐标，$q_n$表示$n^{th}$RX天线的坐标(n=1, 2, … NRX)，那么对于所有可能的m和n的取值，虚拟天线的位置可以用$p_m+p_n$表示。例如图五，p1=0以及p2=4，q1=0，q2=1，q3=2以及q4=3(这里坐标使用d的单位，并且假设TX1(相对的是RX1)是TX (RX)天线的开始)。

图6展示了MIMO雷达的基本原理也能被拓展到多维的阵列。

不同的物理天线配置可以被用来实现同样的虚拟天线阵列。图7展示了这些配置，Fig. (a) 和 Fig. (b)的物理阵列合成了相同的虚拟阵列Fig.(c )。在这种情况，缓和板子上的空间摆放以及布线可能决定最终的选择。

4 Multiplexing Strategies for the MIMO Radar

Section 3 detailed how the MIMO radar works by having the same set of RX antennas process signals from transmissions by multiple TX antennas. It is important to note that the RX antennas must be able to separate the signals corresponding to different TX antennas (for example, by having different TX antennas transmit on orthogonal channels). There are different ways to achieve this separation[3], and two such techniques are discussed here: time division multiplexing (TDM) and binary phase modulation (BPM). These techniques are described as follows, in the context of frequency-modulated continuous-wave (FMCW) radars, though the techniques have much wider applicability. For an introduction to FMCW radar technology, see [5].

4.1 Time Division Multiplexing (TDM-MIMO)

In TDM-MIMO [1], the orthogonality is in time. Each frame consists of several blocks, with each block consisting of NTX time slots each corresponding to transmission by one of the NTX TX antennas. In
Figure 8, for an FMCW radar with NTX = 2, alternate time slots are dedicated to TX1 and TX2. TDM-MIMO is the most simple way to separate signals from the multiple TX antennas and is therefore widely used.

In a typical processing scheme for TDM-MIMO FMCW radar, the 2D-FFT (range-Doppler FFT[5]) is performed for each TX-RX pair. Each 2D-FFT corresponds to one virtual antenna. A radar with NTX = 2 and NRX = 4, would compute 4 × 2 = 8, and such range-Doppler matrices as shown in Figure 9. The 2D- FFT matrices are then noncoherently summed to create a predetection matrix, and then a detection algorithm identifies peaks in this matrix that correspond to valid objects. For each valid object, an angle- FFT is performed on the corresponding peaks across these multiple 2D-FFTs, to identify the angle of arrival of that object. Prior to applying angle-FFT, a Doppler correction step must be performed in order to correct for any velocity induced phase change.

4.2 BPM-MIMO

The TDM-MIMO scheme previously described is simple to implement, however, it does not use the complete transmission capabilities of the device (because only one transmitter is active at any time). Techniques exist which are centered on modulating the initial phase of chirps in a frame, which allow simultaneous transmission across multiple TX antennas while still ensuring separation of these signals. In BPM-MIMO, these phases are either 0o or 180o (equivalent to multiplying each chirp by +1 or –1). One such variant of BPM-MIMO is described as follows.

Similar to TDM-MIMO, a frame consists of multiple blocks, each block consisting of NTX consecutive transmissions. However, unlike TDM-MIMO (where only one TX antenna is active per time slot), all the
NTX antennas are active in each of the NTX time slots of every block. For each block, the transmissions from multiple TX antennas are encoded with a spatial code (using BPM), which allows the received data to be subsequently sorted by each transmitter. In TDM-MIMO, the power that can be transmitted in each time slot is limited by the maximum power that can be radiated by one TX antenna. Allowing simultaneous transmission on all the NTX transmitters (while still ensuring perfect separation by use of suitable spatial code) lets users increase the total transmitted power per time slot. This translates to an SNR benefit of 10log10 (NTX).

Figure 10 shows the technique, for the case of NTX = 2. Assume S1 and S2 represent chirps from the two transmitters. The first slot in a block transmits a combined signal of Sa = S1 + S2. Similarly the second slot in a block transmits a combined signal of Sb = S1 – S2. Using the corresponding received signals (Sa and Sb ) at a specific received RX antenna, the components from the individual transmitters can be separated out using S1 = (Sa+ Sb) / 2 and S2 = (Sa - Sb) / 2. For an example of NTX = 4, where separation is achieved using a 4 × 4 Hadamard code, see [3].

The processing chain is almost identical to the flow as described earlier in the context of TDM-MIMO, with the exception of a decoding block which enables the signal contributions from the individual TX antennas to be separated in the received data. This decoding must be performed before the angle-FFT (and ideally after the Doppler-FFT, in order to enable phase corrections due to non-zero velocity to be applied prior to decoding).

5 Implementing MIMO Radar on mmWave Sensors

The TI product line of mmwave sensors has the analog front end closely coupled with digital logic. This coupling allows considerable flexibility in designing the TX signal. Further, the state machine within the digital logic allows multiple chirp types and various kinds of frame sequences to be programmed up front, relieving the processor from the burden of controlling the front end on a real-time basis. APIs[4] which abstract out all the registers in the digital logic and present a simple and intuitive interface to the programmer are also provided. All this content amounts to a programming model that is easy to learn and easy on the processor.

Remember three concepts in mind when programming a TX signal: profile, chirp, and frame. Each of these concepts is briefly described as follows.

  • Profile: A profile is a template for a chirp and consists of various parameters that are associated with the transmission and reception of the chirp. This includes TX parameters such as the start frequency, slope, duration, and idle time, and RX parameters such as ADC sampling rate. Up to four different profiles can be defined and stored.

  • Chirp: Each chirp type is associated with a profile and inherits all the properties of the profile. Additional properties that can be associated with each chirp include the TX antennas on which the chirp should be transmitted and any binary phase modulation that should be applied. Up to 512 different chirps types can be defined (each associated with one of the four predefined profiles).

  • Frame: Frame is constructed by defining a sequence of chirps using the previously defined chirp types. It also possible to sequence multiple frames, each consisting of a different sequence of chirps.

    Thus, programming the device for a specific MIMO use case amounts to suitably configuring the profile, chirp, and frame.

Figure 11 shows the steps to configure a device for TDM-MIMO operation and Figure 12 shows the steps to configure a device for BPM-MIMO operation. For the message description corresponding to the profile, chirp, and frame configurations, see [4].

6 Reference

  1. FCRobeyetal.,MIMORadarTheoryandExperimentalResults,38thAsimolarConferenceonSignal, Systems, and Computers

  2. RYChiaoetal.,SparseArrayImagingwithspatially-encodedtransmits,IEEEUltrasonicsSymposium

  3. H.Sunetal.,AnalysisandComparisonofMIMORadarWaveforms,2014InternationalRadar

    Conference.

  4. mmWave SDK User’s Guide that is incuded in http://www.ti.com/tool/mmwave-SDK

  5. Introduction to mmWave Sensing: FMCW Radars

Appendix.1

Consider an object with an angle of arrival θ with respect to the radar. The signal reflected from the object and arriving at the RX antenna array has a spatial frequency of $\omega_1=\frac{2\pi}{\lambda}dsin(\theta)$.

Likewise, an object with an angle of arrival of θ + Δθ has a spatial frequency of $\omega_2=\frac{2\pi}{\lambda}dsin(\theta + \Delta \theta)$. Here the term spatial frequency refers to the phase-shift across consecutive antennas in the RX array.

Equation 5 gives the difference in the spatial frequency corresponding to these two objects.
$$
\Delta \omega=\omega_2-\omega_1=\frac{2\pi d}{\lambda}(sin(\theta + \Delta \theta)-sin(\theta))\tag5
$$
Noting that the derivative of sin(θ) is cos(θ), the expression sinM (θ + Δθ) – sinM (θ) can be approximated as cosM (θ)Δθ. Equation 5 now becomes Equation 6.
$$
\Delta\omega=\frac{2\pi d}{\lambda}(cos(\theta) \Delta \theta)\tag6
$$
We assume that two spatial frequencies separated by Δω will have distinct peaks in an N-point FFT, as long as their peaks are more than 2π / N away (corresponding to the size of an FFT bin). Thus, Equation 7 shows the condition for resolving the two objects in the angle-FFT.
$$
\Delta\omega>\frac{2\pi}{N}\rightarrow \frac{2\pi d}{\lambda}(cos(\theta)\Delta\theta)>\frac{2\pi}{N}\rightarrow \Delta\theta>\frac{\lambda}{Ndcos(\theta)} \tag7
$$
The resolution capability, θres, is usually quoted for an interantenna spacing of d = λ / 2 and for a bore- sight view (θ=0), yielding Equation 8.
$$
\theta_{res}=\frac{2}{N}\tag8
$$