Wireless Pers CommunDOI 10.1007/s11277-012-0766-4

SER Computation in M-QAM Systems with Phase Noise

Mohammad Lari · Abbas Mohammadi ·Abdolali Abdipour · Inkyu Lee

© Springer Science+Business Media, LLC. 2012

Abstract This paper presents an exact closed-form expression for the symbol error rateof the square and rectangular quadrature amplitude modulation (QAM) constellations, underthe assumption that the transmitted and/or received signals are corrupted by the phase noisefluctuation. Phase noise is one of the most important radio frequency (RF) imperfectionswhich usually comes from the local oscillator (LO) at the transmitter and/or receiver. In thispaper, the additive white Gaussian noise (AWGN) channel is assumed. Although AWGN isa simple channel, but our exact analysis of the symbol error rate in this paper can be led tothe precise study of the real communication systems in the fading channel. Hence, an exactclosed-form solution for the symbol error rate is derived here as a finite summation of thetwo-dimensional Q-function and verified by the simulation.

Keywords Phase noise · Quadrature amplitude modulation · RF imperfections ·Symbol error rate

1 Introduction

Next generation of the wireless networks such as third and fourth generation (3G and 4G)wireless systems demand high data rate and high-quality communication links. An M-aryquadrature amplitude modulation (QAM) is a suitable choice for this purpose. However,high sensitivity of the high-order modulations to the radio frequency (RF) imperfectionssuch as phase noise, amplifier nonlinearity, phase and amplitude imbalance and DC offsetis an important issue and should be considered carefully. The system performance may beseverely degraded if the destructive effects of the RF chains are not compensated.

M. Lari · A. Mohammadi (B) · A. AbdipourAmirkabir University of Technology, Tehran, Irane-mail: abm125@aut.ac.ir

I. LeeKorea University, Seoul, South Korea

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Phase noise is a random fluctuation in the phase of an oscillator waveform. An ideal oscil-lator would generate a pure sine wave and this would be represented as a single pair of thedelta function at the oscillator’s frequency in the frequency domain. All real oscillators havephase modulated noise components. The phase noise components spread the power of thesignal to adjacent frequencies, resulting in noise sidebands.

Phase noise is an important issue in the wireless systems and it has been discussed inmany papers such as [1,2]. The oscillator phase noise model is studied in [3,4] and theanalysis of the practical devices such as phase-locked loop (PLL) with the phase noise hasbeen reviewed in [4,5]. Orthogonal frequency division multiplexing (OFDM) modulation iswidely suffered from the phase noise. The performance of the OFDM modulation with thephase noise, power amplifier nonlinearity and in-phase (I) and quadrature (Q) imbalance isstudied in [6–8]. In [6], the oscillator phase noise and power amplifier nonlinearity effectsare investigated analytically and in [7], the authors focus on inter-carrier interference (ICI)and a closed-form solution for the signal to interference plus noise ratio (SINR) is derived.In addition, the results of the phase noise in multiple-input multiple-output (MIMO) channelsounding and multi-antenna beamforming are also discussed in [9] and [10] respectively.Carrier recovery system in a digital transmission system which is impacted by the phasenoise is studied in [11]. Also, the phase noise effects on error vector magnitude (EVM) ofa system are proposed in [12,13] where a theoretical expression is derived for the EVM inthe M-QAM systems. Some analysis on the symbol error rate of the digitally modulatedsystems is executed in [12] and a union bound for the symbol error rate is derived. The sameintegral-form expression is also obtained in [13], but there is no closed-form solution for thesymbol error rate of the M-QAM systems until now.

Symbol error rate is a very important tool for investigating the performance of telecom-munication systems and it is studied in various systems and problems for many years. In thephase noise context, there are many studies and different approximate representations for thebit and symbol error rate in digital modulations and OFDM systems [2,5,6]. To the best ofour knowledge, there is no exact closed-form expression for the symbol error rate of M-QAMdigital communication systems with the phase noise imperfection. In this paper we assumesquare and rectangular M-QAM constellation in the additive white Gaussian noise (AWGN)channel and error probability for each symbol of the constellation is derived over the decisionboundary of the symbol. Then, the symbol error rate is obtained as a finite summation oftwo-dimensional Q-function over the whole points of the constellation. Although AWGNis a simple channel, but the analysis in the AWGN channel is the first step for the furtherinvestigations in the fading channels. After the exact calculation of the symbol error rate atthe AWGN channel, using the distribution of the signal to noise ratio (SNR) in the fadingchannel, the symbol error rate in the fading channel is extracted.

This paper is organized as follows: The system model with the phase noise is explainedin Sect. 2. The symbol error rate is derived in Sect. 3. In Sect. 4, with the numerical results,the proposed theory is verified and finally the paper is concluded in Sect. 5.

2 System Model

The system model is presented in Fig. 1. This system is included an M-QAM digital mod-ulator and demodulator, a digital to analog converter (DAC) and analog to digital converter(ADC), a pulse shaper filter and matched filter (MF), an analog modulator and demodulatorwhich up-converts and down-converts their input signal respectively, a high power amplifier(HPA) and low noise amplifier (LNA), and finally an antenna at transmitter and receiver.

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Fig. 1 M-QAM system model

We simply assume direct conversion [14] transmitter and receiver. This type of transceivercontains one up/down-converter piece and it has some advantages such as small dimensions,low power consumption and cost for the wireless telecommunication systems [15]. The othertypes such as superheterodyn transceiver [14] have their own advantages too, and their phasenoise study can be achieved in a similar way of this paper.

The digital modulator maps the input bit stream to the constellation symbols. DAC devicesproperly make the analog signals from the digital input. After that, pulse shaper filter createsa suitable shape for each symbols. Next, the analog modulator up-converts the I and Q com-ponents to the transmitted frequency and delivers the sum of the I and Q signals to the HPAsection. The signal is amplified at the HPA and finally transmitted via the the antenna intothe AWGN channel and then, received by the antenna at the receiver. LNA, the first sectionin the receiver, filters and amplifies the received signal. The analog demodulator down-con-verts the LNA signal and restores the I and Q signals. Next, the MF rejects the out-of-bandcomponents of the signal after the analog demodulator and removes the applied pulse shapefor ‘ the symbols. After that, ADCs produce the digital I and Q components of the symbolsand digital demodulator demaps the symbols and reconstructs the transmitted bit stream. Inthis paper, the nonlinearity of the HPA and the other RF imperfections are not considered.Therefore, we assume perfect RF chains at the transmitter and receiver.

The square and rectangular M-QAM constellations are our interest in this paper. HereM = M I .M Q where M is the number of points in the constellation, M I is the numberof points in the I direction of the constellation and M Q is the number of points in the Qdirection of the constellation. The square constellations are symmetric where M I = M Q ,but rectangular constellations are not symmetric and M I = 2M Q (or M I = M Q/2). A two-dimensional number (i, j), is assigned to each constellation point. This type of numberingis more suitable for the following analysis. Here, −→s (i, j) where {i = ±1,±2, . . . ,±M I /2}and { j = ±1,±2, . . . ,±M Q/2} represents the (i, j)-th symbol of the constellation and−→s (i, j) = [si s j ]T where (.)T stands for the vector and matrix transpose, si = (2i − 1)α

and s j = (2 j − 1)α represent the I and Q components of −→s (i, j) respectively. α is an scal-ing factor. We assume a unit power for the constellations. In this case, α in the 4-QAM to

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Table 1 Scaling factor α for theunit power of the constellationsin the different modulationorders M

M 4 8 16 32 64 128 256

α√

1/2√

1/6√

1/10√

1/26√

1/42√

1/106√

1/170

Fig. 2 32-QAM constellation and its decision boundary

256-QAM is determined in Table 1. The decision boundaries versus the scaling factor α

are written in Table 2. For more convenience, a rectangular 32-QAM constellation and thedecision boundaries for each symbols are plotted in Fig. 2. The decision boundaries also canbe written versus α. The decision boundaries are plotted with the solid lines in Fig. 2 and theconstellation points are plotted on the dash lines in this figure.

In this paper we consider the symbol error rate. The two-dimensional symbol at theoutput of the digital modulator is given by −→s (i, j) = [si s j ]T . After digital to analog con-verter and pulse shaping filter at time t , the two-dimensional analog signal is presented by−→s (i, j)(t) = [si s j ]T .p(t) where p(t) is the applied pulse shape with a unit power and ’.’denotes the scaler multiplication. The analog modulator up-converts the I and Q componentsand delivers the sum to the HPA. The output of the analog modulator is given by

x(t) = si p(t) cos(2π f0t) + s j p(t) sin(2π f0t) (1)

where f0 is the carrier frequency which is generated by the transmitter LO. The output of

the analog modulator can be written as x(t) = −→U T (t)−→s (i, j)(t) where

−→U (t) represents the

I and Q components of the transmitter LO as

−→U (t) = [cos(2π f0t) sin(2π f0t)]T . (2)

The both oscillators at the transmitter and receiver have the phase noise. However, weaggregate the the effect of the phase noise at the receiver LO. Our analysis in this paper istrue for the other cases and it can be simply rewritten for the transmitter LO or both trans-mitter and receivers LOs. We assumed an ideal HPA and LNA. Therefore, they just have aconstant gain without any phase distortions. For a simple notation, we assume this constantgain equals to one. The received signal after LNA, y(t), is the corrupted version of the trans-mitted signal, x(t), by w(t). In this paper, w(t) represents the added noise by the circuitssuch as the mixer, HPA, LNA and also AWGN channel respectively. In addition, the zeromean white Gaussian model is assumed for w(t). The analog demodulator down-convertsy(t) to the I and Q components. Similar to (2), we can define the I and Q components of thereceiver LO as

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−→D (t) = 2[cos(2π f0t + φ) sin(2π f0t + φ)]T (3)

where φ represents the added phase noise at the receiver LO. The I and Q received signalsbefore the MF can be expressed as

−→D (t).y(t) =−→

D (t).[x(t) + w(t)]=[−→D (t) × −→

U T (t)] × −→s (i, j)(t) + −→D (t).w(t)

=2

[cos(2π2 f0t+φ)+cos(φ)

2sin(2π2 f0t+φ)−sin(φ)

2sin(2π2 f0t+φ)+sin(φ)

2− cos(2π2 f0t+φ)+cos(φ)

2

]× −→s (i, j)(t) + −→

D (t).w(t)

=2

[cos(2π2 f0t+φ)+cos(φ)

2sin(2π2 f0t+φ)−sin(φ)

2sin(2π2 f0t+φ)+sin(φ)

2− cos(2π2 f0t+φ)+cos(φ)

2

]×

[si

s j

].p(t)

+ −→D (t).w(t) (4)

where ’×’ denotes the matrix multiplication.After the analog demodulator, the MF acts as a low-pass filter, rejects the out-of-band

signal and removes the applied pulse shape p(t). Then, the ADC converts the continuoussignal to the discrete one and restores the I and Q components of the transmitted symbol.Therefore, after the MF and ADC we have

−→s (i, j) =[

si

s j

]=

[cos(φ) − sin(φ)

sin(φ) cos(φ)

]×

[si

s j

]+

[ni

n j

]= H × −→s (i, j) + −→n (5)

as an estimation of the transmitted symbol. In (5), H is the consequence of the transmitter andreceiver LOs after the low-pass filter [12,13], and −→n is the baseband equivalent of w(t). ni

and n j are the I and Q components of −→n and they are independent and identically distributed(i.i.d.), zero mean Gaussian noise where σ 2 denotes the variance of each components [16].Here, the covariance matrix of −→n can be written as C−→n = σ2I2, where Ik represents the kdimensional identity matrix.

The statistical modeling with the normal distribution is a conventional model for the phasenoise [6,12,13]. Therefore, we assume zero mean normally distributed φ with the varianceσ 2

φ . Also it can be written as φ ∼ N (0, σ 2φ ). In the case with the weak phase noise variance

σ 2φ � 1, H can be simplified as [13]

H ≈[

1 −φ

φ 1

]=

[1 00 1

]+

[0 −11 0

]φ (6)

and therefore (5) becomes

−→s (i, j) = −→s (i, j) +[

0 −11 0

]× −→s (i, j).φ + −→n

= −→s (i, j) +[−s j

si

].φ + −→n

= −→s (i, j) + −→n p + −→n (7)

where −→n p = [−s j si ]T .φ is a new added perturbation which depends on the phase noise. Inaddition, −→n p also depends on the signal components si and s j . Note that, when the trans-mitter and receiver LOs are ideal, we have φ = 0. Therefore, −→n p = 0 and (7) becomes thetypical notation for the received signal at the AWGN channel [16].

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Since the phase noise φ is a normal random variable, −→n p is also normal with the covariancematrix of

C−→n p= E{−→n p × −→n T

p }

= E{φ2}[ |s j |2 −s j si

−si s j |si |2]

= σ 2φ

[ |s j |2 −s j si

−si s j |si |2]

(8)

where E{.} and |.| denote the expectation and amplitude of their arguments. We assumednormal distribution for the channel noise −→n too. Consequently, (7) is the sum of a constantand two independent normally distributed random variables. In this case, the whole distri-

bution of −→s (i, j) will become normal [17]. The unit power is assumed for the transmitted

signal. Hence, the distribution of −→s (i, j) is normal with the mean −→s (i, j) and covariance

matrix C−→n p+ C−→n . The probability density function (PDF) of −→s (i, j) is expressed as [16,

eq. 2.1-150]

f (−→s (i, j)) =N (

−→s (i, j), C−→n p+ C−→n )

= 1

2π det[C−→n p+ C−→n ]1/2 .

exp

⎛⎝−

(−→s (i, j) − −→s (i, j))

T (C−→n p+ C−→n )−1(

−→s (i, j) − −→s (i, j))

2

⎞⎠ (9)

where det[.] represents the matrix determinant. By substitution of −→s (i, j),−→s (i, j), C−→n p

andC−→n into (9) we have

f (−→s (i, j)) = 1

2π

√(σ 2φ |s j |2 + σ 2

) (σ 2φ |si |2 + σ 2

)−

(−σ 2

φ si s j

)2.

exp

⎛⎜⎜⎝−

(si − si )2(σ 2φ |si |2 + σ 2

)+ (s j − s j )

2(σ 2φ |s j |2 + σ 2

)− (si − si )(s j − s j )2(−σ 2

φ si s j )

2

[(σ 2φ |s j |2 + σ 2

) (σ 2φ |si |2 + σ 2

)−

(−σ 2

φ si s j

)2]

⎞⎟⎟⎠ .

(10)

In the digital demodulator, if the received symbol with the derived PDF is out of the decisionmaking boundary, the transmitted symbol is detected incorrectly and we have one symbolerror. The symbol error calculation will discuss in the next section.

3 Symbol Error Rate Calculation

If the received symbol −→s (i, j) lies outside their decision boundary, the error will occur. There-fore, the probability of error is calculated for each point and then, averaged over all symbols.Since the constellation is square or rectangular, the decision boundary of each symbol arealso square or rectangular. In this case, Ai , Bi , C j and D j denote the left, the right, the bottomand the top borders of the decision boundary around the symbol −→s (i, j) respectively. For thesymbols on the borders of the constellation, one decision boundary is infinity, i.e. Bi = +∞

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Table 2 The decisionboundaries of the symbols Ai = (2i − 2)α, 1 ≤ i ≤ M I /2 C j = (2 j − 2)α, 1 ≤ j ≤ M Q/2

Bi ={

(2i)α, 1 ≤ i < M I /2+∞, i = M I /2

D j ={

(2 j)α, 1 ≤ j < M Q/2+∞, j = M Q/2

or D j = +∞. In addition, for the symbols on the corners of the constellation, two decisionboundaries are infinity, i.e. Bi = +∞ and D j = +∞. The decision boundaries versus thescaling factor α are written in Table 2. For more simplicity, the decision boundaries of thesymbol −→s (1,1) is tagged in Fig. 2 as A1, B1, C1 and D1. Now, the probability of error forthe (i, j)-th symbol in the constellation can be written as [18], [19, eq. 9]

pe(i, j) = 1 −

Bi∫Ai

D j∫C j

f (−→s (i, j))dsi ds j . (11)

In the M-QAM constellation, there are M points with equal probability of occurrence.But, there is no difference between the error probability of symbols in each quarter of theconstellation. Therefore, the symbol error rate is the same for the symbols at each quarter ofthe constellation. Consequently, the symbol error rate can be written as

Se = 1

M/4

M I /2∑i=1

M Q/2∑j=1

pe(i, j). (12)

To determine the integral of (11), first we define si = (si − si )/√

σ 2φ |si |2 + σ 2, s j =

(s j − s j )/√

σ 2φ |s j |2 + σ 2 as a normalized variable and

ρ(i, j) =√

(σ 2φ si s j )2/[(σ 2

φ |s j |2 + σ 2)(σ 2φ |si |2 + σ 2)]

as a correlation coefficient. Now, by changing the variables, (11) is reduced to

pe(i, j) = 1 −

B(i, j)∫A(i, j)

D(i, j)∫C(i, j)

1

2π√

1 − ρ2(i, j)

exp

(−|si |2 + |s j |2 − 2ρ(i, j)si s j

2(1 − ρ2(i, j))

)dsi s j (13)

where A(i, j) = (Ai − si )/√

σ 2φ |s j |2 + σ 2, B(i, j) = (Bi − si )/

√σ 2

φ |s j |2 + σ 2, C(i, j) =(C j − s j )/

√σ 2

φ |si |2 + σ 2 and D(i, j) = (D j − s j )/√

σ 2φ |si |2 + σ 2 are modified decision

boundaries which are given at Table 1. Now, the integral in (13) has a closed-form solution as

pe(i, j) =1 −

[Q( A(i, j), C(i, j); ρ(i, j)) + Q(B(i, j), D(i, j); ρ(i, j))

−Q( A(i, j), D(i, j); ρ(i, j)) − Q(B(i, j), C(i, j); ρ(i, j))]

(14)

where

Q(M, N ; ρ) =∞∫

M

∞∫N

1

2π√

1 − ρ2exp

(− X2 + Y 2 − 2ρXY

2(1 − ρ2)

)d XdY (15)

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Table 3 The modified decision boundaries and correlation coefficient ρ(i, j) versus γ0

A(i, j) = (Ai −si )√σ2φ|s j |2+σ2

= −√

α2

σ2φ(2 j−1)2α2+σ2 = −

√2γ0α2

1+2γ0α2σ2φ(2 j−1)2

B(i, j) =

⎧⎪⎨⎪⎩

(Bi −si )√σ2φ|s j |2+σ2

=√

α2

σ2φ(2 j−1)2α2+σ2 =

√2γ0α2

1+2γ0α2σ2φ(2 j−1)2 , i < M I /2

+∞, i = M I /2

C(i, j) = (C j −s j )√σ2φ|si |2+σ2

= −√

α2

σ2φ(2i−1)2α2+σ2 = −

√2γ0α2

1+2γ0α2σ2φ(2i−1)2

D(i, j) =

⎧⎪⎨⎪⎩

(D j −s j )√σ2φ|si |2+σ2

=√

α2

σ2φ(2i−1)2α2+σ2 =

√2γ0α2

1+2γ0α2σ2φ(2i−1)2 , j < M Q/2

+∞, j = M Q/2

ρ(i, j) =√

(σ2φ

si s j )2

[(σ2φ|s j |2+σ2)(σ2

φ|si |2+σ2)]

=√

[−σ2φ(2i−1)(2 j−1)α2]2

[σ2φ(2 j−1)2α2+σ2][σ2

φ(2i−1)2α2+σ2]

=√

[−2γ0α2σ2φ(2i−1)(2 j−1)]2

[1+2γ0α2σ2φ(2 j−1)2][1+2γ0α2σ2

φ(2i−1)2]

represents the two-dimensional Q-function [20]. Note that, when an argument of the two-dimensional Q-function goes to the infinity, the function goes to the zero. This is importantwhen the error rate of the symbols on the borders of the constellation is calculated. Finally,substituting (14) into (12) yields

Se = 4

M

⎛⎝ M

4−

M I /2∑i=1

M Q/2∑j=1

[Q( A(i, j), C(i, j); ρ(i, j)) + Q(B(i, j), D(i, j); ρ(i, j))

−Q( A(i, j), D(i, j); ρ(i, j)) − Q(B(i, j), C(i, j); ρ(i, j))] ⎞

⎠ . (16)

For more flexibility, the modified decision boundaries and correlation coefficient ρ(i, j) arewritten versus the SNR γ0 = 1/(2σ 2) in Table 3 when we have si = (2i − 1)α and s j =(2 j − 1)α. Consequently, the symbol error rate is calculated with the knowledge of the SNRγ0 and the phase noise variance σ 2

φ .Now, the symbol error rate is a function of γ0 and φ and it can be written as Se(γ0, φ) to

presents this dependency. In the fading channels, γ0 is not constant and it has a proper dis-tribution such as Rayleigh model. In this case, the average symbol error rate can be obtainedfrom

Se(φ) =∞∫

0

Se(γ0, φ) f (γ0)dγ0 (17)

where f (γ0) represents the PDF of the SNR in the fading channel. Since Se(γ0, φ) has anexact solution, the integral of (17) can be found with the accurate numerical integrationtechniques [21].

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0 5 10 15 20 25 3010

−4

10−3

10−2

10−1

100

10(a)

(b)

1

8−QAM

64−QAM

4−QAM16−QAM

32−QAM

128−QAM

256−QAM

0 5 10 15 20 25 3010

−4

10−3

10−2

10−1

100

101

4−QAM

8−QAM

16−QAM

32−QAM

128−QAM

256−QAM

64−QAM

Fig. 3 Symbol error rate versus SNR γ0 for different modulation orders, a σ 2φ = 0.01, b σ 2

φ = 0.001

4 Simulation Results

In this section, the simulation results are presented. In all simulations, 107 symbols are sim-ulated in the AWGN channel. In addition, we assume M = 2m and m = 2, . . . , 8. Thesymbol error rate for different modulation orders versus the SNR γ0 is depicted in Fig. 3a, bwith σ 2

φ = 0.01 and σ 2φ = 0.001 respectively. The simulations tightly follow the theoretical

curves. The symbol error rate for the 32-QAM and 256-QAM are also plotted with fourdifferent phase noise variances, σ 2

φ = 0.1, σ 2φ = 0.01, σ 2

φ = 0.001 and σ 2φ = 0.0001 in Fig.

4a, b respectively. An exact agreement between simulation and theory is also clear in thisfigure.

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0 5 10 15 20 25 30

10−4

10−3

10−2

10−1

100

10(a)

(b)

1

0 5 10 15 20 25 30 35 40 45 50

10−4

10−3

10−2

10−1

100

101

Fig. 4 Symbol error rate versus SNR γ0 in the different phase noise variance a 32-QAM, b 256-QAM

Some points can be observed in these figures. The distance between two neighbor pointsin the constellation is 2α. Whit the unit power assumption for the constellation, α is specifiedin Table 1. When the modulation order M increases, the value of α is reduced. Therefore, inthe high-order modulation, two neighbor points in the constellation are closer to each other.So, the probability of error between two neighbor points is higher. Consequently, in Fig. 3, itis clear that the sensitivity of the high-order modulation to the phase noise is certainly morethan the sensitivity of the low-order counterpart. Hence, more attention have to be payed tothe high-order modulation systems in the practical situations with the phase noise fluctuation.In Fig. 4, it is evident that the system performance is improved when the phase noise varianceis decreased. The saturation of the symbol error rate at specific SNR is the other significantpoint in Fig. 4. This is expectable, because after a certain value, the phase noise becomes the

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dominant noise and therefore, increase in the SNR does not improve the symbol error rateperformance of the system.

5 Conclusion

In this paper an exact closed-form solution for the symbol error rate of the square and rect-angular M-QAM constellation, under the assumption of the phase noise at the transmitterand/or receiver LOs is derived. In the practical systems, there is some disturbance at the RFsections which can severely degrade the whole performance of the system. Here, the phasenoise fluctuation of the transmitter and/or receiver LOs are considered and an exact expres-sion for the symbol error rate of the system in the AWGN channel is extracted. The derivedexpression is depicted as a finite summation of the two-dimensional Q-function. The AWGNlink is a simple channel. However, our study in the AWGN channel can be led to the analysisof this issue in the more practical channels such as fading and MIMO channels, which is ourconcern for the future research. Consequently, the extracted closed-form symbol error ratein this paper will be useful for farther investigations.

Acknowledgments We acknowledge the support of the Research Institute for Information and Commu-nication Technology, Tehran, Iran, under Contract No. T/18128/500 for its role in the development of thisresearch.

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Author Biographies

Mohammad Lari was born in Iran in 1983. He received the B.Sc. andM.Sc. degrees in Electrical Engineering in 2005 and 2007 respectivelyand is working toward the Ph.D. degree in Communication Engineer-ing at Amirkabir University of Technology (Tehran Polytechnic), Teh-ran, Iran since 2007. His research interests include wireless commu-nication systems. He is currently a member of Microwave/mm-Waveand Wireless Communication Research Lab in Electrical EngineeringDepartment of Amirkabir University of Technology.

Abbas Mohammadi received the B.Sc. degree in Electrical Engi-neering from Tehran University, Iran in 1988, the M.Sc. and Ph.D.degrees in Electrical Engineering from the University of Saskatchewan,Canada, in 1995, and 1999, respectively. He was a researcher atTelecommunications Research Lab (TRLabs), Canada, from 1995to 1998. In 1998, he joined to Vecima Networks Inc., Micro-waveResearch Lab, Victoria, Canada, as a senior research engineer wherehe conducted research on Microwave and Wireless Communications.Since March 2000, he has been with the Electrical EngineeringDepartment of Amirkabir University of Technology (Tehran Polytech-nic), Tehran, Iran. In 2008, he joined to Electrical and Computer Engi-neering Department of the University of Calgary, Canada as a visitingprofessor. He has published over 110 Journal and Conference papersand holds three U.S. and one Canadian Patents. His current researchinterests include broadband wireless communications, adaptive modu-lation, MIMO Systems, Mesh and AdHoc Networks, Microwave andWireless Subsystems, and direct conversion transceivers.

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Abdolali Abdipour was born in Alashtar, Iran, in 1966. He receivedhis B.Sc. degree in electrical engineering from Tehran University,Tehran, Iran, in 1989, his M.Sc. degree in electronics from LimogesUniversity, Limoges, France, in 1992, and his Ph.D. degree in elec-tronic engineering from Paris XI University, Paris, France, in 1996. Heis currently a professor with the Electrical Engineering Department,Amirkabir University of Technology (Tehran Polytechnic), Tehran,Iran. He has authored three books, Noise in Electronic Communica-tion: Modeling, Analysis and Measurement (AmirKabir Univ. Press,2005, in Persian), Transmission Lines (Nahre Danesh Press, 2006,in Persian) and Active Transmission Lines in Electronics and Com-munications: Modeling and Analysis (Amirkabir Univ. Press, 2007,in Persian - top selected book of year). His research areas includewireless communication systems (RF technology and transceivers),RF/microwave/millimeter-wave circuit and system design, electromag-netic (EM) modeling of active devices and circuits, high-frequency

electronics (signal and noise), nonlinear modeling, and analysis of microwave devices and circuits.

Inkyu Lee received the B.S. degree (Hon.) in control and instrumen-tation engineering from Seoul National University, Seoul, Korea, in1990, and the M.S. and Ph.D. degrees in electrical engineering fromStanford University, Stanford, CA, in 1992 and 1995, respectively.From 1995 to 2001, he was a Member of Technical Staff at Bell Lab-oratories, Lucent Technologies, where he conducted research on high-speed wireless system designs. He later worked for Agere Systems (for-merly Microelectronics Group of Lucent Technologies), Murray Hill,NJ, as a Distinguished Member of Technical Staff from 2001 to 2002.In September 2002, he joined the faculty of Korea University, Seoul,Korea, where he is currently a Professor in the School of ElectricalEngineering. During 2009, he visited University of Southern Califor-nia, LA, USA, as a visiting Professor. He has published over 80 jour-nal papers in IEEE, and has 30 U.S. patents granted or pending. Hisresearch interests include digital communications and signal process-ing techniques applied for next generation wireless systems. Dr. Leecurrently serves as an Associate Editor for IEEE TRANSACTION ON

COMMUNICATIONS and the IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS. Also, hehas been a Chief Guest Editor for the IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS(Special Issue on 4G Wireless Systems). He received the IT Young Engineer Award as the IEEE/IEEK jointaward in 2006, and received the Best Paper Award at APCC in 2006 and IEEE VTC in 2009. Also he wasa recipient of the Hae-Dong Best Research Award of the Korea Information and Communications Society(KICS) in 2011.

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