# Radar MIMO Virtual Antenna Array Formation

Referring to the figure attached above, is the ordering of the virtual antenna arrays (shown on the right) to measure azimuth and elevation angles of arrival correct? In my understanding, the ordering of virtual antennas arrays doesn't seem right. For example, the top horizontal row, which is supposed to measure the azimuth angle of arrival, should be 4 (TX1-RX4), 1 (TX1-RX1), 8 (TX2-RX4), 5 (TX2-RX1).

My reasoning for this order is that the distances between all the virtual antennas should be the same i.e., lambda/2 (e.g., as shown in Wenguang Mao - Approaches for Angle of Arrival Estimation, slide 9).

Assume the distance between TX1 and RX1 is d. Then, the effective distances for all four pairs (based on the order shown in the figure) will be d, d-lambda/2, d+lambda, and d+lambda/2. As you can see, they are not equally spaced.

Based on the order I mentioned i.e., 4 (TX1-RX4), 1 (TX1-RX1), 8 (TX2-RX4), 5 (TX2-RX1), the effective distances will be d-lambda/2, d, d+lambda/2, and d+lambda. In this case, all elements have an equal spacing of lambda/2.

An application report from Texas Instruments, MIMO Radar (Rev. A), gives a good insight into the MIMO radar virtual antenna array arrangement method.

In the report, on Slide-4; $$p_{m}$$ and $$q_{n}$$ notations dictate the cartesian coordinates of $$m^{th}$$ and $$n^{th}$$ TX (transmitter) and RX (receiver) in terms of the distance $$d$$ which is;

$$d = {\lambda}/2m$$

for providing the MIMO radar with the widest posible view angle (field of view, FOV) $$\theta_{FOV}$$ of $${\pm}90^{\circ}$$ or $$180^{\circ}$$ in total.

Those coordinates are found by creating separate axes for both TX and RX group. And, the reference points i.e. origins of those axes are determined so that a suitable virtual antenna array is formed by naming each virtual antenna group as $$TX_{m}-RX_{n}$$ as in the figure in your question.

So, in order for us to go further, we need to examine the hardware of concern. When I’ve first examined the PCB configuration, in order for me to be able to apply the principles in TI’s document, I’ve assumed that the RX group forms a square and the center of gravity of this square and both TX1 and TX2 are on the same axis. I’ve wanted to illustrate this assumption in the figure below:

The axis that is shared between the RX square’s centre of gravity and TX1-TX2 automatically places the correct origin points for the TX and RX cartesian coordinate systems. Now, we can continue to analyse the MIMO radar. The below image shows the build-up process and the result of the analysis:

According to the results that I’ve obtained, the virtual antenna array formation is correct. Both the horizontal and vertical spacings between each one of the TX-RX couples are the same and their magnitude is $$d = {\lambda}/2 m$$.

• Thanks! I had a misunderstanding. Your answer cleared it up. Commented Aug 11, 2021 at 22:30