A Holistic Approach to Wireless Design Through Physics Based Simulations
Geometry
For this workflow we use a base-station with 3 separate antenna arrays each covering a 120 degree sector. For each individual array we use a connected slot array with 16 elements backed by a pec plate. The arrays are designed at 5 [GHz] with elements spaced at half-wavelength. The city geometry is imported from open street maps with latitude and longitude specified to represent the city center of Los Angeles. The import consists of buildings, roads and terrain each assigned as concrete. The base-station array locations are chosen so that they are at the top of buildings. For the user-equipments (UEs), we use omnidirectional uniform linear arrays with 2 Hertzian dipole elements. The 4 users are placed on the road at different locations. Each individual UE to base-station link is a 2x16 MIMO system.
Uplink System Configuration
Consider an uplink system in which the 4 UEs are transmitting to the base-station utilizing an orthogonal frequency division multiple access scheme. The 4 devices are operating at 5 [GHz] over a frequency band of 100 [MHz]. As an example, we consider a system with 10 subcarriers where each subcarrier has a dedicated 10 [MHz] bandwidth. We assume that users 1 and 3 share the first 5 subcarriers in the lower part of the band while users 2 and 4 share the other 5 subcarriers in the upper part of the band. The image on the right displays the locations of the users 1 and 3 interfering over the first 5 subcarriers as well as the base station sector which was designed to connect the two users to the cellular network. The next section will demonstrate how this particular sector base-station achieves the highest rate for the two UEs.
Post-Processing
Assuming -90 [dBm] of noise power at the base station and 100 [mW] of transmit power for the UEs (50mW per antenna), we calculate the MIMO capacity of user 3 over each subcarrier to every one of the base stations. As can be seen, base station 4 has the best connection to user 3 with about 110 [Mb/s] of rate for each subcarrier which is equivalent to about 11 bits per transmission and would require 2048 QAM modulation order. The base-station with the best connection is also displayed above in the uplink system configuration section. This is intuitively expected from the geometric set-up as that base station's sector has its main beam pointing at the two UEs. Also notice that even while the two UEs are interfering over the subcarriers at the base station, with a MIMO array and optimal receiver processing the interference is mitigated and very high rate per symbol is achieved.
Choosing base station 4 as our choice to connect user 3, we compare 3 linear detection schemes to the ultimate achievable rate limit. The 3 linear detection schemes are maximal ratio combining (MRC), zero forcing (ZF) and linear minimum mean squared error (LMMSE) detection. As is expected the LMMSE is the best linear detection scheme. LMMSE utilizes the knowledge of the interference channel to obtain the best estimate of the transmitted symbols before decoding. However the rate achieved by LMMSE is significantly lower than the ultimate achievable rate due to its symbol by symbol decoding structure. ZF and MRC detectors fail to deliver good data rates because of strong interference from user 1.
When we plot mutual information against transmit power we expect the ZF receiver to be inferior to MRC at low transmit powers and to become increasingly better at higher transmit powers. In the ideal scenario with no noise/interference the zero-forcing receiver can perfectly invert the channel and so it would become equivalent to the LMMSE detector. On the other hand at low transmit powers, the MRC and LMMSE receivers are essentially equivalent. Both of those intuitive results are verified in this workflow.