terisation
Using the experimental setup, this section explores two important aspects of the proposed implant communication system. First we evaluate the bit error rate (BER) verses signal to noise ratio (SNR) of the communication. This is done by mathematically analysing and simulating the system followed by experimental measurements of the BER as a function of communication distance. This measurement is an essential step to calculate the SNR of the channel as a function of distance. Since we know the transmitted power and the channel path loss, the SNR verses distance curve translates to noise power spectral density (PSD) as a function of distance.
6.3.1
AWGN Communication Channel Model of the Sys-
tem
The simplified physical layer communication scheme used in this work is shown in Fig. 6.3. The received signal r(t) can be expressed as
160 6.3 – Performance evaluation and noise characterisation r(t) = s(t)∗h(t) +n(t) (6.1) Digital input Spreading PRS BPSK Modulator Channel Path loss Coherent demodulator Despreading PRS Recovered output n(t)→ N(0, σ2 n) h(t) mn pn qn s(t) c(t) r(t) q0n pn m0 n
Fig. 6.3 communication channel model
The channel transfer function h(t) is due to the path loss introduced by the
human body. This transfer function for implant communication varies with frequency and communication distance as shown in [13].
A sample of the noise corrupted received signal picked up by the electrodes, band limited signal and the detected signals normalised to unity amplitude are shown in Fig. 6.4. 1.714 1.715 1.716 1.717 1.718 1.719 1.72 1.721 1.722 1.723 10-3 -0.5 0 0.5 1 1.5 2
The noise signal n(t) is assumed to be and AWGN distributed as N(0, σn2)
where σ2
n is the variance of the noise process. AWGN has a flat power spectral
density of No = σ
2
2 over the entire spectrum. Each chip has an average chip
energyEc = A
2T
c
2 where A is the amplitude of the line waveform andTc is the
chip period. From these, the chip error probability as a function of Ec
No is given by pc=Q s2E c No . (6.2)
Thus for a spreading factor of M, the bit error rate (BER)pb is a binomial
distribution ofpc when the bit is decoded by majority voting. It is given by
pb = M
X
i=M/2
pic(1−pc)M−i. (6.3)
The power spectral density (PSD) of the received signal is shown in Fig. 6.5. Here we can see that the signal at the input of the receiver maintains similar spreaded power of the transmitted signal except with a nearly constant noise floor. This roughly confirms our assumption that the noise is AWGN.
-2 -1.6 -1.2 -0.8 -0.4 0 0.4 0.8 1.2 1.6 2 frequency (Hz) 107 1 2 3 PSD (W/Hz) 10-6
162 6.3 – Performance evaluation and noise characterisation
6.3.2
Experimental and Simulation Results Discussion
The presented system was simulated and compared with theoretical BPSK modulated DSSS with respect to BER as a function of SNR (i.e., Eb
No ) is shown
in Fig. 6.6. The comparison was done for different spreading factors. As shown the given system follows the theoretical performance closely. Hence, this can be related with BER as a function transmission distance to evaluate the SNR as function of distance to characterise channel noise.
-8 -6 -4 -2 0 2 4 6 8 10 10-6 10-5 10-4 10-3 10-2 10-1 100
Fig. 6.6 Simulated BER performance of the the transceiver
Measurement of BER requires long sequence of data and repeated experiment. For this purpose the receiver was modified to include an error detection system. The error count and the data counts were registered using 32 bit long registers (i.e., capable of counting 4.295×109 that do not fill up for 30 minutes per single
measurement and sufficiently large for an error floor of 10−6). These error
implemented in the PC on the right side of Fig. 6.1. For every transmission distance set, the error and data counts were reset five times. Averaging this values the BER was measured by varying the transmission distance and is presented in Fig. 6.7. 10 20 30 40 50 60 70 80 90 100 Transmission distance (mm) 10-6 10-5 10-4 10-3 10-2 10-1
Fig. 6.7 BER verses transmission distance
Using equation (6.3) and the measurements in Fig. 6.7, the SNR can be expressed as a function of distance and the relationship is plotted as shown in Fig. 6.8.
The mean received energy of the signalEr =EcPL wherePL is the path loss
as a function of distance analytically computed in our pervious work [13]. Thus, the received signal will have signal to noise energy ratio of Er
No. Relating these
with the SNR plot in Fig. 6.8, the noise spectral density No can be estimated
and is shown in Fig. 6.9. This shows that the noise spectral density of the AWGN introduced by the channel is also nearly flat as a function of transmission
164 6.3 – Performance evaluation and noise characterisation 10 20 30 40 50 60 70 80 90 100 Transmission distance (mm) 8 9 10 11 12 13 14
Fig. 6.8 SNR verses transmission distance
distance, albeit smaller for short distances. The average value of the noise power spectral density was measured to be -118 dBWatt/Hz.
10 20 30 40 50 60 70 80 90 100 Transmission distance (mm) -150 -140 -130 -120 -110 -100 -90 -80 -70 -60 -50
6.4
Conclusion
In this chapter we have presented design, implementation and characterisation of a sensor integrated galvanically coupled transmitter and receiver. A capacitive sensor represented by a variable capacitance of value 0–50 pF was used as a signal source. The sensor was integrated into an oscillator and a minimalist digital data generation was presented. implant transmitter that galvanically coupled signal to the human body and receiver systems that differentially detects the signal received is implemented. Evaluation of the performance the prototype system presented here demonstrates the practical feasibility of galvanically coupled implant communication. This work also characterised SNR as a function of transmission distance which is a crucial parameter for improved future receiver designs. The channel noise is characterised as AWGN with an average PSD of -118 dbWatt/Hz.