## 6 PSK Modulation and Demodulation
### PSK Modulation for Neural Implants  
Most implantable devices use an inductive coupling link to transmit both power and data between coils using the same carrier frequency. The system circuit configuration is complex. [PERSON] _et al_. [77] separated the power and data, then transmitted them with different frequencies using DPSK modulation employing two transmitters and two receivers. The system power is transmitted with 1 MHz carrier frequency and the data is transmitted with 20 MHz carrier frequency. This method made the system simpler by reducing the circuit complexity. However, the as-developed system is big in size and has higher power consumption compared with other systems. The model of the system is as follows:  
\[\omega_{1}=\frac{1}{\sqrt{l_{1}c_{1}}}\textit{ and }\omega_{2}=\frac{1}{ \sqrt{l_{2}c_{2}}}\textit{ when }k=0 \tag{9}\] \[\omega_{1}=\frac{1}{\sqrt{l_{1}c_{1}}+l_{2}c_{2}}\textit{ and }\omega_{2}=\infty\textit{ when }k=1 \tag{10}\]  
where \(\omega_{1}\) and \(\omega_{2}\) are frequency components of the two resonant tanks, respectively. \(L_{I}\) and \(L_{2}\) are the inductances and \(C_{1}\) and \(C_{2}\) are the capacitances of a linearized model coupling between two resonant tanks, respectively. K is the coupling coefficient between coils that results in frequencies splitting away from their original values. When \(k\
eq\textit{0}\), both resonant tanks will contain frequency components \(\omega_{1}\) and \(\omega_{2}\). However, no interference is present at \(k=0\), _i.e._, the power and data resonant tanks remain at their original frequencies. When \(k=1\), the upper frequency shifts to infinity. Again, when \(L_{I}>>L_{2}\) and \(\omega_{1}\approx\omega_{2}\), the frequency of the power resonant tank is hardly affected due to the small amount of interference from the data transmitter.  
A non-coherent PSK receiver without PLL was developed by using a band pass sampling theory for neural implants [78]. [PERSON] _et al._[79] further developed his prior system [77] using a DPSK modulation in the analog domain to cancel the interference signal for a dual-band. This system is able to cancel 12 dB interferences signals without using complex filters. The system still suffered from high power consumption. In general, wireless powered signal-to-noise ratio (SNR) of the received signal is high for the short-range in neural implants. To overcome this situation, [PERSON] _et al._[80] proposed a quasi-coherent PSK (QCPSK) demodulator employing a direct carrier processing to extract the timing signals.  
In order to eliminate the power interference in the data receiver in neural implants, a fully integrated DPSK is used for high density biomedical implants through dual-band telemetry [81]. The carrier frequency of the power and data rate are separated within a minimum sampling rate which results in reduced chip area and makes it possible for all blocks to be implemented in one chip. This system suffers from relatively high power consumption. Power consumption is an essential key in biomedical implantable devices. To achieve reduced power consumption, a BPSK demodulator based on a digital-analog hybrid COSTAS loop and a digital multiplier is proposed in [82]. The digital multiplier is used in place of an analog multiplier to reduce the power consumption.