IQ imbalance compensation scheme in the presence of frequency offset and dynamic DC offset for a direct conversion receiver

Abstract

A direct conversion architecture reduces the cost and power consumption of a receiver. However, a direct conversion receiver may suffer from direct current (DC) offset, frequency offset, and IQ imbalance. This paper presents an IQ imbalance estimation scheme for orthogonal frequency division multiplexing (OFDM) direct conversion receivers. The proposed IQ imbalance estimation scheme operates in the presence of dynamic DC offset and frequency offset. The proposed scheme calculates IQ imbalance from a simple equation. It employs the knowledge of the preamble symbols of the IEEE 802.11 a/g standards, while it does not require the impulse response of the channel. Numerical results obtained through computer simulation show that the bit error rate (BER) performance for the proposed IQ imbalance estimation scheme has a degradation of about 4 dB with a large DC offset, frequency offset, and IQ imbalance.

Full text

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IQ Imbalance Compensation Scheme
in the Presence of Frequency Offset and Dynamic
DC Offset for a Direct Conversion Receiver
Mamiko Inamori, Anas M.Bostamam, Yukitoshi Sanada
Department of Electronics and Electrical Engineering, Keio University
Yokohama, 223-8522 Japan
Email:{mamiko,anas}@snd.elec.keio.ac.jp, sanada@elec.keio.ac.jp
Hideki Minami
Sony Corporation,
Atsugi, 243-0014 Japan
Email: minami@sabip.semicon.sony.co.jp
Abstract—A direct conversion architecture reduces the cost and
power consumption of a receiver. However, a direct conversion
receiver may suffer from direct current (DC) offset, frequency
offset, and IQ imbalance. This paper presents an IQ imbalance
estimation scheme for orthogonal frequency division multiplexing
(OFDM) direct conversion receivers. The proposed IQ imbalance
estimation scheme operates in the presence of dynamic DC
offset and frequency offset. The proposed scheme calculates IQ
imbalance from a simple equation. It employs the knowledge of
the preamble symbols of the IEEE 802.11 a/g standards, while it
does not require the impulse response of the channel. Numerical
results through computer simulation show that the bit error rate
(BER) performance for the proposed IQ imbalance estimation
scheme has a degradation of about 4dB with a large DC offset,
frequency offset, and IQ imbalance.
I. INTRODUCTION
IEEE 802.11a/g wireless LAN (WLAN) standards are cur-
rently used extensively worldwide. In these standards, high-
rate data transmission is realized because an orthogonal fre-
quency division multiplexing (OFDM) modulation scheme is
used as the 2nd modulation. OFDM achieves high frequency
utilization efficiency due to the orthogonality between subcar-
riers.
At the receiving end, a direct conversion architecture has
been implemented, which reduces the cost and power con-
sumption of the receiver. However, OFDM direct conversion
receivers may suffer from direct current (DC) offset, frequency
offset, and IQ imbalance [1]-[3].
Several joint compensation schemes have been presented
[6]-[9]. The scheme in [9] carries out frequency offset and
IQ imbalance estimation in the time domain. However, these
schemes assume the absence of DC offset.
The level of DC offset varies due to the gain switching in
the LNA. However, none of the above studies take into account
the dynamic DC offset, frequency offset, and IQ imbalance at
the same time.
In this paper, a novel IQ imbalance estimation scheme is
investigated allowing for dynamic DC offset and frequency
offset. In the proposed scheme, a differential filter is employed
to remove the dynamic DC offset. In previous research, it
has been shown that the differential filter effectively estimates
Fig. 1. DC Offset and the Output of Differential Filter
frequency offset in the presence of dynamic DC offset [10]-
[12]. In the proposed scheme, from the output of the differ-
ential filter, the IQ imbalance as well as the frequency offset
is estimated from a simple equation. The proposed scheme
employs the knowledge of the preamble symbols of the IEEE
802.11a/g standards, while it does not require the impulse
response of the channel. Therefore, this scheme is suitable
for low-cost and low-power-consumption receivers.
II. SYSTEM MODEL
A. Preamble Model
Figure 1 shows the IEEE 802.11a/g burst structure of the
preamble signal [4], [5]. In the 802.11a/g preamble, short train-
ing sequence preamble (STSP) symbols are used for coarse
frequency offset estimation and IQ imbalance estimation. Long
training sequence preamble (LTSP) symbols are used for fine
frequency offset estimation and channel estimation.
978-1-4244-2517-4/09/$20.00 ©2009 IEEE

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Fig. 2. Receiver Architecture
A high-pass filter (HPF) can be used to eliminate the static
DC offset without removing the received signal.
B. Automatic Gain Control and Differential Filter
To maintain the received signal amplitude at a suitable fixed
level, automatic gain control (AGC) is used. In a WLAN
receiver, the AGC controls the receiver gain in the middle of
the STSP. In the 802.11a/g standards, gain control of more than
50dB is required [13]. The assumed RF architecture in this
paper is shown in Fig. 2. As shown in the figure, gain control
is applied in both the LNA and the variable gain amplifiers
(VGAs). Here, an LNA with two gain modes is assumed [14]-
[16]. This type of LNA has been discussed in [14] and [17].
The VGAs at baseband compensate the rest of the required
gain.
In the direct conversion receiver, the DC offset may be
eliminated by HPFs, as shown in Fig. 2 [1], [14]. However, as
the gain of the LNA changes, the DC offset level varies [18].
Figures 1 (a), (b), and (c) show the received signal (absolute
value) of the training sequence preamble when the gain of
the LAN is changed. At the beginning of the STSP, the gain
of the LNA is set to the maximum because the power of the
received signal is unknown to the receiver. If the power of
the received signal is sufficiently large, the LNA is switched
to the low-gain mode between t4and t5. The DC offset level
then decreases rapidly and the fluctuating DC offset level is
input into the HPF. Here, the fluctuation of the DC offset level
is modeled as a two-step function as shown in Fig. 1 (a) [18].
The transient response of the HPF due to the fluctuation of
the DC offset level appears at the output of the HPF as shown
in Fig. 1 (b). This component deteriorates the accuracy of
frequency offset estimation and IQ imbalance estimation. In
the proposed scheme, the transient response is removed using
the differential filter. The cutoff frequency of the HPF is set
to relatively low so as not to eliminate the data subcarriers
adjacent to the DC subcarrier in the data period. Since the
cutoff frequency of the HPF is low, the transient response
decreases gradually. Thus, the differential filter can suppress
the effect of the residual DC offset as shown in Fig. 1 (c).
C. IQ Imbalance
The direct conversion receiver introduces the so-called IQ
imbalance in the mixers, as shown in Fig. 2. In the figure,
the phase mismatch and gain mismatch are represented as θ
and β, respectively. Assuming that the kth digitized sample of
the OFDM preamble in the time domain is s(k), the received
signal with frequency offset, r(k), is expressed as
r(k) = s(k)exp(j2πα
N
k) + ω(k),
(1)
where N is the number of samples used for DFT, α is the
frequency offset normalized by subcarrier separation, and ω(k)
is the kth AWGN sample with zero mean and variance N0. In
this paper, because of the symmetry of the upper and lower
paths, the I-phase local signal, LI, and the Q-phase local
signal, LQ, are assumed to be as follows:
I component
:
LI= (1 + β)cos(2πfct − θ/2),
Q component
:
LQ= −(1 − β)sin(2πfct + θ/2),
where fc is the carrier frequency. These local signals are
multiplied by the received signal, and by applying the LPF,
the baseband signals, ˆ rI(k) and ˆ rQ(k), with IQ imbalance are
obtained. The kth digitized signal with a sampling interval of
Tsis given by
ˆ r(k)=ˆ rI(k) + jˆ rQ(k),
(2)
where
ˆ rI(k)=(1 + β){rI(k)cos(θ
2) − rQ(k)sin(θ
2)}, (3)
ˆ rQ(k)=(1 − β){rQ(k)cos(θ
2) − rI(k)sin(θ
2)}, (4)
where rI(k) and rQ(k) are the I component and Q component
of r(k), respectively. Hence, the complex baseband signal ˆ r(k)
is
ˆ r(k)=ˆ rI(k) + jˆ rQ(k)
{cos(θ
+ {β cos(θ
=
2) + jβ sin(θ
2) − j sin(θ
2)}r(k)
2)}r∗(k),
(5)
where the * denotes the complex conjugate.
III. FREQUENCY OFFSET ESTIMATION
A. Frequency Offset, DC Offset, and IQ Imbalance Model
From Eq. (5), the received signal with the IQ imbalance is
given as
ˆ r(k) = φr(k) + ψ∗r∗(k) + δ(k) + ω(k),
(6)

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where
φ
= cos(θ
2) + jβ sin(θ
2),
(7)
ψ
=
β cos(θ
2) + j sin(θ
2),
(8)
and δ(k) is the DC offset.
The frequency offset is estimated in the presence of the
dynamic DC offset and the IQ imbalance. After coarse esti-
mation, the LTSP symbols are used for channel estimation for
each subcarrier.
B. Frequency Offset Estimation Using Differential Filter
In this frequency offset estimation scheme, the received
signal with IQ imbalance is substituted into the differential
filter used to eliminate the residual DC offset that passes
through the HPF. The kth outputˆdSP(k) after the differential
filter is
ˆdSP(k)=ˆ rSP(k) − ˆ rSP(k − 1)
=
φ{rSP(k) − rSP(k − 1)}
+ ψ∗{r∗
+ Δδ(k,k − 1), k ≥ 1,
where
SP(k) − r∗
SP(k − 1)}
(9)
ˆ rSP(k) = φrSP(k) + ψ∗r∗
SP(k),
(10)
rSP(k) is the kth signal with the frequency offset in the STSP
period, and Δδ(k,k−1) is the difference between the kth and
(k − 1)th residual DC offsets. In the STSP, a short preamble
with a period of N/4 samples is repeated 10 times. From Eq.
(9), the autocorrelation value for frequency offset estimation
with the DC offset and the IQ imbalance is given by
N
4
)
dˆ∗
SP(k)dˆSP(k +
)
=
|φ|2
N
4
|rSP(k +
N
4−− rSP(k +
2
1)
|2
πα
4
exp(j
)
(11a)
2
πα
4
(11b)
N
4
+φ∗ψ∗(rSP(k +
N
4−
)
− rSP(k +
1))
2
exp(−j
)
N
4
+φψ(rSP(k +
N
4−
)
− rSP(k +
2
1))
2
πα
4
exp(j
)
(11c)
πα
4
(11d)
+|ψ|2
N
4
|rSP(k +
N
4−
)
− rSP(k +
2
1)
|2
exp(−j
)
N
4
4,k +N
4−1) and Δδ(k,k−1)∗, N is the number
of samples, and α is the normalized frequency offset in one
OFDM symbol period. By averaging over 10 STSP symbols,
the normalized frequency offset α is estimated.
The additional mean square error (MSE) in frequency offset
estimation due to the IQ imbalance is less than 10−3of the
+O(Δδ(k +
N
4−
4−1),Δδ(k,k −1)) is the product
,k +
1),Δδ(k,k
1)).
(11e)
−
Here, O(Δδ(k +N
of Δδ(k+N
4,k+N
square of the frequency offset [12]. Thus, the IQ imbalance is
neglected at this stage for estimation of the frequency offset.
IV. IQ IMBALANCE ESTIMATION
A. IQ Imbalance Estimation
The IQ imbalance is also estimated from the outputs of
the differential filter. From Eq. (9), the 3 preamble symbols
repeated in N/4 samples in the STSP can be expressed as
ˆdSP(k −N
4)
=ˆ rSP(k −N
φdSP(k)γ−1+ ψ∗d∗SP(k)γ,
4) − ˆ rSP(k −N
4− 1)
=
(12)
ˆdSP(k)=
=
ˆ rSP(k) − ˆ rSP(k − 1)
φdSP(k) + ψ∗d∗SP(k),
(13)
ˆdSP(k +N
4)
=ˆ rSP(k +N
4) − ˆ rSP(k +N
4− 1)
=
φdSP(k)γ + ψ∗d∗SP(k)γ−1.
(14)
Here, dSP(k) = rSP(k) − rSP(k − 1) and γ = exp(j2πα
Solving Eqs. (12), (13), and (14) as simultaneous equations,
the following equation is derived.
ˆdSP(k −N
(ˆdSP(k)γ−1−ˆdSP(k +N
Here, with the assumption of small θ, φ and ψ are approxi-
mated as
cos(θ
4).
4) −ˆdSP(k)γ−1
4))∗=ψ∗
φ∗= ε.
(15)
φ
=
2) + jβ sin(θ
β cos(θ
2) ≈ 1 + jβθ
2) ≈ β + jθ
2,
(16)
ψ
=
2) + j sin(θ
2,
(17)
using the first-order approximation of the Taylor expansionD
Thus, Eq. (15) becomes
β + jθ
1 + jβθ
2
2
≈ εI+ jεQ.
(18)
β and θ can then be calculated as follows.
β ≈
2εI
2 − εQθ,
?
εQ
(19)
θ ≈
−(ε2
I+ ε2
Q− 1) −
(ε2
I+ ε2
Q− 1)2+ 4ε2
Q
.
(20)
To obtain ε in Eq. (15), α is substituted with the value
estimated in Section III.
In terms of complexity, the estimation of ε requires the
following number of calculations;
Cε= Nsp× [2·Cadd+ 1·Cmult] + 1·Cdiv,
where Cadd, Cmult, and Cdiv are the numbers of complex
additions, multiplications, and divisions, respectively, and Nsp
represents the number of samples in the STSP. The complexity
is almost equivalent to the conventional scheme in [9].
Note that, similar to [9], the proposed scheme works well
if α is more than 0.1. This can be understood by considering
(21)

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Eq. (15). If the frequency offset is smaller, the time difference
among the outputs of the differential filter in Eqs. (12), (13),
and (14) should be set to longer than N/4. The effective fre-
quency offset then increases although the number of samples
required to calculate Eq. (15) decreases.
B. IQ Imbalance Compensation
In the LTSP and the following data period, IQ imbalance
is compensated on the basis of the phase mismatch and gain
mismatch estimated in the STSP. By consolidating Eqs. (7)
and (8) into a system of equations, we arrive at
?
=
Ω
rdQ
where ˆ rdI, ˆ rdQ, rdI, and rdQare the I and Q components of the
received signal with and without IQ imbalance, respectively.
The IQ imbalance is compensated using Ω−1.
ˆ rdI
ˆ rdQ
?
=
?
(1 + β)cos(θ
−(1 − β)sin(θ
?
2)
2)
−(1 + β)sin(θ
(1 − β)cos(θ
2)
2)
??
rdI
rdQ
?
rdI
?
,
(22)
V. SIMULATION RESULTS
A. Simulation Conditions
The MSE of the IQ imbalance estimation is evaluated
through computer simulation. The number of DFT/IDFT
points is set to 64, while 52 subcarriers are used for the
LTSP symbols, which follows the IEEE 802.11a/g standards.
A 1st-order Butterworth filter is employed as the HPF. The
cutoff frequency of the HPF is set to 10[kHz]. The normalized
frequency offset, α, is 0.3. The gain mismatch is set from 0.01
to 0.05 and the phase mismatch is set from 0 to 5[degree] [9].
The gain of the LNA can be selected between 35 and 15[dB]
[19]. The isolation between the LO output and the LNA input
is assumed to be -60[dB]. Therefore, if the power of the LO
signal is set to 0[dBm], the DC offset level is -25/-45[dBm].
On the other hand, the received signal power is set to -
53[dBm], which is equivalent to -70[dBm] on each subcarrier
in the LTSP. In this case, the DC offset is 10[dB] larger than
the signal power on each subcarrier.
1) Normalized MSE Performance of Phase Mismatch Es-
timation: Figure 3 shows the normalized MSE performance
of phase mismatch estimation. In this figure, ‘Conventional’
refers to the IQ imbalance estimation scheme in the time
domain presented in [9]. The gain mismatch β is set to 0.05
and the normalized frequency offset α is set to 0.3. In Fig. 3,
the proposed scheme has better estimation performance. The
reason for this is that the conventional scheme suffers from
the residual DC offset. In this figure, the MSE improves as
the phase mismatch increases. This is because the MSE is
normalized by the mismatch θ. Furthermore, the normalized
MSE performance improves as Eb/N0 increases from 20
to 25[dB]. The normalized MSE of the phase mismatch θ
fluctuates when Eb/N0=20[dB]. This is because Eq. (20) has
εQin the denominator. If the estimated value of εQapproaches
0 due to noise, the MSE of the phase mismatch, θ, increases.
This case rarely happens and does not change the average
BER.
2) Normalized MSE Performance of Gain Mismatch Esti-
mation: Figure 4 shows the normalized MSE performance of
the gain mismatch estimation with dynamic DC offset and
frequency offset when the gain mismatch value is varied.
The phase mismatch θ is set to 5[degree] and the normalized
frequency offset α is set to 0.3. Eb/N0in the LTSP is set to
{20, 25, or 30}[dB].
It can be seen from Fig. 4 that the normalized MSE
performance improves as the gain mismatch increases. This is
because the MSE is normalized by the gain mismatch β. As
Eb/N0increases to 10[dB], the normalized MSE is reduced
by a factor of about 10.
3) BER Performance: The BER performance versus Eb/N0
in the AWGN channel is shown in Fig. 5. The simulation
conditions are the same as those with the static DC offset.
From Fig. 5, it can be concluded that the performance degra-
dation due to the proposed scheme is about 4[dB]. This plot is
simulated using 1st interpolation for phase compensation using
pilot subcarriers. 125 OFDM symbols are considered for each
packet and 64QAM is assumed. The number of DFT/IDFT
points is set to 64. The OFDM receiver is considered with nor-
malized frequency offset α = 0.3, gain imbalance β = 0.05,
and phase mismatch θ = 5[degree].
‘With Foffset and IQ Compe (Conventional)’ refers to the
case with frequency offset compensation and IQ imbalance
compensation presented in [9]. ‘Without Compe’ represents
the simulation in the case of no frequency offset compensation
or IQ imbalance compensation, ‘With Foffset Compe’ refers
to frequency offset compensation, and ‘With Foffset and IQ
Compe’ refers to the case of frequency offset compensation
and IQ imbalance compensation. In addition, ‘Reference’
represents the simulation when phase compensation by pilot
subcarriers is carried out under frequency offset and IQ
imbalance. In each OFDM symbol, following the IEEE 802.11
a/g standards, 4 pilot subcarriers are inserted. ‘Theory’ is the
theoretical BER curve for 64QAM.
As shown in this figure, the proposed scheme exhibits su-
perior estimation performance since the conventional scheme
suffers from the residual DC offset. Moreover, neither fre-
quency offset compensation nor IQ imbalance compensation
degrades the performance significantly. Comparing the pro-
posed scheme with theoretical results, there is difference of
8[dB], in which 4[dB] of the difference is due to nonideal
channel equalization by the pilot subcarriers. Thus, the BER
using the proposed IQ imbalance estimation scheme exhibits
about 4[dB] degradation with large DC offset, frequency
offset, and IQ imbalance. However, our proposed scheme has
less complexity than existing algorithms.
VI. CONCLUSION
The direct conversion receiver has disadvantages such as
DC offset, frequency offset, and IQ imbalance. In this paper, a
low-complexity IQ imbalance estimation scheme allowing for
dynamic DC offset and frequency offset has been proposed.
The IQ imbalance is calculated using a simple equation with-
out requiring the impulse response of the channel. Therefore,

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Fig. 3.
(β=0.05, Normalized Freq. Offset = 0.3)
Normalized MSE Performance of Phase Mismatch Estimation
Fig. 4.
5[degree], Normalized Freq. Offset=0.3)
Normalized MSE Performance of Gain Mismatch Estimation (θ=
the proposed scheme is suitable for low-cost and low-power-
consumption terminals. Computer simulations show that the
BER performance using the proposed IQ imbalance estimation
scheme is satisfactory when Eb/N0is more than 20[dB], in
which 64QAM is used for the 1st modulation. The system
exhibits a degradation of about 4[dB] with a large dynamic
DC offset, a frequency offset, and an IQ imbalance. In future
studies we plan to focus on enhancing the estimation accuracy
of frequency offset and IQ imbalance recursively over multiple
frames.
ACKNOWLEDGMENT
This work is supported in part by a Grant-in-Aid for the Global Center of
Excellence for high-Level Global Cooperation for Leading-Edge Platform on
Access Spaces from the Ministry of Education, Culture, Sport, Science, and
Technology in Japan.
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