QPSK Constellation Distortion: IQ Imbalance Versus Phase Noise
A QPSK link runs at Rs = 20 Msym/s with a root-raised-cosine filter α = 0.35. The measured occupied bandwidth is close to the expected value, but the demodulator reports EVM = 18% and BER = 2×10⁻⁵ at an Eb/N0 that should give near 10⁻⁶. The recovered constellation is rotated by about 12° and its I rail is 15% larger than its Q rail. There is also low-level phase noise at 1 MHz offset. The ADC uses a 140 MHz IF, and the LO leakage is 35 dB below carrier. The team must decide whether the dominant impairment is AWGN, IQ gain/phase imbalance, or phase noise, and whether a blind equalizer alone will fix the link.
1. Compute the expected occupied bandwidth and explain why bandwidth alone does not identify the impairment.
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For RRC signalling, the occupied bandwidth is approximately (1 + α)Rs = 1.35 × 20 MHz = 27 MHz. The measurement being close to 27 MHz indicates that the pulse-shaping and symbol rate are approximately correct, so excessive spectral regrowth or severe filtering is not the first-order problem. Bandwidth is not a sufficient diagnostic because AWGN, IQ imbalance, and phase noise can all leave the occupied bandwidth nearly unchanged while degrading EVM and BER. The constellation shape and the BER versus Eb/N0 curve are more informative than the spectrum mask in this case.
2. Diagnose the dominant impairment from the constellation and EVM evidence.
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AWGN would produce a symmetric, roughly circular cloud around each ideal point; it would not rotate the whole constellation or make one rail systematically larger. Phase noise produces tangential spreading around each point, especially at large radius, not a fixed 12° rotation. A fixed rotation plus a 15% I/Q gain mismatch is the signature of IQ gain and phase imbalance: the phase error rotates the constellation, while the gain error stretches one rail relative to the other. An EVM of 18% is of the order expected from a 15% gain error and about 12° (0.21 rad) phase error, so IQ imbalance is the dominant impairment. Residual phase noise and AWGN may contribute, but they are secondary.
3. Recommend a correction and state whether a blind equalizer alone is sufficient.
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Apply an IQ compensation before or inside the demodulator: estimate the gain ratio and phase error from the received symbols, then correct with a 2×2 correction matrix or a Gram-Schmidt/ellipse-correction algorithm. Calibrate the analog I and Q paths and the LO phase so the residual rotation and rail mismatch are small. A blind equalizer alone is not sufficient: it can correct linear channel distortion and some cross-coupling, but it does not inherently know the correct QPSK phase reference or remove a systematic I/Q gain mismatch without an additional IQ-imbalance model. After correction, re-measure EVM and BER; if phase noise still dominates, improve the LO phase noise or increase loop bandwidth as appropriate.