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Modeling the Effect of Clipping and Power Amplifier Non-Linearities on OFDM Systems

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Modeling the Effect of Clipping and Power Amplifier Non-Linearities on OFDM Systems Ubiquitous Computing and Communication Journal Modeling the Effect of Clipping and Power Amplifier Non-Linearities on OFDM Systems Ashraf A. Eltholth*, Adel R. Mekhail*, A. Elshirbini*, M. I. Dessouki† and A. I. Abdelfattah †† * National Telecommunication Institute, Cairo, Egypt † Faculty of electronic Engineering, Menouf, Egypt †† Faculty of Engineering, Mansoura, Egypt ABSTRACT The high Peak to Average power Ration (PAR) levels of Orthogonal Frequency Domain Multiplexing (OFDM) signals forces to the utilization of linear power amplifiers. However, linear amplifiers have low power efficiency which is problematic considering that battery life is a critical resource in mobile systems; also linear amplifiers have a clipping effect when considered as a limiter. Amplifier nonlinearities affect drastically the performance of OFDM systems. In this paper, the effects of Clipping and amplifier nonlinearities are modeled in an OFDM system. We showed that the distortion due to these effects is highly related to the dynamic range it self rather than the clipping level or the saturation level of the nonlinear amplifier. Computer simulations of the OFDM system using Matlab are completely matched with the deduced model in terms of OFDM signal quality metrics such as BER, ACPR and EVM. 1. INTRODUCTION efficiency, the amplifier can be biased so that current flows only half the time on either the positive or In OFDM systems, the combination of different signals negative half cycle of the input signal. An amplifier with different phase and frequency give a large dynamic biased like this is called a class B amplifier. The cost of range that is used to be characterized by a high PAR, the increased efficiency is worse linearity than in a class which results in severe clipping effects and nonlinear A amplifier. High demands on linearity make class B distortion if the composite time signal is amplified by a unsuitable for a system with high PAR. On the other power amplifier, which have nonlinear transfer hand, the large scale of the input signal makes it function. This degrades the performance of an OFDM difficult to bias an amplifier operating in class A. In system. A measure of the degradation can be very practice, the amplifier is a compromise between classes helpful in evaluating the performance of a given system, A and B, and is called a class AB amplifier. [1] and in designing a signaling set that avoids degradation. Several options appear in the literature related The high PAR sets strict requirements for the linearity with OFDM systems and nonlinearities. PAR reduction of the PA. In order to limit the adjacent channel using clipping or coding or phase optimization leakage, it is desirable for the PA to operate in its linear techniques or a combination of any two of them [2], are region. High linearity requirement for the PA leads to the tools to combat nonlinearities used in the low power efficiency and therefore to high power transmitter. Also a good work have been done in consumption. PAs are divided into classes according to modeling the performance of OFDM systems with the biasing used. A class A amplifier is defined as an power amplifiers in [1], but it have assumed the OFDM amplifier that is biased so that the current drawn from signal to have Gaussian distribution which is not very the battery is equal to the maximum output current. The accurate description of the composite time OFDM class A amplifier is the most linear of all amplifier signal. In this paper, the effect of power amplifier types, but the maximum efficiency of the amplifier is nonlinearities is modeled in OFDM systems. Section 2 limited to 50%. In reality, due to the fact that the depicts OFDM signal statistical properties while Section amplitude of the input signal is most of the time much 3 introduces power amplifier models. The derivation of less than its maximum value, the efficiency is much less clipping noise and distortion is presented in Section 4, than the theoretical maximum, i.e. only a few percent. OFDM signal quality metrics are discussed in Section 5. This poor efficiency causes high power consumption, Simulation results are included in Section 5. Finally, the which leads to warming in physical devices. This is a conclusions are drawn. problem especially in a base station where the transmitted power is usually high. To achieve a better Volume 3 Number 1 Page 54 www.ubicc.org Ubiquitous Computing and Communication Journal 2. OFDM SIGNAL STATISTICAL PROPERTIES 3. POWER AMPLIFIER MODEL It is well known that according to the central limit A short description of power amplifier models will be theory that, the real and imaginary parts of the OFDM given in this section. Consider an input signal in polar signal completely agree with the normal distribution and coordinates as [1] consequently its absolute agrees with the Rayleigh jϕ distribution with Probability density function expressed x = ρ e by: The output of the power amplifier can be written as x 2 j ( ϕ + P ( ρ )) − g ( x ) = M ( ρ ) e x 2 P( x) e 2 s , x ∈ 0, ∞ Where s is a = [ ] s Where M( ρ ) represents the AM/AM conversion and parameter, and Mean µ = s π 2 and variance P( ρ ) the AM/PM conversion characteristics of the 2 4 − π 2 power amplifier. σ = s 2 Several models have been developed for nonlinear power amplifiers, the most commonly used ones are as Figure (1) listed below explicitly shows that the follows measured amplitude histogram of the (a) in-phase component/Quadrature component and (b) amplitude of 3.1. Limiter Transfer characteristics a 256-subcarrier OFDM signal. A Limiter (clipping) amplifier is expressed as [4]: ⎧ρ ρ < A 0.012 M ( ρ ) = ⎨ (1) ⎩ A ρ ≥ A 0.01 Where A is the clipping level. This model does not consider AM/PM conversion. y t 0.008 i il b a b o r 0.006 3.2. Solid-State Power Amplifier (SSPA) p The conversion characteristics of solid-state power 0.004 amplifier are modeled by Rapp’s SSPA with 0.002 characteristic [4]: vin 0 vout = (2) -4 -3 -2 -1 0 1 2 3 4 1 amplitude 2 p 2 p (1 + ( v / v ) ) (a) in-phase /Quadrature component histogram in sat 0dB 3dB 6dB 9dB 12dB Where vout and vin are complex i/p & o/p, vsat is the 0.01 output at the saturation point ( vsat = A 2 ), and P is “knee factor” that controls the smoothness of the 0.008 transition from the linear region to the saturation region of characteristic curve (a typical value of P is 1). Pow e r Amplifie r Mode ls 0.006 1 0.9 0.004 0.8 Limiter SSPA P=1 0.7 SSPA P=2 0.002 0.6 ut tp 0.5 Ou 0 0 1 2 3 4 5 0.4 0.3 (b) Amplitude histogram 0.2 Figure (1) histogram of a 256-subcarrier OFDM signal 0.1 0 It is clear that the distribution in figure (1-a) obeys a 0 0.5 1 1.5 2 2.5 3 Input Gaussian distribution while that in figure (1-b) Rayleigh distribution. Figure (2) AM/AM conversion of HPA Volume 3 Number 1 Page 55 www.ubicc.org Ubiquitous Computing and Communication Journal ∞ Figure (2) shows the AM/AM conversion of the two x 2 ⎛ − ⎞ described models with A=1. It is clear from the figure; ⎜ 2 s 2 2 2 2 2 2 2 ⎜ 1 e (− x s − (a + 2s )s + 2axs ) as the value of knee factor increases the SSPA model ∴σ lim iter = = ⎜ ⎜ approaches the Limiter Model. s ⎜ 3 x ⎜ One problem with these methods is that the special ⎜ − a 2π s erf ( ) ⎜ model of nonlinear device requires expensive and time ⎝ 2s ⎠ a consuming experimental measurements to identify model parameters. On the contrary, simple measures of a 2 ⎛ − 2 ⎞ 2 s 2 2 2 2 2 nonlinearity directly related to a low-order polynomial ⎜ )s ⎜ 1 3 1 e (−a s − (a + 2s model, such as third and fifth-order intersect points, are = (0 − a 2π s )− = ⎜ ⎜ usually available to a system designer at the early stage s s ⎜ 2 2 3 =a ⎜ + 2a s ) − a 2 s erf ( ) of specification definition or link budget analysis. The ⎜ π ⎜ ⎝ 2s ⎠ third order nonlinearity model can be described by the Taylor series as [3]: This leads to 2 3 y(t ) a a x(t ) a x (t ) a x (t ) a 2 = o + 1 + 2 + 3 − 2 a 3 2 s 2 Where; x(t) is the input, y(t) is the output signal and σ lim iter = a 2π s (erf ( ) − 1) + 2s e {an}are Taylor series coefficients. 2s The nonlinearity of radio frequency circuits is often And finally expressed in terms of the third-order intercept point a 2 − (A ). It can be shown that A and parameters of third 3 2 s 2 2 a IP3 IP3 σ = 2s e + a 2π s erfc( ) (3) order nonlinearity model are related as [3]: lim iter 2s 4a1 AIP 3 = If we consider the solid state power amplifier model 3 a3 given by Rapp: In this study, we only consider the third-order model of x nonlinearity, since the third-order nonlinearity is usually g ( x) = 1 And let p=1 and v sat = a dominated in real systems. (1 + ( x 2 p 2 p In this paper we have simulated the Rapp’s SSPA ) ) v model, and then deduced the third order nonlinearity sat The NLA distortion can be represented by model to formulate the relation between vsat in the ∞ Rapp’s SSPA model and AIP3 in dB widely used to = ( x − g ( x)) 2 P( x)dx express nonlinearity and we have got: σ SSPA ∫ 0 3 2 2 ∞ x vsat = p ( A ) + p ( A ) + p ( A ) + p − 1 IP 3 2 IP3 3 IP 3 4 x 2 x 2 s 2 Where = ∫ ( x − ) e dx 0 x 2 s p = 0.001936, p = −0.09044, 1 + ( ) 1 2 vsat p = 1.438, p = −5.197 3 4 2 ⎛ a 2 ⎞ 2 ⎡ a ⎤ 4.
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