Minimum Redundancy in MIMO Arrays

The concept of multiple-input multiple-output communications dates back to academic papers from the 1970s, primarily concerning transmission of digital data between communications systems over multiple channels. In wireless systems, the same idea applies in an effort to increase the number of end users served by a network or device. This is taken to the extreme in today’s 5G deployments and in the most advanced radar systems, where many antenna elements are placed into a small area.

The goal in these systems is gain maximization through beamforming, as well as serving multiple users during operation (in 5G) or tracking multiple objects (in radar) with a single compact system. Although this offers higher spatial resolution for a given beam, these systems are becoming overly complex due to the large, dense arrays of co-located antennas. The design of minimum redundancy arrays aims to reduce the complexity of MIMO systems without compromising operational performance.

Minimum Redundancy for a MIMO Linear Antenna Array

All MIMO antenna arrays operate as a group of receiving and transmitting antenna elements, and together they operate as an equivalent set of antennas known as a virtual array. The virtual array for a group of MIMO antennas determines the resolution and gain in the system in both broadcast and receive mode. In essence, if we have a group of N(Tx) antennas and N(Rx) antennas in an array, the array performs equivalent to an array with the product of elements:

Because gain and Q-factor for an array are proportional to the number of virtual elements, the recent trend in MIMO array construction is to maximize the number of antenna elements within the available board or enclosure space. MIMO arrays for small 5G cells and small radars can be very dense with dozens of virtual elements.

Packing more and more elements into an antenna array leads us to realize two properties of a virtual array:

• Redundancy, where the spacing between antenna elements is repeated
• Overrepresentation, where virtual elements overlap each other in the virtual array

As the number of elements grows, the complexity of the board increases and the system cost increases, as well as the complexity in the system assembly. If the radar is being packaged as a module on a PCB, then the PCB can get very complex with an entire layer being dedicated only to antennas and transceivers.

Regarding the two properties above, only overrepresentation is a problem that should be avoided with careful antenna spacing. Redundancy is not a problem, but with an alternative placement of the antenna elements, the operation of the array can be improved.

Achieving Minimum Redundancy

Redundancy refers to the property of a virtual array where the virtual elements have repeated spacings. This is most commonly seen in simple linear arrays with co-located Rx and Tx elements, producing the uniform linear array shown below.

These Rx and Tx arrays produce a uniform linear MIMO array with maximum redundancy.

In the above example, it’s clear that we have a single redundant spacing throughout the system. For a given number of antenna elements N, there exists a configuration of Rx and Tx elements that minimizes the number of redundant spacings between the elements in the virtual array. It should be noted that there are also zero-redundancy systems for N = 1 to 4. With a simple rearrangement of the elements, we can achieve a minimally redundant linear array as shown below.

This virtual array exhibits minimum redundancy among repeating Tx groups in the virtual array.

Odd Spacings Give Larger Apertures

Using odd spacing as shown above offers an important advantage in terms of the operation of the radar system: by spreading out the radar elements to minimize redundant spacings, the array’s aperture can be maximized. Because the number of virtual elements has not changed, the resolution of the system remains constant. Beamforming can also still be implemented by setting the phase of the broadcast signals in each antenna (analog beamforming), although digital beamforming or hybrid beamforming will be superior for generalized implementations over broad fields of view.

The simulation example below compares the normalized gain from a uniform MIMO array and a minimally redundant MIMO array without mainlobe interference. The larger array spacing clearly leads to much sharper mainlobe and overall higher gain at broader angles. More about this type of array as used in radars can be found at the following source:

• Chen, Chun-Yang, and Palghat P. Vaidyanathan. "Minimum redundancy MIMO radars." In 2008 IEEE International Symposium on Circuits and Systems (ISCAS), pp. 45-48. IEEE, 2008.

If we build a 2D array with multiple minimally redundant arrays, you can use spatial/temporal multiplexing to separate the subarrays such that each subarray has maximum aperture. Further research into construction of minimal redundancy arrays in a general 2D case is an ongoing problem in the research literature on radar systems.

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