# End-to-end throughput of AdHoc network chain

## End-to-end throughput of AdHoc network chain

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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