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Sensitivity to I/Q imbalance
 In an OFDM transceiver, it requires shifting either the RF
signal or the LO output by 90 o.
I
VLO
cos2f ct 
 900
sin 2f c t 
+
Matching
VRF
network
Power Amp
(PA)
LPF
I
LPF
Q
cos2f c t 
 90 0
Duplexer
sin 2f c t 
Q
 The errors in the nominally 90 o phase shift, and mismatches
between the amplitudes of the I and Q signals corrupt the
converted signal constellation, thereby raising the bit error rate.
Wireless Communication Technologies 2.5.3
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Sensitivity to I/Q imbalance
 If there is a phase imbalance of θand an amplitude imbalance
of β, by assuming no frequency offset, we have the in-phase
local carrier (1   ) cos(0t   / 2) and the quadrature
carrier  (1  ) sin( 0t   / 2) , where
  (10  / 20  1) /(10 / 20  1)

After I/Q mapping and the OFDM demodulation,
the
d
received complex symbol of k-th subcarrier k is written as
[2]:

d k  [cos( / 2)  j sin(  / 2)]d k
(*)
*
 [ cos( / 2)  j sin(  / 2)]d  k  N
Eq. shows the cross relationship between the phase
imbalance and the amplitude imbalance.
Wireless Communication Technologies 2.5.3
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Sensitivity to I/Q imbalance
 In general, we can assume the phase imbalance and amplitude
imbalance small enough to ignore the interactive term
( j sin( / 2)d k ), thus, we can consider the two effects
separately.
 By assuming no amplitude error (   0 ), Eq. (*) can be
reduced as
dˆk  cos( / 2)d k  j sin(  / 2)d *N  k
From above Eq., the power of the interference from (N-k)th
subcarrier to kth subcarrier, PN , can then be expressed as
2
 sin(  / 2) 
  PS  tan 2 ( / 2)
PN  PS  
 cos( / 2) 
Wireless Communication Technologies 2.5.3
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Sensitivity to I/Q imbalance
 Similarly, by assuming no phase error (   0), the interference
from (N-k)th subcarrier to kth subcarrier, PN , can be
expressed as
PN  PS   2
 From the above two Eqs., the SNR will be degraded to SNR ' '
which can be derived as
SNR ' ' 
PS
SNR

PN  PN  PN 1  SNR [tan 2 ( / 2)   2 ]
 The SNR degradation versus the phase imbalance (with an amplitude
imbalance of 0.5dB) for different SNR is shown in Fig. (a) (next page). The
SNR degradation versus the amplitude imbalance (with a phase imbalance
of 5 degree) is shown in Fig. (b) (next page).
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Sensitivity to I/Q imbalance
 If SNR degradation less than 2dB is required to achieve the
typical SNR = 21dB in 802.11a 54 Mbps data-rate mode, from
Figs. (a) and (b), the phase imbalance should be less than 5
degree, and the amplitude imbalance should be less than 0.5
dB.
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