page_title: MIMO radar
section_title: The concept of virtual array
hierarchical_section_title: MIMO radar / The concept of virtual array
caption_attribution_description: English: Scenario of virtual array analysis
context_page_description: Multiple-input multiple-output radar is 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 may also be used to obtain low-probability-of-intercept radar properties.
  In a traditional phased array system, additional antennas and related hardware are needed to improve spatial resolution. MIMO radar systems transmit mutually orthogonal signals from multiple transmit antennas, and these waveforms can be extracted from each of the receive antennas by a set of matched filters. For example, if a MIMO radar system has 3 transmit antennas and 4 receive antennas, 12 signals can be extracted from the receiver because of the orthogonality of the transmitted signals.
context_section_description: The picture shows a M-by-N MIMO radar system. Suppose that a target is located at u, the  transmit antenna is located at  and the  receive antenna is located at . The received signal at  receive antenna  can be expressed as:
  As mentioned earlier, if {, m=1, ..., M} is an orthogonal set, we can extract M signals from  receive antenna, each of which contains the information of an individual transmitting path().
  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. If the placements of the transmit and receive antenna array are expressed as two vectors   and  respectively, the placement vector of the virtual array is equal to the convolution of  and :
  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.
caption: Scenario of virtual array analysis
exif: {}