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Robust Clipping for OFDM Transmissions Over Memoryless Impulsive Noise Channels

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Robust Clipping for OFDM Transmissions Over Memoryless Impulsive Noise Channels 1110 IEEE COMMUNICATIONS LETTERS, VOL. 16, NO. 7, JULY 2012 Robust Clipping for OFDM Transmissions over Memoryless Impulsive Noise Channels Der-Feng Tseng, Member, IEEE, Yunghsiang S. Han, Fellow, IEEE,WaiHoMow,Senior Member, IEEE, Li-Chung Chang, Member, IEEE, and A. J. Han Vinck, Fellow, IEEE Abstract—The detriment arising from strong and frequently by applying Bussgang’s theorem, which produced consider- occurring impulses over an Orthogonal Frequency Division Mul- able symbol error rate performance gain. A decision-directed tiplexing system is paramount because signals on sub-carriers impulsive noise cancelation scheme was proposed in [5] to appear to be corrupted simultaneously. To overcome this obstacle, clipping has been reported as an effective approach. Unlike address impulsive noise with a power level commensurate previous works, this work derived the clipping threshold without with the OFDM signal. Iterative interference cancelation for assuming the a priori knowledge of the probability density clipping noise arising from blanking nonlinearity was inves- function (PDF) of impulsive noise, which is usually unobtainable tigated in [6]. Other than clipping, channel coding [7], [8] in precise measure in most practical scenarios, and may change is effective in tackling impulsive noise and approximating rapidly over time. Then, a decoding metric accommodated to the clipping effect was derived to realize coding gain. To attest the performance to the capacity limit. However, the coding gain proposed scheme, this study conducted computer simulations in may be invalidated under certain practical scenarios, wherein compliance with the IEEE 1901 standard. For various impulse the impulsive noise has an excessive energy level and a fairly noise models under consideration, the proposed scheme was high arrival probability, and wherein the coding epoch is on a promisingly on par with its conventional counterpart, the clipping per-OFDM symbol basis [9]. A limiter, the clipping threshold thresholdofwhich,however,reliesonanassumedPDF. of which was devised based on detection theory [9], [10], can Index Terms—Clipping threshold, impulsive noise, OFDM. enhance bit error rate (BER) performance significantly when placed in front of the FFT demodulator and turbo decoder. These schemes for measuring the clipping threshold as- I. INTRODUCTION sumed perfect knowledge of the probability density function NVESTIGATION of data delivery under non-Gaussian (PDF) of the impulsive noise model, which is not only too I noise in wireless communications, power line communi- difficult and costly to obtain precisely, but may in reality cations (PLC), and digital subscriber line loops has received also change over time [2]. The present work attempts to much attention. In essence, nuisances such as human-made overcome this drawback by relaxing the assumption of having electromagnetic interference and atmospheric noise limit sta- perfect statistical knowledge of impulsive noise at the receiver. ble communication link quality. Orthogonal Frequency Di- Inspired by an efficient decoding scheme in [11], which ap- vision Multiplexing (OFDM) may be applied to reduce the proximates BER to the maximum-likelihood decoding method, adverse effect of impulsive interference caused by the spread regardless of which impulsive noise model the transmitted of noise energy across sub-carriers induced by the Fast Fourier signal is subject to, the clipping threshold was measured with Transform (FFT) operation. Nevertheless, OFDM is outper- only a rough range of the arrival probability of impulses avail- formed by its single-carrier counterpart in uncoded symbol able at the receiver. Furthermore, an adapted log-likelihood error probability within the context of excessive impulsive ratio (LLR) metric for turbo decoding was derived, considering noise energy, coupled with a fairly high arrival probability the clipping effect on both OFDM signaling and impulse prior of impulses [1], which likely exists in contemporary commu- to turbo decoding. Simulations conducted in compliance with nication systems [2]. the IEEE 1901 [12] PLC standard show that the proposed A simple but effective means to mitigate impulsive noise hybrid approach of using clipping and channel coding is not in OFDM systems is to equip the front-end receiver with a only robust, but can also induce BER commensurate with that memoryless nonlinearity. A number of studies, including [3], of [9], which relies on the assumed PDF of impulsive noise. [4] attempted to determine the optimal threshold of clipping The rest of this paper is organized as follows: Section II introduces a review of common impulsive noise models, and Manuscript received March 6, 2012. The associate editor coordinating the then presents the system framework; Section III details the review of this letter and approving it for publication was J. Armstrong. This work was supported in part by the National Science Council (NSC) of schemes for deriving the clipping threshold, as well as an Taiwan under grant no. NSC 100-2221-E-011-089, 99-2221-E-011-158-MY3, adopted decoding metric; Section IV provides the simulation 100-2221-E-011-070, and by the NSF of China (NSFC 61028002). results; and lastly, Section V offers a conclusion. D.-F. Tseng, Y. S. Han, and L.-C. Chang are with the Dept. of Electrical Engineering, National Taiwan University of Science and Technology, Taipei, Taiwan (e-mail: [email protected]). II. SYSTEM MODEL W. H. Mow is with the Dept. of Electronic and Computer Engineering, Hong Kong University of Science and Technology, Hong Kong. A. Prevalent Impulsive Noise Channels A. J. H. Vinck is with the Institute for Experimental Mathematics, Univer- sity of Duisburg-Essen, Essen, Germany. We consider digital signaling transmitted over a memoryless Digital Object Identifier 10.1109/LCOMM.2012.050412.120491 impulsive noise channel, where the noise sample zk is the 1089-7798/12$31.00 c 2012 IEEE TSENG et al.: ROBUST CLIPPING FOR OFDM TRANSMISSIONS OVER MEMORYLESS IMPULSIVE NOISE CHANNELS 1111 combination of additive white Gaussian noise (AWGN) gk measurement element associated with the output LLR of the and impulsive noise ik such as zk = gk + ik , where k is the turbo decoder as time index. In mathematical form, the sample of the Bernoulli- Pr(R |X = E /2) √ R L (R )=ln mR mR s = 2E mR , Gaussian (B-G) model [1] is represented by zk = gk + bkωk, c mR s 2 (3) Pr(Rm |Xm =− Es/2) σN R R mR where bk ∈{0, 1} is a Bernoulli random variable with Pr(bk =1)=pb the probability of impulse occurrences where Es is the modulated symbol energy. Assuming perfect and ωk is an independent and identically distributed (i.i.d.) synchronization, similar formats on the PDF (1) and output N0 ( ) Gaussian random process with a mean zero and variance 2 Γ, LLR (3) can be derived for Nm , which, however, plagues where N0 is the single-sided power spectral density of AWGN, (Xm). and Γ stands for the mean power ratio between the impulsive noise component and AWGN component for the B-G model. III. EFFICIENT CLIPPING AGAINST IMPULSES The PDF of this Gaussian mixture model is thus denoted Γ Pr ( )=(1− )N ( ;0 N0 )+ N ( ;0 N0 (1+Γ)) Under the B-G model with large pb and , one can observe by zk x pb x , 2 pb x , 2 , (x−μ)2 Xm 0 ≤ m ≤ M − 1 2 1 − from (3) that each modulated symbol ( ) N ( ; )= √ 2σ2 where x μ, σ 2πσ2 e is the Gaussian PDF of is likely to be corrupted, irrespective of the sub-carrier, due 2 2 a random variable x with mean μ and variance σ . to the enlarged σN in (2) as stressed in [1]. This drawback mR In addition, popularly adopted in the literature for character- further invalidates the channel coding gain in the proposed izing impulsive noises is the Middleton Class-A (M-CA) noise framework, where a codeword only encompasses an OFDM model [13], which describes the PDF of i.i.d. noise samples zk symbol, prompting an adoption of a limiter prior to the FFT Pr ( )= ∞ N ( ;0 2 ) = −A Am as zk x m=0 αm x ,σm ,whereαm e m! operator to suppress impulses. Arguments on the effectiveness 2 N0 m and σm = 2 (1 + ΛA ),whereA is the impulsive index, and of the turbo decoder can be applied to OFDM transmission Λ is the mean power ratio between the AWGN component under the M-CA noise model with a large A as well as strong and the impulsive noise component for the M-CA model [2]. impulses, which in turn induces a small Λ. To suppress impulses, we followed [3], who used a memo- ryless limiter with real and imaginary clipping B. System Framework & Problem Statement | | = rkI rkI <γ We used a double binary turbo convolutional encoder, rkI , (4) γ cos(∠(rkI )) otherwise followed by a channel interleaver at the front end of the ∠( ) transmitter. Subsequently, the coded bit stream was partitioned where γ is the clipping threshold, and rkI is the phase into segments in accordance with the Quadrature Phase Shift (in units of radian) of the I-phase component at the k-th Keying (QPSK) modulation with Gray mapping. After col- output of IFFT, rkI . Nevertheless, unlike their methods, we lecting M consecutive modulated symbols Xm,wherem is forwent using the PDF of the impulsive noise, and instead the sub-carrier index for the Inverse Fast Fourier Transform relied only on the arrival probability of impulses to devise (IFFT) implementation, the output of IFFT can be expressed threshold γ, such that the variance of the clipped signals after 1 M−1 j2πmk = √ M (0 ≤ ≤ − 1) FFT is properly reduced, irrespective of the impulsive noise as xk M m=0 Xme , k M . Assuming perfect sampling time and frequency control, models. the OFDM symbol, subject to memoryless impulsive noise To illustrate, the B-G noise model was assumed in order sequence nk, can be denoted by rk = xk + nk,k= to highlight the concept of designing γ.
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