Modulation (7): Constellation Diagrams Luiz DaSilva Professor of Telecommunications dasilval@tcd.ie +353-1-8963660 Adapted from material by Dr Nicola Marchetti
Geometric representation of modulation signal q Digital Modulation involves q Choosing a particular signal waveform for transmission of a particular symbol q For M possible symbols, we thus have M possible waveforms S = { 2 s1( t), s ( t),..., sm ( t)} q For binary modulation, each bit is mapped to a signal from a set of signals S, that has two signals q We can view the elements of S as points in a vector space 2
Vector space q We can represent the elements of S as linear combination of basis signals q The number of basis signals is the dimension of the vector space q Basis signals are orthogonal to each other q Each basis is normalized to have unit energy: E = φ ( t) i φ 2 i ( t) dt is the i th = 1 basis signal. 3
Example: BPSK 4 { } ) ( ), ( ) cos(2 2 ) ( ) cos(2 2 ) ( ) cos(2 2 ) ( 1 1 1 2 1 t E t E S t f T t t f T E t s t f T E t s b b c b c b b c b b φ φ π φ π π = = = = b b T t 0 T t 0 E b b E Q I The basis signal Two signal waveforms to be used for transmission Constellation Diagram (Dimension = 1)
Constellation diagram q Properties of modulation scheme can be inferred from constellation diagram q Bandwidth occupied by the modulation decreases as the number of signal points per dimension increases (getting more dense) q Probability of bit error is inversely proportional to the distance between the closest points in the constellation q Bit error decreases as the distance increases (sparse) 5
Demodulation q In ideal coherent detection, prototypes of the possible arriving signals are available at the receiver q These prototype waveforms exactly replicate the signal set q The receiver is then said to be phase-locked to the transmitter q During detection, the receiver multiplies and integrates (correlates) the incoming signal with each of its prototype replicas, and then decides for the most correlated replica among those available 6
Amplitude and phase q Amplitude and phase can be modulated simultaneously and separately, but this is difficult to generate, and especially difficult to detect q Instead, in practical systems the signal is separated into another set of independent components: I (Inphase) and Q (Quadrature) q These components are orthogonal and do not interfere with each other q For representation of these components, we use phasors 7
Phasor representation q A sine wave can also be represented as a phasor (equivalent to a vector in polar form) A A A φ time t = 0 time t = t 1 8
Phasor representation (cont d) q A phasor is a rotating vector A φ 2 time t = t 2 9
Back to modulation q We can think of modulation using phasor/polar format, rather than 10
Speed with which one walks the whole circle 11
In-phase and quadrature 12
In-phase and quadrature (cont d) 13
Constellation points q Most digital modulations map the data to a number of discrete points on the I/Q plane q These are known as constellation points 14
PSK 15
QAM 16
I/Q modulator q I/Q diagrams are particularly useful because they mirror the way most digital communications signals are created using an I/Q modulator q In the transmitter, I and Q signals are mixed with the same local oscillator (LO) q A 90 degree phase shifter is placed in one of the LO paths q Signals that are separated by 90 degrees are also known as being orthogonal to each other or in quadrature 17
I/Q modulator block diagram 18
I/Q demodulator q The composite signal with magnitude and phase (or I and Q) information arrives at the receiver input q The input signal is mixed with the local oscillator signal at the carrier frequency in two forms q One is at an arbitrary zero phase q The other has a 90 degree phase shift 19
I/Q demodulator (cont d) q Signals that are in quadrature do not interfere with each other q They are two independent components of the signal q The main advantage of I/Q modulation is the ease of combining independent signal components into a single composite signal and later splitting such a composite signal into its independent component parts q Exploitation of the symmetry due to the trigonometric identities 20