EE49/EE6720: Digital Communications 1 Lecture 12 Carrier Phase Synchronization
Block Diagrams of Communication System Digital Communication System 2 Informatio n (sound, video, text, data, ) Transducer & A/D Converter Source Encoder Channel Encoder Modulator Tx RF System Channel Output Signal D/A Converter and/or output transducer Source Decoder Channel Decoder Demodulator Rx RF System
Discrete-time QAM Modulator 3 Frequency of interest Basis Function ϕ 0 (t) Direct Digital Synthesizer Basis Function ϕ 1 (t) Note that the baseband signal s(t) may be up-converted (multiplied with carrier signal) to higher frequency (e.g. 9 MHz, 2.4 GHz, 5 GHz, etc) in super-heterodyning Example: 16-QAM Constellation
Discrete-time QAM Demodulator Eye Diagram Eye Diagram 4 x(kt s ) and y(kt s ) contain the original constellation point + noise: Eq. 5.91 Eye Diagram Eye Diagram We will assume that in the super-heterodyne receiver, the highfrequency carrier signal may have been down-converted (with a separate PLL) and we have the baseband signal r(t)
Problem: Carrier Phase Offset Uncompensated carrier phase offset can cause, 1) Counterclockwise (CCW) rotation of 1) Symbols to lie in the wrong Decision Region 5 This can happen regardless of symbol timing synchronization and absence of noise Rotation of constellation due to carrier phase offset How to compensate? Carrier Phase Synchronization: Estimating the phase of the carrier (at n=1 st sample or t=0 th second)
Carrier Phase Synchronization Typically, carrier signal is received and down-converted to the baseband signal: phase and frequency of the received signal are unknown For QAM signals, the received signal has 90 deg. phase shifts PLL designed to track simple sinusoid can not lock 6 Discrete-time QAM Receiver with Intermediate Frequency (IF) Sampling CCW Rotation comes from multiplying the oscillator output with the received I&Q signals
Carrier Phase Synchronization: Approach 1 Carrier phase synchronization will remove the phase shifts and track the remaining phase This task is done by designing a proper phase detector Carrier Phase Synchronization with Phase Adjusted Quadrature Sinusoids 7 1) Eq. 7.7 2) Compute Phase Error generates error signal using the received symbols x & y and projected symbols a 0 & a 1 3) PLL locks when θ = θ Problem: multi-rate system θ = θ 1 sample/symbol N (=Ts/T) samples/symbol
Carrier Phase Synchronization: Approach 2 First, the sinusoids are down-converted with fixed-freq. oscillators Phase compensation is done by Counter Clock Wise (CCW) rotation block This is called Decision-directed PLL (uses symbol estimates to compute phase error) 8 Fig. 7.1.2 Carrier Phase Offset Estimate, θ 1 sample/symbol
9 Carrier Phase Synchronization for QPSK
Carrier Phase Synchronization for QPSK Eq. 7.17: phase detector output = the error signal for k th symbol, e(k) Eq. 7.18: Symbol estimates (decision block) Heuristic Phase Detector
Problem: π/2 Phase Ambiguity Q: Where is the stable lock point? A: Usually, the lock point is when PLL locks at θ e =0. Here the stable lock points are θ e = -π/2 (-90 o or 270 o ), 0 (0 o ), π /2 (90 o ), π (180 o ) θ e = (-90 o or 270 o ) Error Function θ e =0 o θ e = 90 o θ e = 180 o Error The above figure shows that the QPSK carrier phase PLL with heuristic phase detector can lock onto the carrier at 4 possible points: 0 (true), +/- 90, or 180 out of phase
Carrier Phase Synchronization for QPSK Eq. 7.26: phase detector output = the error signal for k th symbol, e(k) Eq. 7.27: Symbol estimates (decision block) Max. Likelihood Phase Detector 12
Problem: π/2 Phase Ambiguity Again, the stable lock points are θ e = -π/2, 0, π /2, π. K=G a /T; where G a = amplitude gain, losses through antennas, channel, amps, mixers, filters, and other RF components T= sampling time of the received signal A= symbol amplitude θ e = (-90 o or 270 o ) Error Function θ e =0 o θ e = 90 o θ e = 180 o 13 Error The above figure shows that the QPSK carrier phase PLL with max. likelihood phase detector can lock onto the carrier at 4 possible points: 0 (true), +/- 90, or 180 out of phase
Design Example Section 7.2.3 Find the loop constants using Eq. C.61 14
15 Carrier Phase Synchronization for MQAM
Carrier Phase Synchronization for MQAM Similar architecture as QPSK: decision block changes Eq. 7.55: phase detector output = the error signal for k th symbol, e(k) Eq. 7.57-58: Symbol estimates (decision block) 16 Fig. 7.1.2 Carrier Phase Offset Estimate, θ 1 sample/symbol
Error Function for MQAM Multiple stable lock points 17 8PSK 16QAM
18 Phase Ambiguity Resolution: Unique Word
How to resolve the phase ambiguity? Unique Word : Commonly used in wired and wireless communication (also known as syncword) 19 Insert pattern of known symbols or Unique Word (UW) of 8-bits in the bit stream in Tx At the receiver, the carrier phase lock is obtained (the Tx will repeat the above packet ~ 4 times to allow the PLL transient time to pass) Next, the detector compares the estimated symbols and UW to figure out the phase ambiguity
Unique Word for QPSK 20 Total of 4 Unique Word Flags Symbol Estimates Correct by rotating the symbol estimates Or Use a different bitto-symbol map
Example1 Unique Word (UW) for QPSK Bit-to-Symbol Map Q (out of phase) I (in phase) Transmitted UW 1 0 1 1 0 1 0 0 +1-1 +1+1-1+1-1-1 21 Received UW Received Data Symbol Index Received Symbol Estimates Received Bits k 0 1 2 3 4 5 6 7 a 0 (k) -1 +1 +1-1 +1 +1-1 -1 a 1 (k) -1-1 +1 +1-1 +1 +1-1 Q: Which data bits were transmitted? A: First we need to find out the phase rotation based on the UW. Transmitted UW: Received UW:
Example1 (cont. ) Transmitted UW Received UW Unique Word (UW) for QPSK Q: Which one of the following rotations happened? 22 0 o CCW 90 o CCW 180 o CCW 270 o Q: Which data bits were transmitted? or CW 90 o
Example2 Unique Word (UW) for QPSK Bit-to-Symbol Map Q (out of phase) Transmitted UW 1 0 1 1 0 1 0 0 +1-1 +1+1-1+1-1-1 23 I (in phase) Received UW Received Data Symbol Index Received Symbol Estimates Received Bits k 0 1 2 3 4 5 6 7 a 0 (k) -1-1 +1 +1 +1 +1-1 -1 a 1 (k) +1-1 -1 +1 +1 +1-1 +1 Q: Which data bits were transmitted? A: First we need to find out the phase rotation based on the UW. Transmitted UW: Received UW:
Example2 (cont. ) Transmitted UW Received UW Unique Word (UW) for QPSK Q: Which one of the following rotations happened? 24 0 o CCW 90 o CCW 180 o CCW 270 o Q: Which data bits were transmitted? or CW 90 o
Example3 Unique Word (UW) for QPSK Bit-to-Symbol Map Q (out of phase) Transmitted UW 1 0 1 1 0 1 0 0 +1-1 +1+1-1+1-1-1 25 I (in phase) Received UW Received Data Symbol Index Received Symbol Estimates Received Bits k 0 1 2 3 4 5 6 7 a 0 (k) +1-1 -1 +1 +1 +1-1 -1 a 1 (k) +1 +1-1 -1 +1 +1-1 +1 Q: Which data bits were transmitted? A: First we need to find out the phase rotation based on the UW. Transmitted UW: Received UW:
Example3 (cont. ) Transmitted UW Received UW Unique Word (UW) for QPSK Q: Which one of the following rotations happened? 26 0 o CCW 90 o CCW 180 o CCW 270 o Q: Which data bits were transmitted? or CW 90 o
27 Phase Ambiguity Resolution: Differential Encoding
How to resolve the phase ambiguity? Differential Encoding Commonly used in Satellite Communication Instead of inserting 8-bits of UW, we rely on the phase shifts in Diff. Encoding Usually, the data are mapped to the phase of the carrier Here, the data are mapped to the phase shifts of the carrier signal 28 Eq. 7.75, Eq. 7.77-7.79: show that the data symbols a 0 and a 1 select the phase of the carrier Eq. 7.80-7.81: show that the data symbols a 0 and a 1 select the phase shifts of the carrier
29 Differential Encoding for BPSK
Differential Encoding: Modulator 30 Encoded Bits n=bit number Current bit (n) defines phase shift (of the carrier signal) from the previous phase based on the encoded bit (n-1)
Differential Encoding: Demodulator 31 Encoded Bit Estimates are produced that must be decoded
Example Differential Encoding for BPSK Please follow pages 4-402 of the book 32 1) Data Bits-to-Phase Shift Table 2) Encoded Bits-to-Symbol Map 3) Encoding Rule Truth Table Data Bits: 10 1) Encoding of Data 2) Decoding Rule Truth Table Output when Phase Ambiguity is 0 o Output when Phase Ambiguity is 180 o
33 Differential Encoding for QPSK
Example Differential Encoding for QPSK Please follow pages 402-405 of the book 34 1) Data Bits-to-Phase Shift Table 2) Encoded Bits-to-Symbol Map 3) Encoding Rule Truth Table Data Bits: 1) Encoding of Data 2) Decoding Rule Truth Table Output when Phase Ambiguity is 0 o Output when Phase Ambiguity is 180 o