End-to-end throughput of AdHoc network chain

End-to-end throughput of AdHoc network chain

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We can derive end-to-end throughput decline curve as the length of AdHoc chain increases.

$$ Capacity = B log_2(1 + SNR) $$

This is Shannon capacity, and the following is the derived equation.

$$ Throughput = C log_2\left(1 + \frac{SNR}{1 + SNR \sum\limits_{n = 2\frac{IR}{D}}^{h – 1} \frac{1}{\left(\left\lfloor \frac{n}{2}\right\rfloor + 1\right)^2}}\right) / min\left(2 \frac{IR}{D}, h\right) $$

where \(C\) is a magic constant number, \(SNR\) is signal-to-noise ratio (not in dB), \(IR\) is interference radius obtained by experiment, \(D\) is the distance between two adjacent nodes, and \(h\) is the number of hops in the adhoc chain. Note that \(SNR\) is not in dB. \(SNR\) = Signal_in_Watt / Noise_in_Watt.

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