1. Suppose you are designing a system to send a set of analog sensor data streams over a wireless point-to-point digital communication link. Each signal is 10 kHz and we have the following requirements for the system:
- Data streams will be frequency multiplexed over a channel
- Quantization error should be at most 0.1% of peak
- Error-correcting code overhead is 15%
- 500 Hz guard bands must be used between each multiplexed signal and on the edges of the band utilized by the system
The modulation for the system is 16QAM which has a spectral efficiency of 4 bps/Hz.
(a) What is the required data rate of each sensor data signal (before overhead)?
(b) What is the error-correcting coding overhead that will be added to each signal?
(c) What spectrum is required for each of the sensor signals?
(d) If the spectrum allocated for the system is 5 MHz, how many of these sensor signals can be supported?
2. A binary pulse position modulation (PPM) is a modulation technique where the position of the pulse indicates whether a zero or one was sent as shown in the figure below.
This modulation is used over channel where the noise is additive, white and Gaussian, with spectrum level N/2. Random bits are sent over the channel with equal ones and zeros.
(a) What is the optimum matched filter receiver design for this binary system?
(b) What is the matched filter response in the time domain?
(c) What is the system bit error rate?
(d) If link sends more ones than zeros, would the threshold in your receiver increase or decrease? Why?