In a previous post, we have seen that MIMO fading capacity is much higher than AWGN capacity with multiple antennas. How is this possible? How can randomness added by a fading channel help us? In this post, we try to find the reason for this. Letâ€™s assume the following signal model for a Multi Input Multi Output antenna system.

x=Hs+w

Here s is the N_{T} by 1 signal vector, w is the N_{R} by 1 noise vector and H is the N_{R} by N_{T} channel matrix. The received signal vector is represented by x which has dimensions of N_{R} by 1. In expanded form this can be written as (assuming N_{R}=4 and N_{T}=4):

In a previous post we had discussed MIMO capacity in a fading environment and compared it to AWGN capacity. It sometimes feels unintuitive that fading capacity can be higher than AWGN capacity. If a signal is continuously fluctuating how is it possible that we are able to have reliable communication. But this is the remarkable feature of MIMO systems that they are able to achieve blazing speeds over an unreliable channel, at least theoretically. It has been shown mathematically that an NxN MIMO channel is equivalent to N SISO channels in parallel.

There is a 3 way race for 5G leadership in the US between T-Mobile(+Sprint), Verizon and AT&T. There are competing claims for the number of 5G subscribers, coverage area and download speeds. But let us look where the 5G industry stands today compared to the expectations a few years back. More than 80% of US population lives in urban areas which comprise of 2% of the total land area of about 10 million squared kilometers. That is 80% of the population lives in an area of about 200,000 squared kilometers.

Frequency Reuse is a well known concept that has been applied to wireless systems over the past two decades e.g. in GSM systems. As the name suggests Frequency Reuse implies using the same frequencies over different geographical areas. If we have a 25MHz band then we can have 125 GSM channels and 125*8=1000 time multiplexed users in a given geographical area. Now if we want to increase the number of users we would have to reuse the same frequency band in a geographically separated area. The technique usually adopted is to use a fraction of the total frequency band in each cell such that no two neighbor cells use the same frequency. Typically the frequency band is divided into 3 or 7 cells.

The division of the frequency band in to smaller chunks reduces the system capacity e.g. one cell with 25 MHz bandwidth would have much higher capacity then 7 cells having 3.5 MHz each. To overcome this problem a frequency reuse of 1 has been proposed i.e. each cell has the full system bandwidth (nearly). The problem of co-channel interference at the cell boundaries is resolved by dedicating a small chunk of the available spectrum for the cell edges.

In Soft Frequency Reuse (SFR) the cell area is divided into two regions; a central region where all of the frequency band is available and a cell edge area where only a small fraction of the spectrum is available. The spectrum dedicated for the cell edge may also be used in the central region if it is not being used at the cell edge. The lack of spectrum at the cell edge may result in much reduced Shannon Capacity for that region. This is overcome by allocating high power carriers to the users in this region thus improving the SINR and the Shannon Capacity.

Note:
1. The Signal to Interference and Noise Ratio is given as:
SINR=Signal Power/(Intercell Interference+Intracell Interference+AWGN Noise)
2. Typically the term capacity was used to describe the number of voice channels (or users) that a system can support. But with modern digital communication systems it usually refers to the Shannon Capacity that can be achieved (in bits/sec/Hz).

[1] Yiwei Yu, Eryk Dutkiewicz, Xiaojing Huang, Markus Mueck and Gengfa Fang, “Performance Analysis of Soft Frequency Reuse for Inter-cell Interference Coordination in LTE Networks”, ISCIT 2010.

The uplink capacity of a WCDMA cell also known as the pole capacity is given as:

N=(W/R)/((Eb/Nt)*v*(1+a))

where

W is the spreading bandwidth fixed at 3.84MHz

R is the radio access bearer bit rate e.g. 12.2kbps

Eb/Nt is the energy per bit to noise power spectral density ratio e.g. 5dB

v is the voice activity factor which depends upon the vocoder, channel coding and actual application e.g. 0.5

a is the other-cell to in-cell interference ratio e.g. 0.65

Using the above values the pole capacity of the WCDMA cell is calculated as 120. In the case of a mobile UE (3km/hr) the required Eb/Nt may be as high as 12dB resulting in pole capacity of 24. The actual capacity is obtained by multiplying the pole capacity with network loading factor which maybe taken as 0.75 in this example resulting in an uplink capacity of 18.