# FM-UWB: Towards a Robust, Low-Power Radio for Body Area Networks
## 4 Multi-User FM-UWB Communication
The same FM-UWB receiver can be used to adapt to different conditions in the network, maximizing system efficiency and providing more room for improvement at the protocol level. To measure the performance in the presence of multiple FM-UWB signals the same setup from Figure 6 was used. The measured BER performance is presented in Figure 13a for a number of users varying from 1 to 4. The data rate on each sub-channel is 100 k\(\mathrm{b}\)/s resulting in 200 kHz bandwidth, with 100 kHz separation between the channels. Orthogonal 2-FSK modulation without pulse shaping is used in all cases. The output spectrum is shown in Figure 13b. The multi-user interference and noise performance of the FM-UWB were studied in [5; 8] for the case of a delay-line demodulator. However, the results from [5] only addressed limits due to inter-user interference and did not take noise into account. Inter-user interference becomes a dominant factor only at large variations in power between the sub-channels, and it is of interest to assess the BER performance and sensitivity degradation in other cases. Following the same reasoning used by [PERSON] in [5; 8], assuming that the delay is sufficiently small and the noise autocorrelation function \(R_{n}(\tau)=0\) the demodulator output voltage, in the case of two users, becomes  
\[V_{o,2} = k(V_{s1}+V_{s2}+V_{n})^{2} \tag{2}\] \[= k\left[V_{s1}^{2}+V_{s2}^{2}+V_{n}^{2}+2V_{s1}V_{s2}+2V_{s1}V_{n }+2V_{s2}V_{n}\right], \tag{3}\]  
where \(k\) is the constant of the demodulator that has a dimension \(\mathrm{V}^{-1}\). Since this constant does not affect the output Signal to Noise Ratio (\(SNR\)), it can be dropped from further consideration. The factors \(V_{s1}^{2}\) and \(V_{s2}^{2}\) are the two demodulated sub-channels. The useful signal power on channel \(i\) is then proportional to  
\[S_{out,i}\propto V_{si}^{4}\propto S_{i}^{2}, \tag{4}\]  
Figure 12: Block diagram of a single sub-channel demodulator. where \(S_{i}\) is the input signal power on channel \(i\). The other terms in Equation (3) correspond to cross-products of signal and noise (\(V_{si}V_{n}\)) and the two input signals (\(V_{si}V_{sj}\)), and noise squared (\(V_{n}^{2}\)) [8]. We can then write:  
\[2\sqrt{S_{i}S_{j}} \propto 2V_{si}V_{sj}, \tag{5}\] \[2\sqrt{S_{i}N} \propto 2V_{si}V_{n},\] (6) \[N \propto V_{n}^{2}, \tag{7}\]  
where \(N\) is the input noise power. The total output noise power, as a function of input signal power and noise power is then given by  
\[N_{out}=N^{2}+4S_{1}N+4S_{2}N+4S_{1}S_{2}. \tag{8}\]  
Finally, the \(SNR\) at the demodulator output is given by  
Figure 11:0  
where factor \(B_{RF}/B_{sub}\) is the processing gain coming from the spread spectrum FM-UWB technique [8]. Let us now assume that the two sub-carrier channels have equal power \(S_{1}=S_{2}\). The output SNR becomes  
Figure 11:1  
This expression can be compared to the SNR in the case of a single user FM-UWB:  
Figure 11:2  
It should be noted that the output SNR is a non-linear function of the input SNR, which is a consequence of the square characteristic of the demodulator. Although the derived SNR expressions are a rather coarse approximation, they provide some intuitive insight into the performance limitations. First, the achievable BER is now limited by the inter-user interference (\(4S_{1}S_{2}\)), which fundamentally limits the number of users or the maximum difference in powers between the two users. This factor, however, remains relatively small compared to noise at low SNR values. What can be noted in this region is that the \"noise floor\" has now increased due to cross-modulation of several input signals with noise (\(8S_{1}N\)). In case a small number of channels is used, and the power difference between channels is small, this factor will dominantly determine the sensitivity degradation.