Molecular Communications and Nanonetworks by Barış Atakan

Author:Barış Atakan
Language: eng
Format: epub
Publisher: Springer New York, New York, NY

where μ x and σ x are

(2.258)

Using X n and Z n , for the case in which the TN sends 1 at slot n, the total number of molecules received during slot n, i.e., Y n , can be expressed as

(2.259)

Hence, Y n also follows a normal distribution, i.e.,

(2.260)

where and . Then, for the case in which the TN emits bit 1, the probability of error, i.e., p e 1, is

(2.261)

where is the cumulative distribution of Y n and can be given as

(2.262)

where erf(⋅ ) is the error function. In the case in which the TN emits bit 0, the TN emits no molecule at the beginning of slot n. This can be interpreted as X n  = 0. Therefore, in this case, Y n is equal to Z n and the probability of error, i.e., , can be given as

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