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# Channel Capacity Definitions

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#### urwelcome

##### Banned
Dear friends,

What capacity is when defined as "bits per channel use"
"bits per complex dimension"
"bits per symbol"
"bits per second"

I dont understand the difference between them..

plz if you can explain it..

thanks ...A lot of thanks

capacity bits per channel use

Those four are definition (in information and comm. theory) which you have to understand within the context.

1. Bits per channel use: Number of bits a transmiter send at one time to a receiver via a channel. You can imagine there is a pipe with a certain diameter (ex: 10 cm). Let say one end of the pipe is at a roof, and the other end is close to the ground. You are at the roof and try to "send" apples to the ground through the pipe. Let assume also that an apple has dimension of 4 cm. So at one time (i.e. per pipe use) you can only "transfer" 2 apples. If you have oranges, then you might be able to transfer more than 2 oranges per pipe use.

2. Bits per complex dimension.
A signal can be represented as a point in signal space which is a complex plane. For example a QPSK signal has 4 points at +1, -1, +j, -j. For QPSK, each point corresponds to two bits, i.e. +1 -> 00, +j -> 01, -1 -> 11, -j -> 10 (with gray coding). So for QPSK you have 2 bits per complex dimension.

3. Bits per symbol.
One symbol (M-ary modulation) corresponds to several bits. Ex.: QPSK, one symbol (+1 or -1 or +j or -j) corresponds to two bits.

4. Bits per second.
This must be clear, i.e. how many bits in one second. You can transmit one bit per second with the period of each bit is 1 second, or you can transmit 2 bits per second with period for each bit is 1/2 second, or you may transmit one QPSK symbol in 1 second (1 QPSK symbol corresponds to 2 bits).

best

mtaheri

Points: 2

### mtaheri

Points: 2
Re: Channel Capacity

Bit per symbol:

for example if the channel capacity of certain fading channel is 2bits per symbol than does it mean that we can use only QPSK (2 bits per symbol) and we can not use 16QAM (4bits per symbol) ??

If this is so than again this does not give us rate i,e how fast can we send the data on a channel. It says how many bits can be transmitted by one symbol but does not say how many symbols can be sent per second.

If channal capacity is given in "bit per channel use" than how to covert that capacity in "bits per second"

thank .........thanks a lot.

Channel Capacity

Capacity is measured by number of bits per channel use. Time needed for one channel use depends on the system and channel. It can be one channel use is 1 second or only 1 ms.

If you are given a channel able to transmit 2 bits (QPSK) per 1ms (one channel use), then you can still transmit 4 bits (16QAM) within 2 ms. But you cannot transmit this 4 bits in 1 ms interval.

Usually, in practice, the capacity of a channel is measured by number of bits per second.

To convert bits per channel use to bits per second, it is simply you have to know how long is one channel use, then divide 1s with that number.

best

Points: 2