1. Wireless Communications

2. Wireless Communications
Wireless is more and more widely deployed – cellphone, wireless LAN, …
The fundamental fact is that if the sender sends a sine wave, the receiver will receive a sine wave at the same frequency. But with
A different phase
A new amplitude
How do you design communication schemes based on that?

3. Wireless Communications
AM – stronger signal when `1’, weaker signal when `0’.
FM – faster waveform when `1’, slower signal when `0’.
BPSK – 0 degree when `0’, 180 degree when `1’.

4. Basic Wireless System The very basic wireless communication system
Sender: given the bit stream, convert it to the baseband waveform by a Low Pass Filter, then multiply with the carrier waveform (2.4GHz if g, 1.8GHz if some cellphones), and send.
Receiver: given the signal received from the antenna, multiply it with a locally generated carrier, send it to the low pass filter, regenerate the baseband waveform.

5. Basic Wireless System
The sender cannot send the square waveform but has to send I(t) which is bandwidth limited from 0Hz to some cutoff frequency BHz. The signal in the air in this simple system occupies frequency range [f-B,f+B].
Because cos(2πf1t)cos(2πft) = cos[2π(f1t+f)t] + cos[2π(f1-f)t] (constant dropped)
The [f-B,f+B] must be within the frequency band allocated for this system (around 20MHz in g, around 25MHz in GSM) because the medium is shared

6. Basic Wireless System
How can the receiver regenerate the baseband waveform? A simplified explanation:
The sender sends I(t)cos(2πft).
Assume there is no phase difference, the receiver multiplies I(t)cos(2πft) with cos(2πft), and gets
I(t)cos2(2πft) = I(t)[1/2 + 1/2cos(4πft)].
Then, after the low pass filter, what is left is the low frequency component I(t).

7. Two Orthogonal Channels
The sender sends I(t)cos(2πft) + Q(t)sin(2πft).
The receiver multiplies the received signal with cos(2πft) , and will get
[I(t)cos(2πft) + Q(t)sin(2πft)] cos(2πft) = I(t)[1+cos(4πft)] + Q(t) sin(4πft)
(constant dropped), and after the LPF, will have I(t).
At the same time, the receiver also multiplies the received signal with sin(2πft) , and will get
[I(t)cos(2πft) + Q(t)sin(2πft)] sin(2πft) = I(t) sin(4πft) + Q(t) [1-cos(4πft)]
(constant dropped), and after the LPF, will have Q(t).
So, the sender can send TWO baseband waveforms at the same time. We often use a complex number to represent the symbol, where I(t) is the real part and Q(t) is the imaginary part.

8. BPSK, QPSK, QAM
BPSK is using only one channel. And in this channel, only two possible voltages.
Quadrature phase-shift keying (QPSK) is using both channels. In each channel, only two voltages.
Quadrature amplitude modulation (QAM) is using both channels. In each channel, multiple voltages. If 4 levels of voltage, it is 16QAM. If it 8 levels of voltage, 64QAM.

9. Modulation/Demodulation
Modulation is the process of turning the bits into the baseband waveforms.
Demodulation is the reverse.