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# What is ergodic channel

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#### cwjcwjcwj

##### Full Member level 5
ergodic channel

What is ergodic and non ergodic channel in MIMO systems?

#### House_Cat

ergodic capacity definition

Definition of Ergodic: A stochastic process is ergodic if no sample helps meaningfully to predict values that are very far away in time from that sample.

- Ergodic channel

* The channel gain process is ergodic, i.e., the time average is equal to the ensemble average. In other words, the randomness of the channel gain can be averaged out (removed) over time. So long-term constant bit rates can be supported.

- Non-ergodic channel

* The channel gain is a random variable and does not change with time. The channel gain process is stationary but not ergodic, i.e., the time average is not equal to the ensemble average. In other words, the randomness of the channel gain can not be averaged out (removed) over time. So long-term constant bit rates can not be supported

hatimha85

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### hatimha85

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#### springf2000

##### Full Member level 6
definition of ergodic capacity

the time average of the signal is the same as the collective average

#### amir_rastegar2003

ergodic channel capacity

ergodic is equal to " quasi-static"?? or they are two differet concepts?

#### boy

what is meant by ergodic channel capacity

Ergosic and quasi-static are different. In the quasi-static case the shannon capacity does not exist. THey have to use the outage capacity instead while in the ergodic channel, the shannon capacity is well define since the shannon capacity is the average concept. Hence, the channel must be varied in some senses. To make thing simple...

Ergodic capacity -> you get a number as a capacity such as 10 bps/Hz
Quasi-static capacity -> you get a cdf/ccdf plot of the capacity and you get only a probability to communicate at a given rate.

ahmeddeia

### ahmeddeia

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#### amir_rastegar2003

ergodic channels

boy said:
Ergosic and quasi-static are different. In the quasi-static case the shannon capacity does not exist. THey have to use the outage capacity instead while in the ergodic channel, the shannon capacity is well define since the shannon capacity is the average concept. Hence, the channel must be varied in some senses. To make thing simple...

Ergodic capacity -> you get a number as a capacity such as 10 bps/Hz
Quasi-static capacity -> you get a cdf/ccdf plot of the capacity and you get only a probability to communicate at a given rate.

thanks for your help. can you introduce a good reference to understand these concepts?

thanks again

#### boy

non-ergodic channels

i understand all from this paper

Tahid and ahmeddeia

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### Tahid

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V
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#### amir_rastegar2003

how to plot ergodic capacities

again thanks for your help "boy"

it is a cery good paper about MIMO system's capacity.

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