## 3 Simulation Results and Discussion
As in the previous case, the optical power contribution from a bulb \(E\) can be calculated by:  
\[P_{bg}=\frac{1}{d^{2}}R_{E}(\theta,\,2)A_{eff}(\psi)+\sum_{j=1}^{M-1}p_{k}. \tag{34}\]  
Figure 5: Delay spread for the sectored angle-diversity receiver (SDR), the conventional angle-diversity receiver (CDR) and the self-orienting receiver (SOR) as a function of the emitter-receiver distance along the diagonal from northwest (negative values) to southeast (positive values). Assuming typical parameters for a receiver that relies on a FET-based transimpedance preamplifier, i.e., \(k\) = 1.38 \(\times\) 10\({}^{-23}\) J/K, \(T\) = 295 K, \(\eta\) = 175 pF/cm\({}^{2}\), \(R_{f}\) = 10 k\(\Omega\), \(g_{m}\) = 40 mS, \(C_{g}\) = 1 pF, \(R_{D}\) = 146 \(\Omega\), \(\Gamma\) = 1.5, \(K\) = 294 fA, \(a\) = 1, \(I_{D}\) = 20 mA, \(I_{2}\) = 0.562, \(I_{3}\) = 0.0868, and \(I_{f}\) = 0.184, Equation (25), which defines the thermal noise, can be expressed just in terms of the physical area of the photodetector. Thus, the thermal noise can be easily computed for each photodetector element of the angle-diversity receiver used in the link. Figure 7 shows the SNR as function of the emitter-receiver distance along the northwest-southeast diagonal for the three angle-diversity receivers, when MRC, EGC, and SB are applied. In general, CDR  
Figure 6: Path loss for the sectored angle-diversity receiver (SDR), the conventional angle-diversity receiver (CDR) and the self-orienting receiver (SOR) as a function of the emitter-receiver distance along the diagonal from northwest (negative values) to southeast (positive values). Figure 7: SNR for the sectored angle-diversity receiver (SDR), the conventional angle-diversity receiver (CDR) and the self-orienting receiver (SOR) as a function of the emitter-receiver distance along the northwest- southeast diagonal. and SDR exhibit the highest and the lowest SNR, respectively, with a difference of about 20 dB for the emitter located in the centre of the room. Independently of the receiver, the SNR degrades when the emitter is moved towards the corners of the room, similar to the path loss. Furthermore, when emitters are located along the southeast diagonal of the room, the SNRs are a little lower than along the northwest diagonal. In the southeast corner, the emitters are close to the windows, so the desired signal and the contribution from the shot noise due to the natural ambient light are received of the same direction. In short, the conventional angle-diversity receiver exhibits the best simultaneous SNR and path loss. Furthermore, as expected, for conventional and sectored angle-diversity receivers, the MRC scheme provides the best results, followed by SB and EGC. However, the MRC and SB combining techniques require estimating the SNR at each diversity branch, and the difference between the SNR obtained by MRC and EGC is only about 5 dB for the CDR structure. This is not significant when selecting the receiver and the combining technique that offer the best performance in a link operating at 115 kbps. Assuming the emitter transmits at 115 kbps using on-off keying (OOK) with non-return-to-zero (NRZ) pulses, the channel is distortionless, the preamplifier is followed by an equalizer that converts the received pulse to one, having a raised-cosine Fourier transform with 100% excess bandwidth, and the equalizer gain is chosen so that when sampled, its output is either 0 or \(2R_{S}\) (A), ignoring noise. Each sample of the equalizer output contains Gaussian noise having a total variance that is the sum of contributions from shot and thermal noises. In these conditions [4], the Bit Error Rate (BER) is given by:  
\[BER=Q\left(\sqrt{SNR}\right),\quad\textit{where}\ Q\left(x\right)=\frac{1}{ \sqrt{2\pi}}\int\limits_{x}^{\infty}e^{-\frac{y^{2}}{2}}dy \tag{35}\]  
According to Equation (35), to achieve a BER = \(10^{-9}\) requires a SNR = 15.6 dB. Based on the results shown in Figure 7, the CDR and SOR receivers ensure a BER below \(10^{-9}\) for any location along the diagonal of the room.