# US 12,184,314 B2 · Frequency-dependent IQ mismatch calibration for radio frequency (RF) transmitters

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- Number: US 12,184,314 B2
- Document ID: US12184314B2
- Status: Granted
- Kind: B2
- Application number: 18/316,050
- Filed: 2023-05-11
- Published: 2023-11-16
- Granted: 2024-12-31
- Earliest claimed: 2022-05-11
- Assignees: Newracom, Inc.
- Applicants: NEWRACOM, Inc.
- Inventors: Seong-Sik Myoung; Ryunwoo Kim; Jong-Han Lim; Jeongki Choi; Jaeyoung Ryu
- Web page: https://patentgrep.com/patent/US12184314B2

## CPC

- H04B 1/0475: {with means for limiting noise, interference or distortion (H04B1/0483 takes precedence)}
- H04L 27/0008: {arrangements for allowing a transmitter or receiver to use more than one type of modulation (negotiating modulation type for two-way transmission paths H04L5/1453)}
- H04L 27/364: {Arrangements for overcoming imperfections in the modulator, e.g. quadrature error or unbalanced I and Q levels}
- H04B: TRANSMISSION
- H04L: TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION (arrangements common to telegraphic and telephonic communication H04M)

## Abstract

A method for calibrating a radio frequency (RF) transmitter to compensate for a frequency-dependent in-phase quadrature (FDIQ) mismatch is disclosed. The method may include determining in-phase quadrature (IQ) amplitude and phase mismatches of the RF transmitter for a lower side band (LSB) and an upper side band (USB), determining a FDIQ mismatch based on linear fitting the IQ amplitude and phase mismatches for the LSB and the USB, modifying the FDIQ mismatch based on flipping a FDIQ phase mismatch in the LSB and flipping a FDIQ phase mismatch in the USB to generate a modified FDIQ mismatch, determining Fourier coefficients based on applying an inverse fast Fourier transform to the modified FDIQ mismatch, and determining FIR coefficients for a finite impulse response (FIR) filter of the RF transmitter based on windowing the Fourier coefficients.

## Claims

### Claim 1

A method for calibrating a radio frequency (RF) transmitter to compensate for a frequency-dependent in-phase quadrature (FDIQ) mismatch of the RF transmitter, the method comprising:
determining an in-phase quadrature (IQ) amplitude and phase mismatch of the RF transmitter for a lower side band (LSB) and an IQ amplitude and phase mismatch of the RF transmitter for an upper side band (USB);
determining the FDIQ mismatch based on linear fitting the IQ amplitude and phase mismatch for the LSB and the IQ amplitude and phase mismatch for the USB;
modifying the FDIQ mismatch based on flipping a FDIQ phase mismatch in the LSB and flipping a FDIQ phase mismatch in the USB to generate a modified FDIQ mismatch;
determining Fourier coefficients based on applying an inverse fast Fourier transform to the modified FDIQ mismatch; and
determining FIR coefficients for a finite impulse response (FIR) filter of the RF transmitter based on windowing the Fourier coefficients.

### Claim 2 (depends on 1)

The method of claim 1, further comprising:
configuring taps of the FIR filter using the FIR coefficients so that the FIR filter compensates for the FDIQ mismatch.

### Claim 3 (depends on 2)

The method of claim 2, wherein the FIR filter is included in an IQ mismatch compensation module of the RF transmitter.

### Claim 4 (depends on 3)

The method of claim 3, wherein the IQ mismatch compensation module receives signals from a RF digital pre-distortion (DPD) module of the RF transmitter and outputs signal to an I path baseband DPD module and a Q path baseband DPD module of the RF transmitter.

### Claim 5 (depends on 1)

The method of claim 1, wherein the flipping the FDIQ phase mismatch in the LSB includes regenerating a FDIQ phase mismatch from frequencies −fs/2 to −fs/4 based on flipping a FDIQ phase mismatch from frequencies −fs/4 to 0 Hertz and the flipping the FDIQ mismatch in the USB includes regenerating a FDIQ phase mismatch from frequencies fs/4 to fs/2 based on flipping a FDIQ phase mismatch between frequencies 0 Hertz to fs/4, wherein fs represents a sampling rate of the FIR filter.

### Claim 6 (depends on 5)

The method of claim 5, wherein the modified FDIQ mismatch and the Fourier coefficients are expressed according to the following equations:
ε
⁡
(
ω
)
=
ε
FI
⁢
φ
⁡
(
ω
)
=
φ
FI
+
Δ
⁢
φ
2
·
(
Tri
⁡
(
f
+
f
s
/
4
f
s
/
4
)
-
Tri
⁡
(
f
-
f
s
/
4
f
s
/
4
)
)
⁢
ε
⁡
(
ω
)
+
j
⁢
φ
⁡
(
ω
)
=
ε
FI
+
j
⁢
φ
FI
+
j
·
Δ
⁢
φ
2
·
(
Tri
⁡
(
f
+
f
s
/
4
f
s
/
4
)
-
Tri
⁡
(
f
-
f
s
/
4
f
s
/
4
)
)
c
[
n
]
=
F
-
1
⁢
{
ε
FI
+
j
⁢
φ
FI
+
j
·
Δ
⁢
φ
2
·
(
Tri
⁡
(
f
+
f
s
/
4
f
s
/
4
)
-
Tri
⁡
(
f
-
f
s
/
4
f
s
/
4
)
)
}
=
(
ε
FI
+
j
⁢
φ
FI
)
·
δ
[
n
]
+
j
·
Δ
⁢
φ
2
·
F
-
1
⁢
{
Tri
⁡
(
f
+
f
s
/
4
f
s
/
4
)
-
Tri
⁡
(
f
-
f
s
/
4
f
s
/
4
)
}
=
(
ε
FI
+
j
⁢
φ
FI
)
·
δ
[
n
]
+
Δ
⁢
φ
·
F
-
1
⁢
{
Tri
⁡
(
f
f
s
/
4
)
}
·
sin
[
π
2
⁢
n
]
=
(
ε
FI
+
j
⁢
φ
FI
)
·
δ
[
n
]
+
Δ
⁢
φ
4
·
sinc
2
[
1
4
⁢
n
]
·
sin
[
π
2
⁢
n
]
,
wherein
ε(ω) represents a modified FDIQ amplitude mismatch,
jφ(ω) represents a modified FDIQ phase mismatch,
ε(ω)+jφ(ω) represents the modified FDIQ mismatch,
c[n] represents the Fourier coefficients,
n represents an index,
F−1{⋅} represents the inverse Fourier transform,
εFI represents a frequency-independent IQ (FIIQ) amplitude mismatch or (ε(−fm)+ε(fm))/2,
φFI represents a FIIQ phase mismatch or (φ(−fm)+φ(fm))/2,
Δφ represents a phase mismatch difference or φ(−fs/4)−φ(fs/4),
Δφ′ represents a measured phase mismatch difference or φ(−fm)−φ(fm),
fm, represents a measured frequency,
fs represents the sampling rate of the FIR filter,
Tri(f) represents a triangular function, and
δ[n] represents a delta function.

### Claim 7 (depends on 6)

The method of claim 6, wherein the FIR coefficients are determined using the following equation:
ε
[
n
]
+
j
⁢
φ
[
n
]
=
c
[
n
]
∘
w
[
n
]
=
(
ε
FI
+
j
⁢
φ
FI
)
·
δ
[
n
]
+
(
Δ
⁢
φ
4
·
sinc
2
[
1
4
⁢
n
]
·
sin
[
π
2
⁢
n
]
)
∘
w
[
n
]
=
(
ε
FI
+
j
⁢
φ
FI
)
·
δ
[
n
]
+
(
Δ
⁢
φ
′
16
·
f
s
f
m
·
sinc
2
[
1
4
⁢
n
]
·
sin
[
π
2
⁢
n
]
)
⋆
w
[
n
]
ε
[
n
]
+
j
⁢
φ
[
n
]
=
c
[
n
]
⋆
w
[
n
]
=
(
ε
FI
+
j
⁢
φ
FI
)
·
δ
[
n
]
+
(
Δ
⁢
φ
4
·
sinc
2
[
1
4
⁢
n
]
·
sin
[
π
2
⁢
n
]
)
∘
w
[
n
]
,
-
(
2
⁢
N
-
1
)
≤
n
≤
(
2
⁢
N
-
1
)
,
wherein
(∘) represents an element-wise product operator,
w[n] represents a hamming window with a length of (4N+1), and
N represents a number of addition real coefficients for FDIQ mismatch compensation.

### Claim 8 (depends on 1)

The method of claim 1, wherein the windowing uses a Hamming window.

### Claim 9 (depends on 1)

The method of claim 1, wherein the IQ amplitude and phase mismatch for the LSB is determined at a frequency of −400 kilohertz (kHz) and the IQ amplitude and phase mismatch for the USB is determined at a frequency of +400 kHz.

### Claim 10

A non-transitory machine-readable storage medium having computer code stored therein, which when executed by one or more processors of a computing system, causes the computing system to perform operations for calibrating a radio frequency (RF) transmitter to compensate for a frequency-dependent in-phase quadrature (FDIQ) mismatch of the RF transmitter, the operations comprising:
determining an in-phase quadrature (IQ) amplitude and phase mismatch of the RF transmitter for a lower side band (LSB) and an IQ amplitude and phase mismatch of the RF transmitter for an upper side band (USB);
determining the FDIQ mismatch based on linear fitting the IQ amplitude and phase mismatch for the LSB and the IQ amplitude and phase mismatch for the USB;
modifying the FDIQ mismatch based on flipping a FDIQ phase mismatch in the LSB and flipping a FDIQ phase mismatch in the USB to generate a modified FDIQ mismatch;
determining Fourier coefficients based on applying an inverse fast Fourier transform to the modified FDIQ mismatch; and
determining FIR coefficients for a finite impulse response (FIR) filter of the RF transmitter based on windowing the Fourier coefficients.

### Claim 11 (depends on 10)

The non-transitory machine-readable storage medium of claim 10, wherein the operations further comprise:
configuring taps of the FIR filter using the FIR coefficients so that the FIR filter compensates for the FDIQ mismatch.

### Claim 12 (depends on 11)

The non-transitory machine-readable storage medium of claim 11, wherein the FIR filter is included in an IQ mismatch compensation module of the RF transmitter.

### Claim 13 (depends on 12)

The non-transitory machine-readable storage medium of claim 12, wherein the IQ mismatch compensation module receives signals from a RF digital pre-distortion (DPD) module of the RF transmitter and outputs signal to an I path baseband DPD module and a Q path baseband DPD module of the RF transmitter.

### Claim 14 (depends on 10)

The non-transitory machine-readable storage medium of claim 10, wherein the flipping the FDIQ phase mismatch in the LSB includes regenerating a FDIQ phase mismatch from frequencies −fs/2 to −fs/4 based on flipping a FDIQ phase mismatch from frequencies −fs/4 to 0 Hertz and the flipping the FDIQ phase mismatch in the USB includes regenerating a FDIQ phase mismatch from frequencies fs/4 to fs/2 based on flipping a FDIQ phase mismatch between frequencies 0 Hertz to fs/4, wherein fs represents a sampling rate of the FIR filter.

### Claim 15 (depends on 14)

The non-transitory machine-readable storage medium of claim 14, wherein the modified FDIQ mismatch and the Fourier coefficients are expressed according to the following equations:
ε
⁡
(
ω
)
=
ε
FI
⁢
φ
⁡
(
ω
)
=
φ
FI
+
Δ
⁢
φ
2
·
(
Tri
⁡
(
f
+
f
s
/
4
f
s
/
4
)
-
Tri
⁡
(
f
-
f
s
/
4
f
s
/
4
)
)
⁢
ε
⁡
(
ω
)
+
j
⁢
φ
⁡
(
ω
)
=
ε
FI
+
j
⁢
φ
FI
+
j
·
Δ
⁢
φ
2
·
(
Tri
⁡
(
f
+
f
s
/
4
f
s
/
4
)
-
Tri
⁡
(
f
-
f
s
/
4
f
s
/
4
)
)
c
[
n
]
=
F
-
1
⁢
{
ε
FI
+
j
⁢
φ
FI
+
j
·
Δ
⁢
φ
2
·
(
Tri
⁡
(
f
+
f
s
/
4
f
s
/
4
)
-
Tri
⁡
(
f
-
f
s
/
4
f
s
/
4
)
)
}
=
(
ε
FI
+
j
⁢
φ
FI
)
·
δ
[
n
]
+
j
·
Δ
⁢
φ
2
·
F
-
1
⁢
{
Tri
⁡
(
f
+
f
s
/
4
f
s
/
4
)
-
Tri
⁡
(
f
-
f
s
/
4
f
s
/
4
)
}
=
(
ε
FI
+
j
⁢
φ
FI
)
·
δ
[
n
]
+
Δ
⁢
φ
·
F
-
1
⁢
{
Tri
⁡
(
f
f
s
/
4
)
}
·
sin
[
π
2
⁢
n
]
=
(
ε
FI
+
j
⁢
φ
FI
)
·
δ
[
n
]
+
Δ
⁢
φ
4
·
sinc
2
[
1
4
⁢
n
]
·
sin
[
π
2
⁢
n
]
,
wherein
ε(ω) represents a modified FDIQ amplitude mismatch,
jφ(ω) represents a modified FDIQ phase mismatch,
ε(ω)+jφ(ω) represents the modified FDIQ mismatch,
c[n] represents the Fourier coefficients,
n represents an index,
F−1{⋅} represents the inverse Fourier transform,
εFI represents a frequency-independent IQ (FIIQ) amplitude mismatch or (ε(−fm)+ε(fm))/2,
φFI represents a FIIQ phase mismatch or (φ(−fm)+φ(fm))/2,
Δφ represents a phase mismatch difference or φ(−fs/4)−φ(fs/4),
Δφ′ represents a measured phase mismatch difference or φ(−fm)−φ(fm),
fm, represents a measured frequency,
fs represents the sampling rate of the FIR filter,
Tri(f) represents a triangular function, and
δ[n] represents a delta function.

### Claim 16 (depends on 15)

The non-transitory machine-readable storage medium of claim 15, wherein the FIR coefficients are determined using the following equation:
ε
[
n
]
+
j
⁢
φ
[
n
]
=
c
[
n
]
∘
w
[
n
]
=
(
ε
FI
+
j
⁢
φ
FI
)
·
δ
[
n
]
+
(
Δ
⁢
φ
4
·
sinc
2
[
1
4
⁢
n
]
·
sin
[
π
2
⁢
n
]
)
∘
w
[
n
]
=
(
ε
FI
+
j
⁢
φ
FI
)
·
δ
[
n
]
+
(
Δ
⁢
φ
′
16
·
f
s
f
m
·
sinc
2
[
1
4
⁢
n
]
·
sin
[
π
2
⁢
n
]
)
⋆
w
[
n
]
ε
[
n
]
+
j
⁢
φ
[
n
]
=
c
[
n
]
⋆
w
[
n
]
=
(
ε
FI
+
j
⁢
φ
FI
)
·
δ
[
n
]
+
(
Δ
⁢
φ
4
·
sinc
2
[
1
4
⁢
n
]
·
sin
[
π
2
⁢
n
]
)
∘
w
[
n
]
,
-
(
2
⁢
N
-
1
)
≤
n
≤
(
2
⁢
N
-
1
)
,
wherein
(∘) represents an element-wise product operator,
w[n] represents a hamming window with a length of (4N+1), and
N represents a number of addition real coefficients for FDIQ mismatch compensation.

### Claim 17 (depends on 10)

The non-transitory machine-readable storage medium of claim 10, wherein the windowing uses a Hamming window.

### Claim 18 (depends on 10)

The non-transitory machine-readable storage medium of claim 10, wherein the IQ amplitude and phase mismatch for the LSB is determined at a frequency of −400 kilohertz (kHz) and the IQ amplitude and phase mismatch for the USB is determined at a frequency of +400 KHz.

### Claim 19

A radio frequency (RF) transmitter comprising:
a frequency-dependent in-phase quadrature (FDIQ) compensation circuit comprising a finite impulse response (FIR) filter, wherein the FIR filter is configured with FIR coefficients that are determined based on modifying a FDIQ mismatch of the RF transmitter based on flipping portions of the FDIQ mismatch of the RF transmitter, applying an inverse fast Fourier transform to the modified FDIQ mismatch to generate Fourier coefficients, and windowing the Fourier coefficients.