ECE4331 Fall 2009 Zhu Han Department of Electrical and Computer Engineering Class 3 Sep 1st 2009 Review of last class Random Process Stationary Ergodic Mean correlation covariance power spectrum density Gaussian Process Noise Central limit theorem Narrowband Noise In phase and Quadrature phase N0 2 power each Gaussian Envelope Rayleigh distribution and phase uniform Ricean distribution Might not cover everything in the textbook ECE4331 Baseband and Carrier Communication Baseband Describes signals and systems whose range of frequencies is measured from 0 to a maximum bandwidth or highest signal frequency Voice Telephone 0 3 5KHz CD 0 22 05KHz http www youtube com watch v YjO VXHxsRw mode related search Video Analog TV 4 5MHz TV channel is 0 6MHz Digital depending on the size movement frames per second Example wire coaxial cable optical fiber PCM phone Carrier Communication Carrier a waveform usually sinusoidal that is modulated to represent the information to be transmitted This carrier wave is usually of much higher frequency than the modulating baseband signal Modulation is the process of varying a carrier signal in order to use that signal to convey information ECE4331 Modulation Modulation A process that causes a shift in the range of frequencies of a signal Gain advantages Antenna size half of the antenna size Thousands of miles for baseband Better usage of limited bandwidth less side lopes Trade bandwidth for SNR CDMA Robust to inter symbol interference multipath delay Robust to errors and distortions Types Analog AM DSB SSB VSB FM Delta modulation Digital ASK FSK PSK QAM Pulse modulation PCM PDM Fiber phone Advanced ECE4331 CDMA 3G OFDM WLAN WMAN Double Sideband Modulation time m t cos wct freq 0 5 M w wc M w wc Figure 2 4 LSB USB DSB DSB SC suppressed carrier no carrier frequency Wc bandwidth of the signal to avoid aliasing Demodulation e t m t cos wct 2 0 5 m t m t cos 2wct E w 0 5M w 0 25 M w 2wc M w 2wc Low pass filter to remove the higher frequency ECE4331 DSB SC Example t t t t t cos c t m t F cos ct M 0 0 c ECE4331 0 Lower sideband LSB c c Upper sideband USB Frequency Conversion Move the signals to other frequency Multiplying two sinusoids results in two frequencies which are the sum and difference of the frequencies of the sinusoids multiplied t m t cos C t BPF I cos MIX t EXAMPLE Let m t be as shown m t cos t cos t 21 cos t cos t To change the carrier frequency c of a modulated signal to an intermediate frequency I we use an oscillator to generate a sinusoid of frequency MIX such that e 1 t 21 m t cos I t t t 0 21 m t cos 2 c I t cos I t ECE4331 t c c 0 I c MIX Then m t cos c t cos MIX t 21 m t cos c MIX t cos c MIX t t M SPECTRA e1 t E1 I 0 I Amplitude Modulation Why DSB SC not working do not know the carrier frequency in receiver The last impulse functions indicate that the carrier is not suppressed in this case For some M shown the modulated signal spectrum is as shown AM t A m t cos c t 12 M c M c A c c M 0 c 0 c With this type of AM the demodulation can be performed with without a local oscillator synchronized with the transmitter ECE4331 AM Example m t has a minimum value of about 0 4 Adding a dc offset of A 1 results in A m t being always positive Therefore the positive envelope of is just A m t An envelope detector can be used to retrieve this A 1 m t A m t 0 7 1 0 0 4 t t AM t A m t cos c t t ECE4331 AM Example cont The choice of dc offset should be such that A m t should always be positive Otherwise envelope detector cannot be used but coherent still ok For example the minimum value of m t 0 4 Therefore A min m t for successful envelope detection What if A m t In the previous example let A 0 3 A m t m t 0 7 0 0 4 0 t AM t A m t cos c t t ECE4331 t Modulation Index Let mp be the absolute negative peak of m t EXAMPLE Single tone modulation Let m t 2sin 20t A mp A is the carrier amplitude MODULATION INDEX mp A Then we see that for A m p 0 1 When 1 or A m p the signal is overmodulated and envelope detection can not be used However we can still use synchronous demodulation mp m t 2 i 0 5 A 4 ii 1 A 2 A A For dc offset of 1 2 mp 2 1 0 5 t ECE4331 t 2 t t Sideband and Carrier Power AM t A cos c t m t cos c t The first term is the carrier and the second term is sidebands which contain the signal itself The total AM signal power is the sum of carrier power and the sideband power A2 Carrier power Pc 2 Sideband power Ps 21 Pm where Pm is the power of m t The sideband power is the useful power Ps Pm useful power Efficiency Total power Pc Ps A 2 Pm For example let m t Bcos m t mp B B or B A A 2 Pm B2 2A 2 2 For 1 max ECE4331 2 2 2 x100 1 x100 33 2 1 AM Decoder Rectifier Detector synchronous Envelope Detector asynchronous t Coherent detection Receiver can recover the frequency and phase of the transmitter by PLL Error of timing causes the performance error floor t t AM signal R C vc t Non coherent receiver has 3dB worst performance than coherent Cheaper for Non coherent receiver Nextel t ECE4331 QAM AM signal BANDWIDTH AM signal bandwidth is twice the bandwidth of the modulating signal A 5kHz signal requires 10kHz bandwidth for AM transmission If the carrier frequency is 1000 kHz the AM signal spectrum is in the frequency range of 995kHz to 1005 kHz QUADRARTURE AMPLITUDE MODULATION is a scheme that allows two signals to be transmitted over the same frequency range Equations Coherent in frequency and phase Expensive TV for analog Most modems ECE4331 SSB Frequency M baseband 2 B 2 B 0 DSB c 0 SSB c c SSB Upper sideband SSB c ECE4331 0 SSB Math 1 sgn M M U M 21 M M sgn m t 21 m t 21 F 1 M F 1 sgn 2 j 1 1 1 F 1 sgn m t 21 m t jm t m t jm h t j t t t 2 wher e m h t m t 1 1 m d t t m h t is called the Hilbert transform of m t M 1 …