30 Sept. 2009
TELE3113 Analogue and Digital Communications – M-ary Modulation
School of Electrical Engineering and TelecommunicationsThe University of New South Wales
5 May 2009TELE3113 - baseband p. -2
Signaling Formats
[Alternate Mark Inversion (AMI)]
Digital data (a sequence of binary digits) can be transmitted byvarious pulse waveforms which are sometimes called line codes.
2
Multilevel (M-ary) Modulation• The signalling schemes we have considered thus far have been binary, in the sense that each symbol we
send carries one single bit of information. Eg. Binary ASK (OOK)
• By using binary modulation techniques (B-ASK, B-FSK, B-PSK), each symbol carries only one bit information.
• The signalling is binary, as the aspect of the signal we are modulating can only have two discrete values, that we interpret as either “0” or “1”.
BASK: Amplitude +A or 0 BPSK: phase 0 or 180BFSK: frequency f1 or f2.
• Rather than allowing the parameter we are keying to have just two states, we may allow it to have M states, M-ary signalling.
• Usually we choose M to be a power of two and we interpret each symbol as corresponding to k-bits of the input sequence, where k=log2M, or M=2k.
• Transmission rate can be increased by using multilevel modulation, in which each modulated signal may carrier multiple bits information.
• This can reduce the transmission bandwidth compared with the bandwidth required for binary modulation.
3
Example: 4-ASK (M=4, k=log4=2)We group the bits of the input bit stream in pairs (k=2). The carrier amplitude has 4-possible levels, dependent on the value of the pair of bits we are modulating on the carrier:
(0,0) 0 volt(0,1) A volts(1,1) 2A volts(0,1) 3A volts
In this 4-ASK example, let’s assume our input bit stream is 0 1 1 1 0 0 1 0 0 1, We group the bits in pairs, and this maps to the amplitude of the transmitted carrier, A, 2A, 0, 3A, A.The modulated signal is shown as
Question: Why Gray mapping?
4
The attraction of the M-ary signalling is that we may increase our bit rate while keeping the bandwidth used by the system the same as binary signalling.
We make the distinction between the symbol rate (baud rate), Rs, which is the number of symbols sent per second, and the bit rate, Rb, which is the number of bits send per second.
The number of symbols we send per second determines our symbols period. For non-return to zero signalling, we can take Ts=1/Rs. The bandwidth used is inversely proportional to the symbol period, B=1/Ts=Rs.
For M=2k ary signalling, one sent symbol carries k bits of information, so Rb=kRs.
The bandwidth expressed in terms of the bit rate is B=Rs=Rb/k.
We can see that the M-ary achieves a k-folf reduction in the bandwidth needed to maintain a gieven bit rate Rb, compared to the binary case (Rs=Rb, since one symbol is one bit.)
Alternatively, with a given bandwidth, M-ary signalling can achieve a k-fold increase in bit rate of binary signalling.
5
The trade-off in M-ary signalling is its power requirements, and an increase in system complexity.
In M-ary signalling, to achieve the same error performance (called bit error rate, BER) as in binary system, we must transmit more power. The error resilience of the system is related to the spacing between the amplitude levels. To achieve the same amplitude level in M-ary ASK, our average amplitudes must be higher, and so consume more power.
This is the bandwidth-power trade-off common in most communication systems.
M-ary Modulation
1. A digital-to-analogue converter (DAC) can be used to convert k bits of the input to M=2k amplitude levels.
2. The M-ary baseband signal can then be modulated onto the carrier using any modulation technique, like (M-ASK, M-PSK, M-FSK).
6
Example: • Binary data in k-bit slots at bit rate R are converted into PAM data symbols
with M levels using a DAC (reverse of encoding operation). Note: • Each symbol takes k-bit intervals, so symbols rate: D=R/k [baud]
baud rate=symbols/sec, Rs=D=1/Ts, where Ts is the symbol intervalbit rate = bits/sec, Rb=R=1/Tb, where Tb is the bit interval
• Multilevels (M-levels, M>2) of the waveform parameter are used in the modulation such as M-ASK, M-FSK, M-PSK.
There are two types of M-ary modulation:• Digital signals are generated by changing the amplitude, phase, or frequency
of a carrier in M discrete steps (levels). • Digital signals are generated by combining different modulation techniques
into a hybrid form (e.g., both amplitude and phase of the carrier are modulated, such as M-ary QAM).
2logl M=
7
M-ASK:Binary to multilevel digital signal convert
• An k=3 bit DAC is used. • M=23=8 level digital signals• Symbol interval Ts=3Tb• Symbol rate D=R/3
Question: 1. What is average power?2. Can we use envelope detection for this M-ASK?
8
The performance of FSK is heavily dependent on the spacing between the frequencies. However, we will not go into this issue here.
We will just make the comment that a particular type of FSK, called Gaussian minimum shift keying (GMSK) is very popular and is used in GSM mobile phone. It is binary FSK, so two frequencies are used, it is keyed in such a way so as to keep the phase of the modulated carrier continuous, called continuous phase modulation. This minimizes the bandwidth occupied by the signal. The frequency shaping pulse is Gaussian.
9
M-ary Phase Shift Keying (M-PSK)• In binary PSK, the modulated signal is
• Using the analytical signal representation, the complex envelop of the signal is . The phase of the carrier takes either 0 or π.
• In M-ary PSK, the phase of the carrier can take on one of M possible values.
Example: M-ary PSK with M=4 (l=2 bits/symbol)
• There are 4 permitted values of the complex envelope. They are the complex values for each of the 4 multilevels, corresponding to the 4 phases that the carrier can take.
• Each symbol carries l=2 bits, so transmission rate increased twice.
( ) ( )cos( )cos( ), ( ) 1
cos( ), ( ) 1cos( ), where 0, or
c c
c c
c c
c c i i
x t A m t tA t m t
A t m tA t
ωω
ωω θ θ π
= −
− =⎧= ⎨ = −⎩= + =
( ) cos( )
Re{ }
Re{ ( ) }
i c
c
c c ij j t
cj t
x t A t
A e e
g t e
θ ω
ω
ω θ= +
=
=
( ) ijcg t A e θ=
( 1) 2 , 1,2, ,ii i MM
θ π−= = L
10
Signal Constellation
• The maps of the permitted values of the complex envelope g(t) in a complex domain are known as signal constellations.
• Because M=4 in this case, 4-PSK is also known as quadrature PSKor QPSK.
11
12
• MPSK can also be generated by using two quadrature carrriersmultiplied by the x and y components of the complex envelope (instead of using phase modulator)
( ) ( ) ( )( ) cos( ) sin
ijc
c i
c i
g t A e x t jy tx t Ay t A
θ
θθ
= = +==
( ) Re{ }
Re{ ( ) }( )cos ( )sin
i c
c
j j tc c
j t
c c
x t A e e
g t ex t t y t t
θ ω
ω
ω ω
=
== −
13
14
Quadrature Amplitude Modulation (QAM)• This is the combination of Quadrature multiplexing with M-ASK. • Recall for quadrature-multiplexing (QM), we have essentially two
independednt channels at each frequency, an in-phase carrier and a quadrature carrier,
sI=cos(wct), sQ=-sin(wct).• In M-ary QAM, the in-phase and quadrature components are
independent (carry independent information) • The carrier experiences both amplitude and phase modulation. (hybrid
modulation)• QAM signal constellations are not restricted to having permitted
signalling points only on a circle of radius Ac (as was the case for MPSK).
• x(t) and y(t) may take individual discrete values, respectively.
( ) Re{ ( ) }( )cos ( )sin
cj tc
c c
x t g t ex t t y t t
ω
ω ω== −
( )( ) ( ) ( ) ( )j tg t R t e x t jy tθ= = +
15
2 bits in I channel2 bits in Q channel
Question :1. Transmission rate?2. Average symbol energy?3. How to detect QAM?4. 16QAM vs 16 ASK
