Vestigial Sideband Modulation KEEE343 Communication Theory Lecture #11, April 7, 2011 Prof. Young-Chai Ko koyc@korea.ac.kr
Summary Vestigial sideband modulation Baseband representation of modulated wave Baseband representation of pass-band filter Frequency division multiplexing Introduction to Angle Modulation
Generation of LSB SSB Using Wideband Low-Pass Filter DSB Spectrum H L (f) SSB Spectrum H L (f) sgn(f ) sgn(f + )
Generation of USB SSB Using High-Pass (or Passband) Filter DSB Spectrum H HP (f) SSB Spectrum H HP (f) = sgn(f + ) + sgn(f + ) sgn(f + ) sgn(f )
SSB Modulated Wave Lower Sideband SSB s LSB (t) = 1 2 m(t) cos(2 t)+ 1 2 ˆm(t)sin(2 t) Upper sideband SSB s USB (t) = 1 2 m(t) cos(2 t) 1 2 ˆm(t)sin(2 t)
Applications of SSB and Difficulties in Implementing SSB Two difficulties of SSB modulations Designing and implementing the sharp Low-pass (or High-pass/pass-band) filter is not easy for circuit designer. Hence, the message signal which does not contain the significant energy in the DC area is often modulated by the SSB such as the speech signal. Spectrum of Speech Signal (Example) 0 [Hz] However, the SSB cannot be applicable for the message signal which contains the significant energy around zero frequency such as video signal, computer data, and etc.
Vestigial Sideband (VSB) Modulation VSB Modulation Modulation to overcome the two difficulties of the SSB modulations. Allow a small amount, or vestige, of the unwanted sideband to appear at the output of an SSB modulator The design of the sideband filter is simplified since the need for sharp cutoff at the carrier frequency is eliminated. In addition, a VSB system has improved low-frequency response and can even have dc response.
Idea of VSB Modulator Pass-band (or High-pass) filter for USB-SSB modulation 1 H U (f) The filter below is much easier to design and implement 1 1 f 1 + f 1
Consider the two-tone message signal given as m(t) =A cos(2 f 1 t)+b cos(2 f 2 t) Message signal multiplied by the carrier wave, that is, DSB signal e DSB (t) = (A cos(2 f 1 t)+bcos(2 f 2 t)) cos(2 t) = 1 2 A cos(2 ( + f 1 )t)+ 1 2 A cos(2 ( f 1 )t) + 1 2 B sin(2 ( + f 1 )t)+ 1 2 B sin(2 ( f 1 )t)
Spectrum of DSB signal 1 2 B 1 1 2 A 1 2 A 2 B Frequency response of the VSB filter f 2 f 1 f + f 1 + f 2 c 1 1 Output response f 2 f 1 + f 1 + f 2 s(t) = 1 2 A cos(2 ( f 1 )t) + 1 2 A(1 ) cos(2 ( + f 1 )t) + 1 2 B cos(2 ( + f 2 )t) 1 2 A 1 [A(1 )] 2 1 2 B f 1 + f 1 + f 2
Demodulation of VSB Signal (Coherent method) Downconvert (by Multiplying 4 cos(2 t) ) and low pass filtering Downconvert d(t) = s(t) 4 cos(2 t) = 1 2 A cos(2 ( f 1 )t) 4 cos(2 t) + 1 2 A(1 ) cos(2 ( + f 1 )t) 4 cos(2 t) + 1 2 B cos(2 ( + f 2 )t) 4 cos(2 t) cos(2 ( + f 1 )t) cos(2 t)= 1 apple cos(2 (2 + f 1 )t) + cos(2 f 1 t) 2 Low-Pass Filtering 1 2 cos(2 f 1t)
Signal after Low-pass filtering (t) = A cos(2 f 1 t)+a(1 ) cos(2 f 1 t)+b cos(2 f 2 t) = A cos(2 f 1 t)+b cos(2 f 2 t)
Television Signals [Ref: Haykin & Moher, Textbook]
Baseband Representation of Modulated Waves DSB modulated wave signal s DSB (t) =Am(t) cos(2 t) SSB modulated wave signal s SSB (t) = 1 2 Am(t) cos(2 t) ± 1 2 A ˆm(t)sin(2 t) In general, we can write the linear modulated wave as s(t) =s I (t) cos(2 t) s Q (t)sin(2 t) Carrier wave with frequency quadrature-phase version of the carrier c(t) = cos(2 t) ĉ(t) =sin(2 t) Orthogonal each other
We can rewrite the modulated wave as s(t) =s I (t)c(t) s Q (t)ĉ(t) in-phase component of s(t) quadrature(-phase) component of s(t) Introduce the complex envelop of the modulated wave s(t) s(t) =s I (t)+js Q (t) Define the complex carrier wave c(t) =c I (t) jc Q (t)
Consider the following s(t) exp(j2 t) = apple s I (t)+js Q (t) apple cos(2 t)+jsin(2 t) Real term apple s(t) exp(j2 t) = s I (t) cos(2 t) s Q (t) sin(2 t) Imaginary term apple s(t) exp(j2 t) = s I (t)sin(2 t)+s Q (t) cos(2 t) s(t) X apple s(t) exp(j2 t)
Now consider s(t) =s I (t)+js Q (t) =a(t)e j (t) where a(t) = q s 2 I (t)+js2 Q (t), (t) = tan 1 s Q(t) s I (t) Then we can represent the modulated wave as apple s(t) = < apple = < s(t)e j2 t a(t)e j[2 t+ (t)] = a(t) cos[2 t + (t)] apple = < a(t)e j (t) e j2 t
Three different representation of modulated wave using its equivalent baseband signal s(t) = s I (t) cos(2 t) s Q (t)sin(2 t) apple = < s(t)e j2 t = a(t) cos[2 t + (t)]
Superheterodyne Receiver [Ref: Haykin & Moher, Textbook]
Communication Chipset Architecture LNA Receiver PLL 2 ABB Section 90 0 PLL antenna switch 90 0 2 ABB Digital Baseband IC Power Amplifier Switchplexer Transmitter module PA Ctrl 26MHz Osc. LDO s
Frequency-Division Multiplexing To transmit a number oommunication signals over the same channel, the signals must be kept apart so that they do not interfere with each other, and thus they can be separated at the receiving end. FDM (Frequency division multiplexing) TDM (Time division multiplexing) SDM (Space division multiplexing) CDM (Code division multiplexing)
Block Diagram of FDM
Angle Modulation Basic Definition of Angle Modulation s(t) =A c cos[ i (t)] = A c cos[2 t + c ] Phase modulation (PM) if i(t) =2 t + k p m(t) Frequency modulation (FM) if Z t i(t) =2 t +2 k f m( ) d 0