Lecture 10 Digital I/Q Transceiver Digital I/Q Transceiver • Constellation Diagram •SNR • Eye Diagram Lab 5 • Transmitter • Analog Receiver • Digital Receiver 10/17/2006 Digital Modulation Baseband Input Receiver Output Lowpass it(t) ir(t) t t π π 2cos(2 f1t) 2cos(2 f1t) π π 2sin(2 f1t) 2sin(2 f1t) Lowpass qt(t) qr(t) t t Decision Boundaries Sample Times • I/Q signals take on discrete values at discrete time instants corresponding to digital data – Receiver samples I/Q channels • Uses decision boundaries to evaluate value of data at each time instant • I/Q signals may be binary or multi-bit – Multi-bit shown above 10/17/2006 L Lecture 10 Fall 2006 2 Constellation Diagram-16QAM Q 00 01 11 10 Receiver Output 00 01 Decision t Boundaries I 11 10 t Decision Sample Boundaries Times • We can view I/Q values at sample instants on a two- dimensional coordinate system • Decision boundaries mark up regions corresponding to different data values • Gray coding used to minimize number of bit errors that occur if wrong decisions made due to noise 10/17/2006 L Lecture 10 Fall 2006 3 Impact of Noise on Constellation Diagram High Power Low Power • Sampled data values no longer land in exact same location across all sample instants while decision boundaries remain fixed • Significant noise causes bit errors to be made • Increasing signal power increases distance between decision boundaries i.e., increased SNR 10/17/2006 L Lecture 10 Fall 2006 4 Transition Behavior Between Constellation Points Q 00 01 11 10 00 Decision 01 Boundaries I 11 10 Decision Boundaries • Constellation diagrams provide us with a snapshot of I/Q signals at sample instants • Transition behavior between sample points depends on modulation scheme and transmit filter 10/17/2006 L Lecture 10 Fall 2006 5 Need for Transmit Filter data(t) x(t) Td O-Order t t Track & Hold • Steps in waveform x(t) have high frequency components. (Recall Fourier Series applet) • We want spectral efficiency (i.e. narrow bandwidth signals) to conserve spectrum 10/17/2006 L Lecture 10 Fall 2006 6 Transmit Filter data(t) |P(f)|2 x(t) Td t t f 0 1/(2Td) • Special low pass filtering (e.g. raised cosine filter) removes high- frequency content but preserves signal levels as sampling points. • Trade-off bandwidth and signal integrity 10/17/2006 L Lecture 10 Fall 2006 7 Lab 5 Transmitter Block 10/17/2006 L Lecture 10 Fall 2006 8 Σ−Δ Modulator Pushes Quantization Noise to High Frequency • Allows music to be encoded digitally • LPF at receiver is used to remove quantization noise while preserving the signal. Tradeoff is noise vs. signal integrity Time Domain Frequency Domain 10/17/2006 L Lecture 10 Fall 2006 9 Lab 5 Analog Receiver Block Diagram rx = rxa + jrxb Neglecting higher frequency terms rxa = it (t)cos[Δω ct + φOFF (t)] Where Δω c : Difference between transmitter and receiver modulation frequency φOFF (t):Difference in phase between transmitter and receiver. It is a function of time. rxb = qt (t)cos[Δω ct + φOFF (t)] If we can measure Δωc and φOFF(t) we can remove both frequency and phase offset. 10/17/2006 L Lecture 10 Fall 2006 10 Complex Modulation Write rx = rxa + jrxb where rxa = RE (rx ); rxb = IM( rx ) cos(ω ct) cos( ) in exponential form r j()Δωct +θOFF (t ) xa + rx = [it (t) + jqt (t)]e Σ I × × − Multiply × sin( ) − j()Δωct +φOFF (t ) rx by e × + + r × Σ Q I = ir (t) xb sin ω t cos Q = qr (t) ( c ) ( ) Where ()= Δω ct + φOFF (t) 10/17/2006 L Lecture 10 Fall 2006 11 Lab 5 Digital Receiver Block Diagram Output i_raw & q_raw matched freq phase filter analog extract filter offset offset I i_raw i_sliced_data USRP listen to Receive Digital song I rx_a (I) Complex matched receiver analog extract filter rx_b (Q) Mixer filter operations 250 kSample/s 250 kSample/s listen to Q q_raw q_sliced_data song Q rx_a (I) in cos(ωct) sin(ωct) rx_b (Q) ωc = 2π(vco_freq + dco_freq) 10/17/2006 L Lecture 10 Fall 2006 12 Eye Diagram for 1 Gb/s Data Rate [2-level -it(t)] • Wrap signal back onto itself every 2*Td seconds – Same as an oscilloscope would do • Allows immediate assessment of the quality of the signal at the receiver (look at eye opening) Snapshot in Time Eye Diagram 0.4 0.4 0.35 0.35 0.3 0.3 0.25 0.25 0.2 0.2 out out 0.15 0.15 0.1 0.1 0.05 0.05 0 0 −0.05 −0.05 0 0.5 1 1.5 2 2.5 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 TIME −8 −9 x 10 Time (seconds) x 10 10/17/2006 L Lecture 10 Fall 2006 13 Relationship of Eye to Sampling Time and Slice Level • Horizontal portion of eye indicates sensitivity to timing jitter • Vertical portion of eye indicates sensitivity to additional noise Sampling Instant Eye Diagram 0.4 0.35 0.3 0.25 Slice Level 0.2 out 0.15 0.1 0.05 0 0.05 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 9 Time (seconds) x 10 10/17/2006 L Lecture 10 Fall 2006 14 Realistic Eye Diagram Eye Diagram 0.6 0.5 0.4 0.3 out 0.2 0.1 0 −0.1 0 2 4 6 8 −11 Time (seconds) x 10 • Eye more closed due to amplitude noise and timing variation • Line denotes best time to sample 10/17/2006 L Lecture 10 Fall 2006 15 Multi-Level Signaling • Increase spectral efficiency by sending more than one bit during a symbol interval • Example: 4-Level PAM on each channel I and Q Eye Diagram 0.5 0.4 0.3 0.2 out 0.1 0 −0.1 −0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 −10 Time (seconds) x 10 10/17/2006 L Lecture 10 Fall 2006 16.