## 4 Performance Assessment of Optical Wireless Networks-on-Chip
For a given transmitted optical input power \(\mathrm{P}_{\mathrm{in}}\), the received power can be computed as \(\mathrm{P}_{\mathrm{i}}=\mathrm{PG}_{\mathrm{i}}\cdot\mathrm{P}_{\mathrm{in}}\), where \(\mathrm{PG}_{\mathrm{i}}\) is the path gain of the channel between the i-th transmitter and the reference receiver \(\mathrm{RX}_{0}\). The performance analysis carried out in Section 5.2 assumes that all links use intensity modulation OOK with NRZ pulses and direct detection. If the bits of the data sources have the same probability of 1/2, the average power \(\mathrm{P}_{\mathrm{in,av}}\) of the modulated signal is one half of the power of the unmodulated carrier. The BEP is evaluated as a function of signal-to-noise ratio (SNR) and normalized interference powers (\(\mathrm{x}_{\mathrm{i}}\), i = 1,..., J), where \(\mathrm{SNR}=4\gamma^{2}\), with \(\gamma=\mathrm{n}_{\mathrm{PD}}\cdot\mathrm{P}_{0}/(2\sigma_{\mathrm{th}})\) depends on the unmodulated received power, the responsivity \(\mathrm{n}_{\mathrm{PD}}\) of the photodetector and the standard deviation \(\sigma_{\mathrm{th}}\) of the additive Gaussian noise at the receiver. Since the thermal noise is the dominant noise most often associated with p-i-n receivers (at least for low level of detected power) [34], noise variance \(\sigma_{\mathrm{th}}^{2}\) does not depend on transmitted bits and can be computed as \(\sigma_{\mathrm{th}}^{2}=4\cdot\mathrm{K}\cdot\mathrm{T}_{\mathrm{eq}}/(2 \cdot\mathrm{R}_{\mathrm{L}}\cdot\mathrm{T})\), where \(\mathrm{K}\) is the Boltzman's constant, \(\mathrm{T}_{\mathrm{eq}}\) is the noise temperature of the receiver, \(\mathrm{R}_{\mathrm{L}}\) is the resistance of the receiver and \(\mathrm{T}=1/\mathrm{R}_{\mathrm{b}}\) is the bit interval of the transmitted data. Here, as a reference, the values of system parameters in Table 3 are considered for the numerical evaluations [34,42]. Figure 6: Optical Wireless Networks-on-Chip scenario with a single (**a**) and with two (**b**), parallel interfering link(s). In particular, the method in [40; 41] is used to analytically evaluate the BEP by taking into account all the random variables (RVs) in the optical wireless communication system. The RVs include the bits sent by all transmitters, the optical carriers phases and time offsets of the asynchronous interfering links, and the Gaussian noise. It is worth mentioning that inter-symbol interference is here neglected, i.e., the delay spread related to multipath propagation is assumed (much) smaller than the bit time interval. Based on a reverberation model, delay spread was estimated equal to some nsec. at mmWave (300 GHz) and roughly one order of magnitude lower at 100 THz [24]. As the on-chip environment is not fully reverberating, first experimental assessments in the mmWave band returned lower values, e.g., equal to 100 psec. in [12], which might therefore correspond to about 10 psec. in the infrared/optical bands. In order to avoid inter-symbol interference, T >> 10 psec. is required, i.e., \(\rm{R_{b}}\leq 10\) Gbit/s is approximately needed. According to these considerations, \(\rm{R_{b}}=10\) Gbit/sec. has been therefore set in Table 3 as a main target. This value is of the same order of magnitude as the channel throughput considered in previous studies [4; 6; 8; 17; 35; 43].