Digital Phase Modulation Schemes

• Binary Phase Shift Keying (BPSK): 1 bit per symbol
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• Quaternary Phase Shift Keying (QPSK): 2 bits per symbol
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• 8-Phase Shift Keying (8PSK): 3 bits per symbol
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Digital Amplitude Modulation Schemes

• 4-position Quadrature Amplitude Modulation (4-QAM): 2 bits per symbol
• 16-position Quadrature Amplitude Modulation (16-QAM): 4 bits per symbol
• 64-position Quadrature Amplitude Modulation (64-QAM): 6 bits per symbol
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Decision Boundaries

Pulse Shaping

• Purpose: limit the bandwidth of the transmission
• Happens after bit-to symbol mapping above
• Have to avoid introducing inter-symbol-interference (ISI)
• Popular implementation: raised cosine filter (RC)
  • One-half implemented on transmitter end, other half implemented on receive end
  • Each half is a root-raised cosine filter (RRC) filter
  • When combined, the RRC filters provide zero-ISI
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Digital Upconversion and Downconversion

• Modulates and Demodulates a signal
• Additionally moves between the symbol rate f_symbol and the DAC or ADC sampling rate f_system
• Digital Upconverter (DUC): transmitter, f_symbol -> f_system through filtering
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• Digital Downconverter (DDC): receiver, f_system -> f_symbol
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• Multirate R_multirate = f_system/f_symbol

Carrier Synchronization

• On receive side, need to account for phase and frequency offset errors
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• Phase error calculation:
  • Decision Directed: transmitted data symbols unknown, phase error is generated based on symbol decision (closest symbol to received sample)
    • Generally use this method
    • Possible that there is still phase rotation (e.g., a multiple of 90 degrees)
  • Data aided: receiver knows transmitted symbols, derives phase error based on that
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Timing correction

• Goal to sample at an interval at the proper time to get the max signal amplitude
• Done using a timeing error detector (TED)
• Two methods: oversampling and interpolation
  • oversampling: sample at rate much higher than symbol rate, then select the samples closest to the maximum effect points
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  • Interpolation: oversample at small amount (e.g. 2x symbol rate) and interpolate between samples
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• TED produces early and late signals, then subtracts between them to get a 'punctual' (on time) sample time
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• Combined timing and carrier synchronization looks like:
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• Should make I and Q amplitudes converge:
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Coarse Frequency Syncronization

• Calculates an initial frequency offset, for a large value (happens before fine frequency sync)
• Uses FFT on input, raised to 4th power, then selecting FFT bin with highest magnitude as the desired signal
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PSK phase ambiguity

• Once you have a proper PSK (e.g. BPSK or QPSK) signal plot, there is a chance the phase is incorrect, e.g. rotated to the wrong constellation points. This means your resulting bits will be incorrect since they are derived from the wrong constellation point
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• Two ways to handle this: differential encoding or unique word transmission

Differential Encoding

• Encodes input bits so that they can be recovered after incorrect receive due to PSK phase offset
• For BPSK, you use the current bit and previous encoded bit (Default 0) and XNOR them:
• To decode, you do the same thing except your previous bit to use is BEFORE decoding
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• If the phase is incorrect on the received symbols, then the first decoded bit will be incorrect, but the rest will be correct
• QPSK encoding and decoding is similar, except you use the last 2 bits instead of just the last bits, and the output of encoding/decoding is two bits instead of 1 bit
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Unique Word Synchronization

• You transmit a fixed/known bit sequence before your actual payload. On the receive end, we look for that sequence, and if it's not found, check the resulting sequence if we rotate the phase/bit mapping ourselves. Once we find the phase mapping that results in the correct sequence, we apply said phase mappnig to the rest of the input as well
• For BSPK this looks like:
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• For QPSK this looks like:
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