I and Q Components in Communications Signals and Single Sideband 1 SHARLENE KATZ DAVID SCHWARTZ JAMES FLYNN 7/22/2010 OVERVIEW 2 Description of I and Q signal representation Advantages of using I and Q components Using I and Q to demodulate signals I and Q signal processing in the USRP Single Sideband (SSB) Processing I and Q components of a SSB signal in the USRP 7/22/2010 Standard Representation of Communications Signals 3 Modulation Time Domain Frequency Domain AM XAM(f) f -fc fc DSB FM 7/22/2010 Overview of I and Q Representation 4 I and Q are the In-phase and Quadrature components of a signal. Complete description of a signal is: x()()() t I t jQ t x(t) can therefore be represented as a vector with magnitude and phase angle. Phase angle is not absolute, but relates to some arbitrary reference. 7/22/2010 Overview of I and Q Representation 5 In Digital Signal Processing (DSP), ultimate reference is local sampling clock. DSP relies heavily on I and Q signals for processing. Use of I and Q allows for processing of signals near DC or zero frequency. If we use “real” signals (cosine) to shift a modulated signal to baseband we get sum and difference frequencies If we use a “complex” sinusoid to shift a modulated signal to baseband we ONLY get the sum This avoids problems with images 7/22/2010 Overview of I and Q Representation 6 Nyquist frequency is twice highest frequency, not twice bandwidth of signal. For example: common frequency used in analog signal processing is 455 kHz. To sample in digital processing, requires 910 kS/s. But if the signal bandwidth is only 10 kHz. With I & Q, sampling requires only 20 kS/s. 7/22/2010 Overview of I and Q Representation 7 I and Q allows discerning of positive and negative frequencies. If : H() f a jb Then: H() f a jb 7/22/2010 Overview of I and Q Representation 8 Representing familiar characteristics of a signal with I and Q: 22 • Amplitude: A()()() t I t Q t • Phase: 1 Qt() (t ) tan It() • Frequency: Q()() t I t I()() t Q t ()t ft()tt t I22()() t Q t 7/22/2010 DEMODULATION 9 AM: x()()() t i22 t q t SSB: x()() t i t 11 i ()(1) t q t q ()(1) t i t FM: xt( ) tan t i( t ) i ( t 1) q ( t ) q ( t 1) 1 qt() PM: xt( ) tan it() 7/22/2010 Overview of I and Q Representation 10 The traditional FM equation: x( t ) cos( t k x ( t ) dt ) FM c m The analytic equation: xFM( t ) I ( t )cos( c t ) jQ ( t )sin( c t ) Modulation and Demodulation methods are different when I and Q representation is used 7/22/2010 USRP DAUGHTER BOARD 11 LPF ADC I AMP cos ωc t LPF ADC Q sin ωc t 7/22/2010 FPGA 12 cos ωf tn n = sample number I decimate I complex To USB multiply and PC Q decimate Q sin ωf tn 7/22/2010 Complex Multiply 13 cos (ω t ) I f n I Q Q cos (ωf tn ) (A + j B) * (C + j D) = AC – BD + j (BC + AD) cos t + I + j Q f sinft 7/22/2010 Sideband Modulation 14 Where’s the intelligence? A signal carries useful information only when it changes. Change of ANY carrier parameter produces sidebands. The intelligence or information is in the sidebands. Why not just send the sidebands or just a sideband? 7/22/2010 AM Review 15 AM review: Carrier is modulated by varying amplitude linearly proportional to intelligence (baseband) signal amplitude. Block Diagram m x x(t) + xAM(t)=Ac [1+mx(t)]cos ct Accosct 7/22/2010 AM: Time Domain 16 AM in the Time Domain 100% modulated Unmodulated carrier carrier 7/22/2010 AM: Frequency Domain 17 AM in the Frequency Domain carrier lower upper sideband sideband 7/22/2010 Double Sideband Modulation (DSB) 18 Let’s just transmit the sidebands x(t) m x + xDSB(t) = Ac*m*x(t)*cosct Accosct X 7/22/2010 DSB: Time Domain 19 Double Sideband in the Time Domain 7/22/2010 DSB: Frequency Domain 20 Double Sideband in the Frequency Domain carrier was here lower upper sideban sideband d 7/22/2010 Example of a DSB Signal 21 7/22/2010 DSB Spectrum 22 Note: the upper and lower sidebands are the same Do we need both of them? carrier was here lower upper sideband sideband 7/22/2010 SSB Signals 23 A sideband signal is obtained by adding a sideband filter to capture the upper or lower sideband. Low Pass Filter f f f Lower x(t) x Sideband Filter Accosct f 7/22/2010 Example of a USB Signal 24 7/22/2010 Comparison of DSB and SSB 25 Power: SSB requires half of the power of DSB Bandwidth: SSB requires half of the bandwidth of DSB Complexity: SSB modulators/demodulators are more complex 7/22/2010 SSB Example 26 Start with arbitrary waveform in baseband: 7/22/2010 SSB Example 27 Modulate as Upper Sideband Signal: 7/22/2010 SSB Example LPF ADC I AMP cos ωc t LPF ADC Q sin ωc t 28 7/22/2010 SSB Example 29 LPF ADC I AMP cos ωc t LPF AD Q C sin ωc t 7/22/2010 SSB Example LPF ADC I AMP cos ωc t LPF ADC Q sin ωc t 30 7/22/2010 SSB Example LPF ADC I AMP cos ωc t LPF AD Q C sin ωc t 31 7/22/2010 SSB Example LPF ADC I AMP cos ωc t LPF ADC Q sin ωc t 32 7/22/2010 SSB Example cos ωf tn n = sample number I decimate I complex To USB multiply and PC Q decimate Q sin ωf tn 33 7/22/2010 SSB Example cos ωf tn n = sample number I decimate I complex To USB multiply and PC Q decimate Q sin ωf tn 34 7/22/2010 SSB Example cos ωf tn n = sample number I decimate I complex To USB multiply and PC Q decimate Q sin ωf tn 35 7/22/2010 SSB Example cos ωf tn n = sample number I decimate I complex To USB multiply and PC Q decimate Q sin ωf tn 36 7/22/2010 Practical SSB Reception 37 Example above assumed no other signals on the band and perfectly synchronized oscillators Need to isolate (filter) the signal of interest and deal with oscillators slightly out of sync GRC tutorial demonstrates Weaver’s Method of demodulating SSB that solves these problems 7/22/2010.