The picture shows a M-by-N MIMO radar system. Suppose that a target is located at u, the ${\displaystyle \scriptstyle m^{th}}$  transmit antenna is located at ${\displaystyle \scriptstyle x_{T,m}}$  and the ${\displaystyle \scriptstyle n^{th}}$  receive antenna is located at ${\displaystyle \scriptstyle x_{R,n}}$ . The received signal at ${\displaystyle \scriptstyle n^{th}}$  receive antenna can be expressed as:

${\displaystyle y_{n}(t)=\sum _{m=1}^{M}x_{m}(t)e^{j{\frac {2\pi }{\lambda }}u^{T}(x_{T,m}+x_{R,n})}}$ 

As mentioned earlier, if {${\displaystyle \scriptstyle x_{m}(t)}$ , m=1, ..., M} is an orthogonal set, we can extract M signals from ${\displaystyle \scriptstyle n^{th}}$  receive antenna, each of which contains the information of an individual transmitting path(${\displaystyle \scriptstyle u^{T}(x_{T,m}+x_{R,n})}$ ).

In order to make a comparison between phased array radars and MIMO radars, the relationship between transmit/receive antenna arrays and virtual arrays are discussed in several sources.^[5][1][6] If the placements of the transmit and receive antenna array are expressed as two vectors ${\displaystyle \scriptstyle h_{T}}$  and ${\displaystyle \scriptstyle h_{R}}$  respectively, the placement vector of the virtual array is equal to the convolution of ${\displaystyle \scriptstyle h_{T}}$  and ${\displaystyle \scriptstyle h_{R}}$ :

${\displaystyle h_{V}=h_{T}*h_{R}}$ 

Picture above shows the examples of antenna geometry to form a virtual array. In the first example, two uniformly distributed antenna arrays form a 5-element virtual array despite having 6 antennas in total. In the second example, a nine-element virtual array is obtained by increasing the distance between the transmit antennas, implying that a better spatial resolution can be achieved.

To estimate the direction of arrival of the targets according to the N*M signals, methods like MUSIC (algorithm) and maximum likelihood estimation are commonly used with good results.^[7][8]

There are a variety of orthogonal signal sets used in the field of MIMO radar. One of the proposed signal sets is the spectrally interleaved multi-carrier signal, which is a modified version of orthogonal frequency-division multiplexing signal.^[9] In this approach, the total amount of available subcarriers is distributed among different transmit antennas in an interleaved way.

Another proposed signal set is orthogonal chirp signal, which can be expressed as:

${\displaystyle x_{m}(t)=\exp \left(2\pi j(f_{m,0}t+{\frac {1}{2}}kt^{2})\right)}$ 

By choosing different initial frequencies ${\displaystyle \scriptstyle f_{m,0}}$ , these chirp waveforms can be made orthogonal.^[10]