Mm-wave frequency bands are very appealing for telecommunication engineers due to available bandwidth and high data speed possibilities.  However, working with high frequencies brings new challenges such us extremely path loss and diffraction. Combining antennas into arrays to achieve higher gain is one of the possible solutions.

## What is the cumulative distribution function (CDF) and why it is so important?

While working with antenna arrays you might face decreasing beamwidth due to natural array physics and to overcome that antenna systems have to be able to scan in wide angles. The sum of all possible scan angles of an array can be observed as a total radiational pattern. Ideally, we aim to have omnidirectional coverage, but it is not possible in real life. As metrics for spherical coverage antenna gain, transmitter power, and transmission loss are considered. In the 3GPP specification, spherical coverage is specified by the cumulative distribution function (CDF) of EIRP, which is a combination of transmitted power and array gain. On figure 1 difference between array, radiation pattern, and total scan pattern is shown.  Figure 1: On the left – array radiation pattern, on the right – total scan pattern for -60; 60-degree range.

## How to calculate CDF in your design?

CST Studio Suite offers 2 ways to calculate CDF based on total scan pattern: schematic approach and electromagnetic simulation. Schematic way of calculating CDF based on “Array task” and using its default variables for scanning. To get the final result you would create several sweeps for scanning angles in the schematic section.

The electromagnetic (EM) approach allows us to calculate everything in a 3D interface without creating a virtual array but taking into account all coupling between elements. It uses Post Processing features to create combined results, scan through required angles, and calculate CDF. It is possible to assign custom amplitudes for the array to include transmitted power level and calculate real EIRP.

A comparison between 2 approaches of calculation can be seen in figure 2. Figure 2: Blue curve – CDF calculation using the schematic method, red line – CDF calculation using 3D EM method. CDF vs. Realized Gain

As you can notice EM approach shows a much smoother curve than a schematic one. It happens because the second way of calculation uses parametric sweep when creating a total scan pattern, so theoretically it is possible to assign a denser sweeping angle but calculation time will increase dramatically.

## How to understand if the simulation results are trustworthy?

There are two metrics for EIRP: one measured at CDF=50% and means that half of the sphere covered with required EIRP. The second one is the maximum EIRP at CDF=100%, which shows the peak EIRP value of the array. As can be seen in figure 2 both metrics are slightly different in schematic and EM calculation approaches. Overall, based on numerous simulations and comparisons, the EM method is more trustworthy as it takes into account real array behavior.

CDF calculations are very important when it comes to 5G antennas. You should design your array in such a way that it meets all coverage and gain requirements to achieve the best possible performance. When you have a multiband antenna, which covers several mm-wave bands, calculation time becomes a significant factor, because you need to check if you meet requirements over the whole working band. 3D EM approach, which was presented in CST 2020, allows calculating broadband characteristics much faster when in schematic approach calculation time multiply by a number of every additional frequency monitor.

Disclaimer: The views and opinions expressed in this article are those of the author. It is intended only as a sharing of antenna design knowledge for educational purposes.

Katerina GalitskayaSenior Antenna Engineer