Quadrature Amplitude Modulation Forrest Sedgwick UC Berkeley EECS Dept. EE290F October 2003

Analog vs Digital Information Theory vs Signal Analysis Discrete Levels vs Analogous Representation Sacrifice arbitrarily precise representation of signal Gain arbitrary degree of reproducibility of given signal KEY BENEFIT Discrete information can be transmitted with arbitrarily low error rates EVEN ON A NOISY CHANNEL Digital information content measured in units of bits, decimals, or nats

Shannon’s Channel Capacity Channel capacity C (bits/sec) is the speed at which information can travel over a channel with an arbitrarily low error rate i.e. when a system is transmitting bits at or below C then for any BER e>0 there exists a code with block length n which will provide a BER < e. Assumes noise is thermal – Gaussian and White www-gap.dcs.st-and.ac.uk/~history/ Mathematicians/Shannon.html

Modulation All channels consist of some continuous parameter Must map discrete states onto continuous property Must have a decision circuit to map the state of the modulated channel into a discrete state As number of levels or states M  the behavior of the digital system does not approach that of an analog system, due to the decision circuit

Number of Levels Digital communications relies on a finite number of discrete levels Minimum number of levels is two (binary code) Shannon Capacity helps determine optimum number of levels for a given bandwidth, SNR, and BER

Limits on Communication Channels Two types of communication channels r<<1 – Power Limited High dimensionality signaling schemes Binary r>>1 – Bandwidth Limited Low dimensionality Multilevel Proakis and Salehi, pp. 738

Modulation Scheme A channel with lowpass frequency characteristics is called baseband. Digital information is transmitted directly Ex. Pulse Amplitude Modulation (PAM) A channel far removed from DC (like optical) is called a bandpass channel Transmission on a bandpass channel requires modulation of a carrier Amplitude Shift Keying (ASK) Phase Shift Keying (PSK) Frequency Shift Keying (FSK Quadrature Amplitude Modulation (QAM)

Amplitude Shift Keying (ASK) Amplitude of carrier wave is modulated Equivalent BER vs SNR to baseband PAM Proakis and Salehi, pp. 306

Angle Modulation (PSK and FSK) Frequency is time derivative of phase, PSK and FSK are somewhat equivalent Proakis and Salehi, pp. 332

PSK: Digital Angle Modulation Usually in digital communications PSK is chosen over FSK Easier to create multilevel codes Possibility of using differential phase shift keying (DPSK) Uses phase shifts relative to previous bit Eliminates need for local oscillator at receiver Use Gray Code to minimize effect of errors Proakis and Salehi, pp. 631

Quadrature Amplitude Modulation Amplitude and Phase of carrier are modulated Discrete amplitudes and phases form a constellation Can also think of QAM as a “complex” amplitude modulation scheme Proakis and Salehi, pp. 653

Constellations Different constellations require different SNR for a given BER (d) is lowest power by about 1dB (for given BER) (a) and (b) are rectangular Rectangular constellations offer very simple modulation/ demodulation schemes ASK two quadrature carriers - same frequency but 90  out of phase Mix quadrature carriers for output Proakis and Salehi, pp. 653

QAM vs ASK (multilevel) QAM has a tremendous advantage in noise performance Energy in every bit (including zero) Substantially more complex (coherent detection vs photodiode) Proakis and Salehi, pp. 565Proakis and Salehi, pp. 495

QAM vs PSK 4-QAM and 4-PSK have same power penalty For k>4, k-QAM is an improvement over k-PSK Proakis and Salehi, pp. 639

Applications of QAM Used in bandwidth-limited applications Modems: telephones have 3kHz bandwidth, excellent SNR (20dB) => M-ary QAM Cellular Telephones: Bandwidth is at a premium, very expensive (However, POWER is also at a premium...)

Limitations Almost always requires a highly stable local oscillator In the optical domain this is very expensive Possible (but difficult) to use differential phase keying Performance limits still not reached for Direct detection Signal Dimensionality (DWDM) Transmitter Power

References John G. Proakis, Masoud Salehi, Communications Systems Engineering, Prentice Hall 1994