I/Q mismatch calibration of direct conversion transceivers using the OFDM short training sequence
View Patent ↗A system and method are provided for compensating for an I/Q mismatch of either a direct conversion transmitter or a direct conversion receiver based on known short training symbols of a Short Training Sequence (STS) of packets transmitted according to the IEEE 802.11a or 802.11g standard. To compensate for an I/Q mismatch of a direct conversion transmitter, a packet including the STS is transmitted. Due to the I/Q mismatch of the direct conversion transmitter, the transmitter distorts the packet to provide a distorted packet including a distorted STS. Based on one or more short training symbols of the distorted STS and a known ideal short training symbol, a distortion matrix is determined. Subsequent packets transmitted by the direct conversion transmitter are pre-distorted based on the distortion matrix. Compensation of the I/Q mismatch of a direct conversion receiver may be performed in a similar fashion.
1. A method of calibrating an I/Q mismatch of a direct conversion receiver comprising:
receiving a packet comprising a known waveform having a two-dimensional I versus Q trajectory via a direct conversion receiver, wherein an I/Q mismatch of the direct conversion receiver distorts the known waveform such that the direct conversion receiver provides a distorted packet including an observed distorted waveform;
determining a distortion matrix defining the distortion of the known waveform due to the I/Q mismatch of the direct conversion receiver based on the known waveform and the observed distorted waveform by:
correcting the known waveform with a first trial frequency offset to provide a frequency-corrected known waveform;
time aligning the frequency-corrected known waveform with the observed distorted waveform;
computing a first distortion matrix based on a least squares fit of a distorted version of the frequency-corrected time aligned known waveform to the observed distorted waveform with respect to components of the distortion matrix applied to the frequency-corrected time aligned known waveform;
determining a residual error based on the first trial frequency offset and the first distortion matrix;
repeating the correcting, time aligning, computing, and determining the residual error steps for at least one additional trial frequency offset, thereby computing at least one additional distortion matrix; and
selecting the distortion matrix and a desired frequency offset from the first and at least one additional trial frequency offsets and distortion matrices by selecting one of the first and at least one additional trial frequency offsets and distortion matrices having a minimum residual error; and
compensating subsequent packets received by the direct conversion receiver based on the distortion matrix, thereby compensating for the I/Q mismatch of the direct conversion receiver.
2. The method of claim 1 wherein the known waveform is a short training symbol of a short training sequence contained in a preamble of the packet.
3. The method of claim 1 wherein determining the distortion matrix further comprises determining the distortion matrix based on the equation
(
I
OUT
Q
OUT
)
=
K
(
I
IN
Q
IN
)
,
where
K
=
(
K
11
K
12
K
21
K
22
)
,
wherein I IN and Q IN are a quadrature representation of a frequency-corrected version of the known waveform received by the direct conversion receiver, I OUT and Q OUT are a quadrature representation of the observed distorted waveform output from the direct conversion receiver, and K is the distortion matrix.
4. The method of claim 3 wherein compensating the subsequent packets received by the direct conversion receiver comprises determining a correction matrix by computing an inverse of the distortion matrix.
5. The method of claim 1 wherein determining the distortion matrix further comprises determining the distortion matrix based on the equation
(
I
IN
Q
IN
)
=
K
(
I
OUT
Q
OUT
)
,
where
K
=
(
K
11
K
12
K
21
K
22
)
,
wherein I IN and Q IN are a quadrature representation of a frequency-corrected version of the known waveform received by the direct conversion receiver, I OUT and Q OUT are a quadrature representation of the observed distorted waveform output from the direct conversion receiver, and K is a correction matrix.
6. The method of claim 1 wherein the packet is an Orthogonal Frequency Division Multiplexing (OFDM) packet and receiving the packet further comprises receiving the packet according to the IEEE 802.11a wireless standard.
7. The method of claim 1 wherein the packet is an Orthogonal Frequency Division Multiplexing (OFDM) packet and receiving the packet further comprises receiving the packet according to the IEEE 802.11g wireless standard.