Why have five Gsm operators in Nigeria

Telecommunication Frequencies

There are practically four telecommunication frequencies. These frequencies are 850Mhz,  900Mhz, 1800Mhz and 1900Mhz.  The 900Mhz is called the GSM frequency because it is the base frequency for every GSM network. It is usually used for longer coverage. The other GSM frequency is the 1800Mhz (read Eighteen hundred frequency) is used for wider coverage. It can be used together with the 900Mhz frequency to provide both distant coverage and wider coverage at the same time. This can only be in a dual band environment. Nigeria is a dual band country so both frequencies can be used as described above.

Range of Frequencies within the 900Mhz.

The 900Mhz begins from 890Mhz to 960Mhz. The frequency range from 890Mhz to 915Mhz is used as the uplink frequency while the frequency from 935Mhz to 960Mhz is used as a downlink frequency. The difference between the uplink frequency and the downlink frequency is called duplex frequency which is 45Mhz. This is calculated by subtracting 915Mhz from 960MHz.

Range of frequencies within the 1800Mhz 

Like the 900Mhz, the range 1710Mhz to 1785Mhz is used for uplink while 1805Mhz to 1880Mhz is used for downlink. The duplex frequency is 95Mhz.

Frequency Division Multiple access (FDMA)

FDMA is communication protocol that divides a given frequency in carriers or channels such that each user in the network is allowed to stay within a given frequency for a period of time called dwell time before it is hopped to another frequency. FDMA uses a time slot to assign frequencies to subscribers within the network. This time slot is based on The Time Division Multiple Access (TDMA).
How does FDMA work?
In Nigeria the GSM plan is designed to accommodate only 5 operators. This 5 operators is got from a simple mathematics. It is done by subtracting the frequency range, using the uplink range which begins from 890Mhz to 915Mhz use will get 25Mhz when subtracted and if you decide to use the downlink which begins from 935Mhz to 960Mhz you will get same result. See the 25 channels or carriers below.
(1) 890.0   (2) 890.2  (3) 890.4  (4) 890.6 (5) 890.8
(6)  891.0.  (7) 891.2. (8) 891.4  (9) 891.6. (10) 891.8
(11) 892.0  (12) 892.2  (13) 892.4  (14) 892.6 (15) 892.8
(16) 893.0  (17) 893.2  (18) 893.4. (19) 893.6 (20) 893.8
(21) 894.0  (22) 894.2  (23) 894.4 (24) 894.6  (25) 894.8
The difference between each is 200khz which is equivalent 0.2Mhz. This frequency is called the channel frequency and is used to avoid interference. That the difference you get when you subtract 890.0 from 890.2. If that is the  uplink frequency one operator say MTN Nigeria is operating on then the uplink frequency for next operator will begin from 895. For a better understanding see the uplinks and downlink frequency range below.
890, 895, 900, 905, 910, 915, 920, 925, 930, 935, 940, 945, 950 955, 960.  The frequencies 920, 925 and 930 are not assigned to any operator. They are called the Guard band Frequencies. By this plan each operator will operate on one uplink frequency and one downlink frequency. Now FDMA takes one of the frequencies and divides it into 25 carriers or channels and allocate them to different subscribers using a time frame protocol.
The Time Division Multiple Access (TDMA)
This is a protocol that allows many subscribers to share one frequency within a time slot. A TDMA frame consist of 8 short time units. These units are also called physical channels. Each connection is allowed one time slot and a time slot is equal to 0.557ms(milliseconds). A TDMA frame is 4.62ms long.
The E1
The E1 is a broadband link of 32 channels or time slots of which 30 channels are used for traffic carriage and 2 channels for signaling and synchronization. Mathematically the speed of 1 E1 is given as
E1 = 32 x 64 kbps
       = 2048kbps
      = 2.048mbps
Where 64kbps is the speed of one channel which is the standard telephone bit rate. If 64kbps is the telephone bit standard where is the 64 coming from? I know that is the question that will come into your mind now. The world of science is full of laws, principles theorems and hypothesis. This will take us to the theorem below.

The Nyquist theorem: the theorem states that if a signal is sampled at a regular interval of at least twice the highest channel frequency, the sample will contain enough information to accurately reconstruct the signal. By this theorem if 8000 signals are sampled then 8000 multiplied by 8bits/sec will give 64000bits/sec. This is equal to 64kbps, the speed of the E1. 

What is Pulse Code Modulation (PCM)?
PCM is the process of converting analog signal to digital signal. The process is through sampling, quantization, code and compression. The E1 frame is called the PCM-30 frame. The PCM Frame is a 32 channel link of the E1. The frame is numbered from 0 to 31 where channel 0 is used for synchronization and channel 16 for signaling.
The TDMA frame which an eight time slot is got by dividing the PCM frame by four. This accounts for the 8 time slot mentioned earlier above.