# Computer Networks – Physical Links / Encoding

Demo: On-Off Modulation (Matlab)

## Shanno-Hartley

• Shannon-Hartley Theorem gives the theoretical throughput upper bound:
• $C=Blog_2(1+\frac{S}{N})$
• C: Channel Capacity, 带宽理论上限 (bps)
• B: Bandwidth, 信道带宽 (Hz), limited by ADC, DAC rate
• S: Signal Power, limited by safety concern
• N: Noise Power
• S/N or SNR: 信噪比(dB), SNR = 10 × log10(S/N)

• Bandwidth in Hz & Bandwidth in bps
• Rate: throughput (bps)
• Spectrum: the width of the occupied the spectrum (Hz)
• A/D and D/A Converter
• (1/the space of the samples) is defined as the rate of the ADC or DAC
• The rate of the ADC or DAC must 2 times of the bandwidth of analog signal (Sampling Theorem)

## Modulation

• Baseband Transmission 基带传输
• Passband Modulation 频带传输

### Baseband Transmission (Line Coding)

• Symbol/Baud Rate: unit is baud(Bd) i.e. symbols per second
• Covert to bit rate
• Rb = RBlog2M
• M: the number of different symbols
• RB: Baud Rate
• Rb: Bit Rate

### Clock Recovery

• Synchronous Transmission: Manchester Encoding
• Machester: 由低到高的跳变为0, 由高到低的跳变为1
• Features: Transmit the clock; complex, less overhead
• Asynchronous Transmission: 4B/5B Encoding + NRZI
• 4B/5B, 将4位编码映射到5为编码, 保证最多有1个前导0, 2个末尾0 —— 解决连续的0
• Features: Recover the clock from signal; simple, cheap

### Passband Modulation

• Demodulation:
• non-coherent: find the envelop; thresholding
• coherent: $Acos(2\pi ft)*{\color{Red} cos(2\pi ft)}=\frac{1}{2}A(cos(2\pi 2ft)+1)$
• Frequency Shift Keying (FSK)
• Phase Shift Keying (PSK)
• Demodulation:
• $cos(2\pi ft)*{\color{Red} cos(2\pi ft)}=\frac{1}{2}(cos(2\pi 2ft)+1)$
• $cos(2\pi ft + \pi)*{\color{Red} cos(2\pi ft)}=\frac{1}{2}(cos(2\pi2ft)11)$

### Carrier Phase Misalignment

• Opt1: find the accurate state of received signal (猜测对准)
• Opt2: use orthogonal carrier waves
• Transmitter Carrier Wave: cos(2πft + ϕ)
• Local Carrier Wave 1: cos(2πft)
• Local Carrier Wave 2: $cos(2\pi ft + \frac{\pi}{2})$

### Select Suitable Rate

• Rb = RBlog2M
• $C=Blog_2 (1+\frac{S}{N})$
• If Rb > c, there will be error, though it is not 100% correct if Rb < C.
• Bit error rate(BER): error bits/transmitted bits