I/Q Mismatch Calibration

Calibration is executed in two distinct environments with different constraints:

• Factory Calibration: Performed on the manufacturing line using precision vector network analyzers and spectrum analyzers. It establishes the gold-standard reference for a device's I/Q balance.
• Field Calibration: A self-test routine executed at boot-up or during idle slots. It relies on a low-cost on-chip observation receiver and a simple loopback path, trading absolute accuracy for operational convenience.

The accuracy of the extracted coefficients depends entirely on the stimulus signal:

• Single-Tone CW: A continuous wave tone is applied to the I and Q inputs sequentially. The resulting LO leakage and image tone amplitudes are measured directly on a spectrum analyzer to solve for DC offset and gain/phase imbalance.
• Multi-Tone or Modulated Signals: For frequency-dependent calibration, a comb of tones or a wideband modulated signal is used to characterize the mismatch filter across the entire bandwidth of interest.

The calibration algorithm iteratively refines correction parameters:

1. Stimulus Application: A known test vector is transmitted.
2. Observation Capture: The distorted output is downconverted and digitized by the feedback receiver.
3. Parameter Estimation: A least-squares or direct algebraic solver computes the gain imbalance (ε), phase imbalance (φ), and DC offset (C).
4. Convergence Check: The residual Image Rejection Ratio (IRR) is measured; if below the target (e.g., >50 dBc), the loop terminates.

A defining characteristic of calibration is the non-volatile storage of correction data:

• One-Time Programmable (OTP) Memory: Fused values are burned into the chip and cannot be altered, ensuring the calibration survives power cycles.
• Serial Peripheral Interface (SPI) Flash: Coefficients are stored in external flash and loaded into correction registers by firmware during the boot sequence.
• Pre-Distortion Matrix: The stored values directly populate the I/Q mismatch matrix applied to the transmit datapath.

The correction engine implements a widely-linear filter, which is mathematically necessary to compensate for I/Q imbalance:

• Matrix Operation: The correction applies a 2x2 matrix to the I/Q sample pair, mixing the signal with its own complex conjugate.
• Scalar Correction: For pure frequency-independent mismatch, a single complex multiply-add is sufficient: y(n) = x(n) + α * conj(x(n)).
• Filtered Correction: For frequency-dependent skew, a complex Finite Impulse Response (FIR) filter replaces the scalar α.

Calibration success is validated against strict physical layer metrics:

• Image Rejection Ratio (IRR): The primary metric, measuring the power suppression of the unwanted image sideband. A successful calibration achieves an IRR of -50 dBc to -60 dBc.
• Error Vector Magnitude (EVM): The calibration must demonstrably reduce the transmitter EVM floor to meet modulation accuracy requirements (e.g., <1% for 256-QAM).
• Carrier Feedthrough: The residual LO leakage at the carrier frequency must be suppressed below the noise floor.