IQ Imbalance Correction for OFDMA Uplink

Systems

Hisham A. Mahmoud, H seyin Arslan

u Mehmet Kemal Ozdemir, Francis E. Retnasothie

Electrical Engineering Dept., Univ. of South Florida Logus Broadband Wireless Solutions

4202 E. Fowler Ave., ENB-118, Tampa, FL, 33620 1408 Birchmount Road Toronto, ON, M1P 2E3 Canada

E-mail: {kemal, francis}@loguswireless.com

E-mail: abp4ig@r.postjobfree.com, abp4ig@r.postjobfree.com

OFDMA-uplink (UL) systems, IQ imbalance problem be-

Abstract Direct conversion receivers are attractive for low

cost systems as they avoid intermediate frequency (IF) lters. comes more complicated. First, the non-idealities in multiple

However, the direct conversion from radio frequencies (RF) to user front-ends are expected to be different. Second, the total

complex inphase (I) and quadrature (Q) baseband signals in one

IQ imbalance effects on OFDMA systems results in multiuser

mixing step introduces additional front-end distortions. These

interference (MUI) as opposed to inter-carrier interference

IQ distortions lead to a degradation in the system performance.

(ICI) in OFDM systems. In addition, in OFDMA-UL systems,

The problem becomes more signi cant in orthogonal frequency

division multiple access (OFDMA) systems where multiple user preambles are not used for channel estimation. Instead, the

signals with different IQ impairments are combined in the uplink channel is divided into subchannels -that can be assigned

(UL) signal. In this paper, detection methods for OFDMA-UL

to users- with dedicated pilots for each subchannel. Without

signals corrupted by IQ distortions are investigated. The received

preambles, many of proposed algorithms above are inapplica-

signal as a function of transmitted signals, IQ parameters,

ble.

and communication channels is mathematically formulated. We

designed a novel pilot pattern that is used by two proposed In this paper, we consider the effect of IQ imbalance on

estimation and compensation methods of IQ impairments to the the OFDMA-UL system. The received signal as a function

signal. Proposed methods were shown to signi cantly improve

of multiuser transmitted signals, IQ parameters, and commu-

the system performance.

nication channels is mathematically formulated. This signal

model is then used to investigated methods to estimate and

I. I NTRODUCTION

equalized both the multiuser channels and IQ distortions. A

Physical layers (PHY) based on orthogonal frequency divi- novel pilot pattern is designed which is then used by two

sion multiplexing (OFDM) have been proposed for various proposed methods to ef ciently mitigate signal distortions

wireless standards such as IEEE 802.11a, IEEE 802.11g, caused by the combined effect of multipath dispersive channels

digital audio broadcasting (DAB), digital video broadcasting and IQ imbalances of multiple users. The proposed methods

(DVB), and IEEE 802.16e [1] [5]. The direct conversion are shown to signi cantly reduce the impact of IQ imbalance

receiver is an attractive architecture since it avoids costly on OFDMA signals.

intermediate frequency (IF) lters, reduces power consump-

II. S YSTEM M ODEL

tion, and allows for easier integration than super-heterodyne

structure [6]. However, direct conversion receivers cause more We consider an OFDMA-UL system employing N subcar-

distortions to the baseband signal due to the imbalance be- riers per symbol. The DC subcarrier and guard subcarriers are

tween the inphase (I) and quadrature (Q) branches. The IQ disabled. The remaining subcarriers Nused are used for data

imbalance results in a degradation in the system performance. transmission with equal number of subcarriers on each side

This drawback of direct conversion receivers becomes more of the DC subcarrier. The above assumptions are common

signi cant with OFDM systems as they are known to be for most practical implementations of OFDMA systems. Used

sensitive to receiver front-end non-idealities [7]. Thus, there subcarriers are divided into M subchannels, the indexes of

is a need for methods to nullify or reduce the IQ distortions. each subchannel m is in the set Mm . Subchannels can then be

Several techniques have been proposed to reduce the degra- assigned to multiple users. Every user m generates a sequence

dation caused by IQ imbalance in OFDM-based systems [8]. of modulated symbols xm which are mapped to subcarriers of

In [9] [11], the IQ imbalance caused by the receiver front- assigned subchannels. The signal in then fed to an inverse fast

end is investigated. The combined effects of IQ imbalance at Fourier transform (IFFT) block and the cyclic pre x (CP) is

the transmitter and receiver front-ends is investigated in [12] added. The nth sample of the transmitted symbol of user m

[15]. An interesting approach that uses the in uence of IQ is,

imbalance to obtain diversity gain is proposed in [16].

xm (k )ej 2 nk/N,

sm (n) = Ng n N 1

In all of the above, the effects of IQ imbalance on multiuser

k Mm

OFDM systems -also known as orthogonal frequency division

(1)

multiple access (OFDMA) systems- are not considered. In

where Ng + N is the total number of samples per symbol and represents the ICI for v = u or the MUI for v = u, and

Ng is the size of the CP. the last term represents the noise. The interference term can

be canceled by jointly detecting xu (k ) and x (k ). In such a

The IQ imbalance distorts the ideal Tx signal as fol- v

case, the receiver needs to estimate Hm for m = 1, . . ., K .

lows [10],

The pilot subcarriers Np are divided among users/subchannels.

sm = m sm + m sm, (2)

In an IQ distortion free OFDMA system, the system es-

timates the channel response at Nused subcarriers using Np

where is the complex conjugate, and m and m are

pilots. However, for a system suffering from IQ distortion,

related to the IQ imbalance as follows,

every user m transmitting over subcarriers k Mm causes

m = cos m + j sin m, (3a)

m

interference at k as well, as shown in (7). This means that in

/

m = m cos m j sin m, (3b) worst case scenario, where k Mm k, the user effectively

transmits over twice the number of assigned subcarriers. Re-

where m and m are the gain imbalance and the phase

ceiver then needs to estimate two user channels per subcarrier

mismatch, respectively. For the remainder of the paper, m

or a total of 2Nused channel responses using the same number

and m are referred to as the IQ parameters. At the receiver,

of pilots. In addition, estimation of K sets of IQ parameters

the sum of all transmitted user signals is received,

{ m, m } is needed to fully cancel the interference introduced

K

by image carriers as shown in (8).

y (n) = rm (n) + w(n), (4)

III. C HANNEL /IQ E QUALIZATION

m=1

where K is the total number of users in the system at the In this section, equalization of the channel effects and IQ

current symbol, w(n) is thermal noise, and rm is the received distortions in the received signal is discussed. First, the UL

signal of the mth user. frame structure needs to be introduced. In OFDMA systems,

(5) used subcarriers are divided into smaller units, also known

rm (n) = sm (l)hm (n l),

as slots or tiles, which represent the minimum allocation

l

unit (see Fig. 1). The tiles are then assigned to subchannels

where hm (n) is the sampled channel impulse response (CIR) either randomly or depending on user channels. The overall

of the mth user at time t = nTs and Ts is the sampling time of received UL frame is a sum of all current user signals,

received signal. In order to eliminate any interference between which are transmitted over different communication channels.

adjacent OFDMA symbols, i.e. inter-symbol interference (ISI), The use of sophisticated channel estimation algorithms at the

the CP size, Ng is chosen such that Ng l 1 for all user receiver can signi cantly increase the system complexity and

channels. At the receiver, the CP is removed and the signal processing delay. Therefore, pilots are assigned within each

is fed to an N -point fast Fourier transform (FFT) block. The tile. The receiver can then perform channel estimation on

output of the FFT can be expressed as, each tile individually using low complexity channel estimation

N 1 techniques (e.g. linear interpolation). The drawback of this

y (n)e j 2 nk/N,

Y (k ) = 0 k N 1, (6) method is the low spectral ef ciency since more pilots are

n=0 needed to perform suf ciently accurate channel estimation.

where k is the subcarrier index. If received signal is ISI free, An example of how the UL frame is divided into tiles is

shown in Fig. 1. Used subcarriers are divided into Q tiles,

then received subcarriers of user u are,

with equal number of tiles on each side of the DC subcarrier.

Y (k ) = u Hu (k )xu (k ) + v Hv (k )x (k ) + (k ), k Mu

v This means that for every tile q, there is an image tile q =

(7)

Q q + 1. Three different tile structures are shown in the

where (k ) is thermal noise modeled as additive white Gaus- gure, where one tile dimensions are three symbols by four

sian noise (AWGN) with power spectral density (PSD) of N0, subcarriers. The tile bandwidth, Btile = 3 f, where f is the

k is the mirrored subcarrier of k over the DC subcarrier, subcarrier spacing, and the tile duration, Ttile = 3Tsym, where

v {1, . . ., K } is the index of user which subcarrier k Tsym = (N + Ng )Ts is the symbol duration. For the remainder

is assigned to, and Hm is the mth user channel frequency of this paper, Tile C structure is used. Note that a similar

response (CFR) (i.e. Hm is the N -point Fourier transform frame structure is employed by the mobile WiMAX standard.

of hm ). If Hu is perfectly known to the receiver, then the In a system with no IQ distortion, the receiver would

equalized signal of user u is, consider each tile independently. The four pilots within a

tile would be used to obtain least squares (LS) estimates.

Hv (k ) (k )

Y (k ) = u xu (k ) + v xv (k ) +, k Mu . The LS estimates are then used to estimate the channel at

Hu (k ) Hu (k )

the remaining data subcarriers using 2-D linear interpolation.

desired signal

interference If the received signal is distorted by the IQ imbalance, the

(8) receiver processes each tile q along with its image tile q .

It can be seen from the above equation that the rst term is Simpli ed block diagrams of both a conventional OFDMA

the desired signal with an attenuation u, the second term receiver and an IQ distorted OFDMA receiver are depicted in

k=1 q=1

1-tile channel

Subcarriers-to-tiles Mapper

estimation &

Parallel-to-Serial &

equalization

Serial-to-Parallel

Permutation

FFT

RF front-end

1-tile channel

estimation &

N Q

equalization

(a)

k=1 q=1 2-tile

channel+distortion

Subcarriers-to-tiles Mapper

estimation &

Q

Parallel-to-Serial &

equalization

Serial-to-Parallel

Permutation

FFT

RF front-end

Q/2

2-tile

channel+distortion

Q/2+1

N estimation &

equalization

(b)

Fig. 2. Receiver block diagram of (a) conventional OFDMA-UL system, and (b) An OFDMA-UL system for signals with IQ distortion.

Fig. 2. Without the loss of generality, we assume that tile q is in (10) is not suf cient to estimate the channel/IQ parameters

assigned to user u and tile q is assigned to user v = u. The

matrix Zi,j . Two methods are proposed to solve this problem.

received subcarriers of tile q and q are,

The rst proposed method, Method A, assumes that the tile

bandwidth, Btile is less than the channel coherence bandwidth,

yi,j = u Hu,i,j xi,j + v Hv,i,j x, yi,j q, (9a)

i,j

BC, for all users. In this case, the CFR over the tile band is

u Hu,i, x,

yi, = v Hv,i, xi, + yi, q,

(9b) almost constant (i.e. Hm,i,j Hm,i,j +3 for m {1, . . ., K }).

j j j j i,j j

Based on the above assumption, the second pair of pilots at

where the subscript {i, j } represents the ith OFDMA symbol

symbol i and subcarriers {j + 3, 3} can be represented as,

j

and j th subcarrier as shown in Fig. 3. Using (9a) and (9b),

the received signals as function of transmitted signals, users yi,j +3 u Hu,i,j +3 v Hv,i,j +3 xi,j +3

=

CFR, and users IQ parameters is expressed as,

x 3

yi, 3 u Hu,i, 3 v Hv,i, 3

j j j i,j

yi,j u Hu,i,j v Hv,i,j xi,j

xi,j +3

= (10)

x

yi, u Hu,i, v Hv,i, Zi,j (12)

x 3

j j j i,j

i,j

Zi,j

Using (10) and (12), the system can solve for Zi,j . The same

To jointly detect transmitted subcarrier xi,j and its image xi,, procedure is then repeated for the two pilot pairs at symbol

j

the receiver needs to estimate 8 unknowns (4 CFR samples and i + 2 to obtain Zi+2,j . To insure that this set of equations

4 IQ parameters), if the estimation of the channel responses has a unique solution, pilot vector pairs are chosen to be

and IQ imbalances are done separately. Alternatively, the orthogonal [17], [18] such that,

receiver can estimate only the 4 unknowns of Zi,j, if the

xi,j +3

effects of the channels and IQ imbalances are estimated jointly. x

xi,j = 0, (13a)

x 3

i,j

However, in this case, the receiver does not have an estimate of i,j

the IQ distortion introduced by each user. The LS estimation xi+2,j +3

x +2,

xi+2,j = 0. (13b)

of transmitted signal is given by, x +2, 3

i j

i j

xi,j yi,j

= Z 1 (11) Next, Zi+1,j can be estimated using 1-D interpolation between

x i,j y

i,

i,j j

Zi,j and Zi+2,j . Finally, using (11), {Zi,j, Zi+1,j, Zi+2,j } are

IV. C HANNEL /IQ E STIMATION used to estimate the remaining data subcarriers at symbols

Let s assume that {xi,j, xi,, xi,j +3, xi, 3 } are pilots {i, i + 1, i + 2}, in this order. The receiver repeats this process

j j

for each pair of tiles (Q/2 times).

as shown in Fig. 3. Knowing the value of the two pilots

TABLE I

S IMULATION PARAMETERS .

$

Parameter Value

2.5 GHz

Carrier frequency

FFT size, N 1024

CP size, Ng 128

I

Number of used subcarriers, Nused 840

Sampling frequency, 1/Ts 11.2 MHz

Number of tiles, Q 210

Number of subchannels, M 35

G

each pair of tiles. The pilots orthogonality is achieved as

' F & #

follows,

xi+2,j

G

xi,j xi, = 0, (15a)

x +2,

j

i j

xi+2,j +3

xi,j +3 xi, 3 = 0. (15b)

x +2, 3

j

i j

H

To enable the receiver to use either methods, we propose to

use the following pilot pattern, which satis es the conditions

in (13a), (13b), (15a), and (15b).

d

"

xi,j xi,j +3 d1

! #

2

=,

@9

(16a)

4

d

xi+2,j xi+2,j +3 d1

7

2

8

ED 7

d

xi, 3 xi, d2

BC

A6

j j 1

=,

(16b)

d

xi+2, 3 xi+2, d2

j j

1

5

4

where d1 and d2 are arbitrary symbols that belong to the

( $

modulation symbol set used for pilots. The above pilot pat-

)

3210

tern achieves orthogonality between pilot pairs in both the

subcarrier dimension and the symbol dimension. Thus, the

Fig. 1. UL frame structure and subcarrier mapping to tiles.

receiver can improve the system performance by adaptively

using either Method A or Method B depending on the user

symbols

channel conditions (i.e. delay spread and Doppler spread) or

Tile q

Tile q

by using both methods and choosing the estimates with the

i+2

least error vector magnitude (EVM) values.

i+1

V. S IMULATION R ESULTS

i

subcarriers

A system based on the WiMAX standard [5] is considered.

DC j-3 j-2 j-1 j

j+1 j+2 j+3

j

Typical simulation parameters are chosen based on [19] and

are summarized in Table I. We assume three users are transmit-

Fig. 3. Subcarrier indexing of a tile pair.

ting in all UL frames. The available 35 subchannels are divided

among users with 12, 12, and 11 subchannels assigned to

user 1, user 2, and user 3, respectively. Subchannels assigned

The second proposed method, Method B, assumes that the

tile duration, Ttile is less than the coherence time of the to UL users are randomized for every frame. The modulation

channel, TC, for all users. In this case, Hm,i,j Hm,i+2,j for used for data subcarriers is QPSK, and for pilots, BPSK is

used (d1 = d2 = 1). The system is tested over three channels

m {1, . . ., K }. Based on the above assumption, the second

pair of pilots (to be coupled with (10)) at symbols {i, i + 2} based on the ITU channel models [20]: Indoor A, Pedestrian B,

and subcarriers {j, } can be represented as, and Vehicular A, with Doppler spread of 0 Hz (0 km/h), 6.9 Hz

j

(3 km/h), and 138.9 Hz (60 km/h), respectively. It is assumed

yi+2,j xi+2,j

Zi,j that the channel is independent between different frames and

(14)

yi+2, xi+2,

j j between different users. The receiver processes each frame

Using (10) and (14), the system solves for Zi,j . Similarly, individually. At the receiver, the uncoded bit error rate (BER)

the pilot pairs at subcarriers {j + 3, 3} can be used to

j is measured and averaged over all users.

solve for Zi,j +3 . Next, the receiver uses 1-D interpolation For all generated simulations, it is rst assumed that there

to calculate {Zi,j +1, Zi,j +2 } from {Zi,j, Zi,j +3 }. Finally, the are no IQ imbalances introduced to the signal. The receiver

above values of Z are used to estimate the remaining data uses all pilots per tile to estimate and equalize only the channel

subcarriers in both tiles. The procedure is then repeated for effects using 2-D linear interpolation technique. This case is

labeled as Ideal IQ . Next, the UL user signals are distorted 0

10

by IQ imbalances. The IQ gain imbalance and phase mismatch IQ Imbalance / No compensation

IQ Imbalance / Method A

of user 1, user 2, and user 3 are {0.2, 2 }, {0.35, 5 }, and IQ Imbalance / Method B

{0.5, 8 }, respectively. The uncoded BER is measured while 1

Ideal IQ

10

the receiver operates assuming no IQ imbalance is present.

The results are labeled as IQ Imbalance/ No compensation . 2

10

Finally, Method A and Method B are used to estimate and

BER

equalize the combined channel and IQ distortions. The results

are shown in Fig. 4, Fig. 5, and Fig. 6. In all gures, the 3

10

system performance degrades signi cantly when the receiver

ignores the IQ distortions to the signal. At a signal-to-noise 4

10

ratio (SNR) of 35 dB, the IQ distortions increase the BER

by two orders of magnitude. On the other hand, proposed

methods manage to reduce the BER considerably. For the

**-**-**-**-**-** 40 45 50

results over the Pedestrian B channel in Fig. 4, the delay spread SNR

is high while the Doppler spread is low. As a result, Method

B outperforms Method A, since it assumes low Doppler Fig. 4. Average uncoded BER of QPSK signals received over Pedestrian B

spreading. Method B signi cantly reduces the IQ distortion channel and with IQ impairments.

effect on the signal. The loss is around 2 dB from the ideal

IQ case at BER = 10 3 . For the results over the Vehicular A 0

10

channel in Fig. 5, both delay spread and Doppler spread are IQ Imbalance / No compensation

high. In this case, Method A slightly outperforms Method B, IQ Imbalance / Method B

IQ Imbalance / Method A

since its approximation is more accurate. While both methods 1

Ideal IQ

10

A and B improve the BER signi cantly, the loss from the ideal

IQ case is considerable. Under such highly selective channels

2

10

and with IQ distortions, the system can choose to reduce signal

BER

bandwidth which leads to an improved performance of Method

A. Finally, for the results over the Indoor A channel in Fig. 6, 3

10

both delay spread and Doppler spread are low. As expected

in this case, both methods A and B perform very well. The

4

BER degradation due to the IQ distortions is recovered with 10

around 2.5 dB loss from the ideal IQ case at BER = 10 3 .

Note that there is a loss from the ideal IQ case even in

channels with low Doppler spread and delay spread. This **-**-**-**-**-** 40 45 50

SNR

loss is a result of the noise averaging effect. In ideal case,

the estimation of channel response, which is almost constant

Fig. 5. Average uncoded BER of QPSK signals received over Vehicular A

over slot bandwidth and/or slot duration, is averaged by the channel and with IQ impairments.

2D interpolation over twice the number of pilots compared

to proposed methods. A receiver capable of detecting the

presence of IQ distortions can avoid this loss by switching to R EFERENCES

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