A dual protection scheme for impulsive noise suppression in OFDM systems

Int. J. Electron. Commun. (AEÜ) 68 (2014) 51–58

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International Journal of Electronics and Communications (AEÜ) journal homepage: www.elsevier.com/locate/aeue

A dual protection scheme for impulsive noise suppression in OFDM systems Jia Jia ∗ , Julian Meng Department of Electrical and Computer Engineering, University of New Brunswick, 15 Dineen Drive, Fredericton, NB E3B 5A3, Canada

a r t i c l e

i n f o

Article history: Received 28 December 2012 Accepted 7 August 2013 Keywords: Orthogonal frequency division multiplexing (OFDM) Reed–Solomon (RS) code Composite comparison value (CCV) Impulsive noise

a b s t r a c t Orthogonal frequency division multiplexing (OFDM) can be susceptible to impulsive noise arising from numerous sources in a noisy communications environment. Conventional Reed–Solomon (RS) codes are particularly useful for burst-error corrections and have been employed in OFDM systems to manage impulsive noise. The performance gains, however, have been somewhat limited given the sensitivity to other noise types typically present in a noisy channel. In this regard, a novel scheme utilizing a time-domain pre-processing mean filter in combination with RS coding is proposed for impulsive noise suppression in OFDM systems. This scheme is split into two stages. In the first stage, a proposed mean filter effectively detects and removes the impulsive noise using the measured statistics of the impulsive noise. In contrast to a conventional blanking type filter, the traditional mean replacement value is replaced by a composite comparison value (CCV). This principle creates a more accurate estimate of the original OFDM signal after impulsive noise removal. The residual impulsive noise is then managed by a RS decoder in the second stage. Our results show that this dual faceted approach improves OFDM performance when compared to filtering and coding techniques alone. © 2013 Elsevier GmbH. All rights reserved.

1. Introduction Orthogonal frequency division multiplexing (OFDM) is a modulation technology that is widely used in various communications systems, such as wireless local area network (WLAN), digital audio broadcasting (DAB), and power-line communications (PLC). The concept of OFDM is based on multi-carrier technology where data is transmitted over N orthogonal subcarriers. OFDM has several advantages when compared to single carrier communications systems such as resistance to multipath distortion, improved spectral efficiency, and robustness to narrowband noise [1]. However, excessive impulse noise in terms of event probability, duration, and amplitude can cause difficulties in OFDM transmission [2]. Typical impulsive noise is due to power lines, heavy current switches, vehicle ignition systems, high voltage discharge and other sources that cannot be assumed to be additive Gaussian in nature [3–5]. Impulsive noise is formalized as an additive channel noise component with typical characteristics such as: spike-like with short time durations, random occurrence, and a high power spectral density. With respect to the latter, impulsive noise amplitude can be several dB over the received signal and other background noise [6]. As

∗ Corresponding author at: Room D36, Headhall, University of New Brunswick, 15 Dineen Drive, Fredericton, NB E3B 5A3, Canada. Tel.: +1 506 478 1368; fax: +1 506 453 3589. E-mail addresses: [email protected], [email protected] (J. Jia). 1434-8411/$ – see front matter © 2013 Elsevier GmbH. All rights reserved. http://dx.doi.org/10.1016/j.aeue.2013.08.004

a result, impulsive noise can result in the performance degradation of the OFDM system, since its energy spreads to the all OFDM carriers through the discrete Fourier transform (DFT) demodulation process. To decrease the impact of impulsive noise, a basic suppression procedure was proposed, and is formulated using two basic steps: impulsive noise detection and error correction [7,8]. Based on these concepts, filtering and coding methods to manage impulsive noise have been previously proposed. For example, a blanking nonlinearity process [9] is employed to locate and filter an impulsive noise event if its amplitude exceeds an assigned threshold in the time domain. In [10], a novel algorithm was proposed to estimate impulsive noise in the frequency domain based on similar concepts as blanking nonlinearity process. Although these techniques have been found to improve the overall system bit error rate (BER), but the performance gains are somewhat limited due to ill-defined impulse noise thresholds and the blanking of the data content. Recent research demonstrates several advantages of coding methods for error detection and correction in an impulsive noise environment, especially in regard to the Reed–Solomon coding scheme. A creative approach called burst error recovery technique (BERT) is presented for impulsive noise mitigation [11]. In addition to RS coding, an over-sampling procedure is employed to improve robustness to impulsive noise. However, theoretical analysis and simulation results show that this approach is sensitive to increased levels of additive white Gaussian noise (AWGN). This is due to small variations in the infinite impulse response filter coefficients due

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to AWGN result in large variations at the output when the filter poles are close to each other. Kumaresan proposed some decoding strategies based on least-squares errors and a singular value decomposition process to correct for impulse errors [12]. Dlhan described an alternative approach to protect OFDM signals against impulsive noise and AWGN [13]. The proposed syndrome-based decoding algorithm using soft decision making showed promise but is still unable to fully resist the detrimental effects of higher levels of AWGN. Our research is focused on improving the performance of the impulsive noise cancelation process as well as to provide the ability to resist the influence of AWGN in OFDM systems. Hence, in this paper, we present a practical scheme for such a purpose. The reminder of the paper is organized as follows. In Section 2, the theoretical background and impact of impulsive noise on OFDM are introduced. Some existing impulsive noise suppression approaches which are based on filtering techniques are also described in this section. In Section 3, the details of our dual protection scheme are proposed. Several simulations and numerical results are represented in Section 4. Finally, conclusions of our work are provided in Section 5. 2. Impact of impulsive noise on OFDM With a RS coded OFDM transmitter, the signal sequence to be transmitted, given as Y¯ n , is first RS coded and then serial-to-parallel (S/P) converted to form the N data streams Yn , where 0 ≤ n ≤ N − 1. The S/P output is subcarrier modulated using QPSK, QAM, etc., prior to the application of the N-point inverse discrete Fourier transform (IDFT) process [14], that is, xk

= IDFT(Sn ) =

N−1 

 2nk 

Sn exp j

N

0 ≤ k ≤ N − 1,

,

(1)

n=0

where IDFT indicates IDFT process, and Sn is the subcarrier modulated signal. The k output streams of xk are then parallel-to-serial (P/S) converted and used to modulate a radio frequency (RF) carrier for transmission over the desired communications channel. Generally, noise in the channel can be grouped into two classes: AWGN and impulsive noise [15]. The OFDM receiver simply reverses the transmission process and after the RF demodulation, the received OFDM signal rk is modeled as follows: rk = xk ∗ hk + nk = xk ∗ hk + wk + ik ,

(2)

where hk , wk , and ik are the channel impulse response, AWGN, and impulsive noise representations, respectively. * indicates a convolution operation and nk is the aggregation of wk and ik . The resulting sequence rk is then S/P transformed into a parallel format. A N-point DFT process is applied: Rn

= DFT(rk ) =

N−1 

 2nk 

rk exp −j

N

,

0 ≤ n ≤ N − 1,

(3)

ik = bk gk ,

(5)

where bk is a Bernoulli process indicating the arrival of the impulsive noise event and gk is the random Gaussian process with zero mean and i2 variance. bk contains independently distributed zeros and ones where the ones indicate the arrival of impulsive noise events. The arrival rate of the impulsive noise events is represented as p = P(bk = 1). The arrival and variance parameters can be altered to facilitate varying noise conditions. In this research, the probabilistic arrival rate of the impulsive noise events p was set to 1% and 10% and the variance was held constant. In the time domain, the characteristics of impulsive noise can have significant differences when compared to transmitted signal and can be summarized as follows: (1) impulsive noise peak amplitudes can be much higher than that of the transmitted signal; (2) impulsive noise energy is concentrated into short periods. Given this, a method based on a blanking nonlinearity filter was proposed in [9]. The impulsive noise is suppressed by the process:



comp rk

=

 

rk ,

if rk  < A0 ,

0,

otherwise

k = 0, 1, . . ., N − 1

,

(6)

where rk is the time domain signal at the receiver and A0 is the experimental threshold value. Also, Zhidkov proposed a promising peak detection method (VBF) based on the variance of estimated noise to mitigate the effect of impulsive noise at the receiver in the frequency domain [10]. For the peak detection, a threshold value is estimated to recognize impulsive noise sequence uˆ = [uˆ 0 , uˆ 1 , . . ., uˆ N−1 ]: 1  ˆ 2 dk , N N−1

2

 =

k = 0, 1, · · ·, N − 1,

(7)

k=0

 uˆ k =

 2

dk ,

if dˆ k  > C ˆ 2 ,

0,

otherwise

k = 0, 1, . . ., N − 1

,

(8)

where dˆ k is the integrated noise estimation in time domain, N is the number of dˆ k , uˆ k is the estimated representation of impulsive noise, and C is the threshold value that corresponds to the probability of false detection. Although these approaches provide an effective way to reduce the impact of impulsive noise, the evaluation of the threshold value does not respond to changes in the characteristics of the impulsive noise and does not assess any correlation between the additive noise components. 3. Our proposed approach

k=0

where DFT indicates DFT process. The N-point DFT is then P/S converted with a subcarrier demodulation process corresponding to the subcarrier modulation used during transmission. In our research, the fast Fourier transform (FFT) and inverse fast Fourier transform (IFFT) are utilized for the implementation of DFT and IDFT, respectively. When a channel equalizer is not considered, we can represent Rn as Rn = Sn Hn + Wn + In ,

where Hn is the channel frequency response, Wn and In are AWGN and impulsive noise in frequency domain, respectively. The concept of AWGN is known in the area of communications and signal processing, and its model has been well documented. Less popular but still invasive is the impulsive noise component. Referring to previous research work, impulsive noise ik is normally accepted as the following expression [16]:

(4)

As expected, the value of the impulsive noise threshold affects the performance of the impulsive noise suppression methodology. If the threshold value is too small, a significant portion of the transmitted signal is replaced with zeros and the output signal-to-noise ratio (SNR) given by



SNR = 10 log10 

xk2 n2k

(9)

J. Jia, J. Meng / Int. J. Electron. Commun. (AEÜ) 68 (2014) 51–58

53

decreases. However, when the threshold value is set too large, impulsive noise events will go undetected and will corrupt the receiver demodulation process as shown by (3). Thus a good threshold value is needed to balance the false positive and negative detections of impulsive noise events. Theoretically, the idea of a conventional mean filter is simply to replace each element in the transmitted data sequence with the mean or average value of its neighbors including itself [17,18]. With a conventional mean filter only a rough approximation of the original OFDM transmitted signal is obtained. Although this is a poor representation of the original OFDM signal, a gain in receiver performance is achieved through the removal of the impulsive noise energy. In order to improve upon this, a new approach based on an improved mean windowing filter is proposed where the statistical property of every element and its neighbors is considered. The proposed filter attempts to remove impulsive noise rather than replace the OFDM signal with a mean value, thereby retaining the original characteristics of the original OFDM signal less the impulsive noise. 3.1. Estimating noise As shown earlier, the transmitted signal at the OFDM receiver is expressed by (4). With a perfect channel estimate, it is assumed that ˆ n ≡ Hn , where H ˆ n is the estimated channel frequency response. H (eq) The received signal Rn after frequency equalization can be represented as (eq)

Rn

ˆ n−1 = Sn + Wn H ˆ n−1 + In H ˆ n−1 , = Rn H

n = 0, 1, . . ., N − 1.

Fig. 1. Diagram of OFDM receiver with the proposed CCV Filter.

(10)

The total noise component Nn is the FFT of nk , and is the sum of the impulsive noise and AWGN in frequency domain, that is, Nn = Wn + In .

Our goal is to estimate the impulsive noise component In . To do this, the estimation of the integrated noise Nn from (11) represented as ˆ n is given as N ˆn = H ˆ n (Rn(eq) − Sˆ n ), N

Fig. 2. The random sample process.

(11)

n = 0, 1, . . ., N − 1,

(12)

where Sˆ n is the estimated transmitted signal that is obtained using a preliminary estimation processing [10]. This procedure is organized as follows: (1) after removing the cyclic prefix (CP), all null subcarriers, which were previously created for the N-point IFFT, containing noise-induced non-zero data are reset to zero (2) the transmitted data is then de-mapped to the proper constellation points. 3.2. Estimating impulsive noise

nˆ (,m) = sm .

ˆ n is estimated, the following is considered, Once N ˆ n) = w ˆ k + ˆik , nˆ k = IFFT(N

spike of impulsive noise is assumed to be still detectable and in this case, we attempt to obtain the estimated total noise and then proceed with impulsive noise removal. In order to mitigate the impact of impulsive noise, a composite comparison value (CCV) based filter is proposed. Initially, the estimated noise nˆ k is randomly sampled at the sampling rate Q = (M/N × 100%), where M is the number of sampling positions and N is the number of the elements of the estimated noise nˆ in the time domain, where nˆ = [nˆ 0 , nˆ k1 , . . .nˆ k , . . ., nˆ N−1 ]. A sampling sequence s = [s0 , s1 , . . ., sm , . . ., sM−1 ] is then obtained, where 0 ≤ m ≤ M − 1 ˆ This process is shown in Fig. 2. and s ⊂ n. ˆ a sampling position locator (,m) can be defined for Since s ⊂ n, the estimated noise nˆ k as

(13)

where nˆ k is the time domain combination of AWGN and impulsive noise, ˆik indicates the representation of the estimated impulsive ˆ k indicates the representation of the estimated AWGN. noise, and w Once the impulsive noise component is estimated by our proposed filter, it can be subtracted from the received signal prior to decoding. The block diagram of OFDM receiver with proposed filter is shown in Fig. 1.

(14)

This is illustrated in Fig. 3. A windowing process is then applied on every sampling position nˆ (,m) of the estimated noise sequence nˆ k . Fig. 4 illustrates this process. For each sampling position nˆ (,m) , the respective window wm contains the following elements: wm = [nˆ (,m)−W , nˆ (,m)−W +1 , . . ., nˆ (,m) , . . ., nˆ (,m)+W −1 , nˆ (,m)+W ], (15)

3.3. The composite comparison value (CCV) filter In the time domain, the occurrence probability of impulsive noise is fixed to 1% or 10% as discussed in Section 2. The peak amplitude of the impulsive noise is decreased, in order to obtain a large SNR and the peak amplitude of the impulsive noise does not greatly differ from the transmitted signal. But compared with AWGN, the

Fig. 3. Illustration of the sampling position locator.

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After the proposed impulsive noise filtering process, the received signal processed by FFT is ˜ n = FFT(˜rk ). R

(23)

Finally with the processing of equalizer, the received signal is represented as ˜ n(eq) = R ˆ n−1 . ˜ nH R

Fig. 4. The windowing process.

where wm is the window on the estimated noise nˆ k and the width of wm is 2W + 1. Now the CCV m is defined as m =

max |wm | − min |wm | , mean |wm |

(16)

where max indicates the maximum value, min indicates minimum value, mean indicates the mean value, and | | indicates the absolute value. Hence, after applying the window on all sampling positions, ¯ is obtained, another mean value 

M−1

¯ = 

m=0

m

M

3.4. Application of the Reed–Solomon decoding process

w˙ k = [nˆ k−W , nˆ k−W +1 , . . ., nˆ k , . . ., nˆ k−W −1 , nˆ k+W ].

(18)

The CCV ˙ k for every individual element of nˆ k is defined as

    nˆ k  − min w˙ k    . ˙ k = mean w˙ k 

In [19], it is found that RS code has the ability to correct burst errors. This is because RS decoder replaces the entire byte irrespective of the number of bits in error. In terms of m-bit conventional RS (e,k) codes, where k is the number of data symbols and e is the number of code symbols of each coding block, that is, (e, k) = (2m − 1, 2m − 2t − 1),

(19)

A proposed filtering process for impulsive noise removal is then defined as follows: Step 1. If the absolute value of nˆ k , which is also the center of current window, is larger than the mean absolute value in the sampling sequence s = [s0 , s1 , . . ., sm , . . ., sM−1 ]:

In

Step 2. Once (20) is satisfied, the impulsive detection is triggered by considering the following condition:

¯ if ˙ k ≥

0,

otherwise

N−1 

N

,

0 ≤ n ≤ N − 1.

,





⎡

(21)

⎢ ⎣



 

h1,1

...

.. .

..

HT = ⎢ 



he−k,1 













where r˜k is the transmitted signal with the impulsive noise suppressed.



h1,e .. .

.

···

(27)

⎤ ⎥ ⎥, ⎦

(28)



he−k,n



E = (e1 , e2 , . . .ee ), 

(22)

(26)

With the DFT representation of impulsive noise in (26), the impact of a large impulsive noise error can exceed the error correcting capability of RS decoder. One idea is, therefore, to increase the accuracy of decoding. More specifically, a traditional RS decoder employs syndromes to decrease the size of the dictionary which is used to determine the minimum hamming distance [13]. Generally syndrome testing is defined as S = RHT = (C + E)HT = EHT = (s1 , s2 , . . .se−k ),

where ˆik is the representation of impulsive noise obtained by the CCV filtering process. After this processing, the center signal of every window will be classified as either impulsive noise or not. Impulsive noise removal is then achieved as shown in Fig. 1, that is, r˜k = rk − ˆik ,

 2nk 

ik exp −j

k=0



nˆ k ,

= DFT(ik )

(20)

the filtering process moves to Step 2 for further analysis. Otherwise, the impulsive noise detection stops and the filtering process moves to the next data point nˆ k+1 .

(25)

where t is the length of the correcting capability, thus 2t is the length of the parity symbols. Now the impact of a random impulsive noise sequence on RS codeword is considered. As expected, the impulsive noise event will affect all OFDM subcarriers once processed by the DFT demodulation process, that is,

=

  nˆ k  ≥mean |s| ,

ˆik =

In a low SNR environment with a fixed low occurrence probability of impulsive noise, the peak amplitude of the impulsive noise in time domain is assumed to be much larger in comparison with the received signal rk , and the impulsive noise generally results in a failure of the preliminary estimation processing discussed in Section 3.1. This is because the constellation arrangement of the QAM demodulation is incorrect due to the distortion introduced from the impulsive noise and results in additional errors in the estimation of transmitted signal given by Sˆ n . As a result, the estimation of total noise component nˆ k is no longer accurate. To avoid this the CCV filter can be directly applied to the transmitted signal nˆ k rather than nˆ k and some BER improvement can be achieved. It should be noted, however, additional processing overhead is needed to assess the low SNR regime, possibly through power spectrum estimates from the OFDM receiver.

(17)

,

Now the windowing process is applied on every element of the estimated noise nˆ k to obtain the window w˙ k for each element, that is,



(24)

(29) 

where R is the received codeword, C is the original transmitted   codeword, E is the error vector, and HT is the transpose of the parity check. From (27), it is known that the syndrome only reflects the impact of error, irrespective of what the transmitted codeword

J. Jia, J. Meng / Int. J. Electron. Commun. (AEÜ) 68 (2014) 51–58 

Table 1 The arrangement of 16QAM bit-mapping.

is. To solve for the representation of E, it is assumed that the codeword has t errors corresponding to the error correction capability at locations xf1 , xf2 , . . ., xft with error value yf1 , yf2 , . . ., yft . The error polynomial can be deduced as 

E(x) = yf1 xf1 + yf2 xf2 + · · · + yft xft ,

(30)

where the index f refers to the error location and 1,2,. . .,t refers to the first, second,. . ., tth error. In order to determine each location xfl and its error value yfl , where l = 1,2,. . .,t, an error location number is defined as εl = ˛fl , where ˛ represents the basic elements of Galois Field. Next, ˛c is substituted into the received polynomial, where c = 1, 2 . . . , 2t. Then the 2t syndrome symbols are obtained: 



sc = R(ac ) =

t 

yfl εcl .

⎪ ⎩



(40)

(41)

is recorded as the error location number: εl = ε(z) .

(1 − εl x) = t xt + t−1 xt−1 + · · · + 1 x + 0 ,



−3 −1 +1 +3

(x) = (2t) (x) = (ε−1 ) = 0, (z)

(42)

The error value is then evaluated by the Forney Algorithm [22]:

(32)

where the solutions are 1/ε1 , 1/ε2 , . . . 1/εt , indicating the error locations ε1 , ε2 , . . ., εt . In order to solve (32) with the given syndrome  polynomial S, the Berlekamp–Massey (BM) iterative algorithm [20] is employed. The BM algorithm is briefly summarized as follows. We define

⎧ S(x) ⎪ ⎨

Q channel

−3 −1 +1 +3

where z = 0,1,. . .,e, and any ε−1 , satisfying the following condition (z)

(31)

(x) = (1 − ε1 x)(1 − ε2 x)· · ·(εt x) l=1

I channel

00 01 10 11

ε−1 = a−z , (z)

l=1

=

Baseband bit block

For (39), the Chien-search algorithm [21] is employed to find the error locations with (32). With the RS encoder, we have

Hence the task is to find out the error value yfl and the location xfl . The error location polynomial ϒ(x) is defined as

t

55

yfl = −

w(ε−1 ) l

 (ε−1 ) l

,

(43)

where  indicates a derivative operation. Once the error polynomial  E(x) is obtained, decoding with error correction then follows.



= 1 + s1 x + s2 x2 + · · · + s2t x2t 











ω(x) = S(x) (x) = 1 + (s1 + 1 )x + (s2 + s1 1 + 2 2 )x2 + · · · + (st + 1 + st−2 2 + · · · + t )xt . = 1 + ω1 x + ω2

x2

+ · · · + ωt

(33)

xt

The key equation is obtained as 

S(x) (x) ≡ ω(x)(mod x2t+1 ),

(34)

where mod indicates a modulo division operation. For the BM iterative processing, a step-difference function dj is employed, that is 

S(x) (j) (x) ≡ (w(j) (x) + dj xj+1 )(mod xj+2 ),

(35)

where j indicates the jth iteration. Once the initial d, ϒ(x), w(x) are given, the iterations can be achieved as

⎧ ∂w(j) (x)  ⎪ ⎪  (j) ⎪ d = s + sj+1−c ωc ⎪ j j+1 ⎪ ⎪ ⎪ c=1 ⎪ ⎪  (j) ⎨ −1

(x) − dj dv xj−v (j) (x), dj = / 0 ,

(j+1) (x) = ⎪ ⎪ ⎪

(j) (x), dj = 0 ⎪ ⎪  (j) ⎪ ⎪ ω (x) − dj dv−1 xj−v ω(j) (x), dj = / 0 ⎪ ⎪ ⎩ ω(j+1) (x) = (j)

(36)

ω (x), dj = 0

where ∂ indicates a partial derivative operation, and v is corresponding to max(v − ∂ (j) (x)). The initial values are given as

(−1) (x) = 1, ω(−1) (x) = 0,

d−1 = 1, j = 1,

(37)

4. Simulation results For our OFDM simulations, a 276k bits baseband signal is transmitted via 200 subcarriers and a 512-point FFT/IFFT process. 16QAM is used for baseband modulation and RS coding is added to provide additional impulsive noise resistance. A conventional bit-mapping arrangement for the 16QAM symbol-to-voltage conversion process was used and is shown in Table 1. Block interleaving then follows to provide additional channel robustness. At the receiver, the deinterleaver operates in reverse to arrange the encoded symbols in the original sequence. Since the effect of the impulsive noise on OFDM systems is the focus of this research, in order to lessen the impact of AWGN, the signal-to-AWGN ratio is fixed to 20 dB and the impulsive noise amplitude was varied to achieve the desired SNR for all the following simulations. For the CCV filter, experimental results indicate that a reasonable sampling rate, Q, and window width, 2W + 1, are 10% and 41, respectively. Additionally, in order to manage multipath propagation, a CP is added in the simulations [23]. The structure of our simulation tests is shown in Fig. 5. With the above configuration, several simulations with various probabilities of impulsive noise occurrence and RS code rates were performed to demonstrate the performance of CCV filter with our practical RS decoding scheme.

then we obtain

(0) (x) = 1, ω(0) (x) = 1,



d0 = s1 , j = 0.

(38)

According to (36), the error location polynomial is obtained after 2t iterations:

(x) = (2t) (x).

(39)

4.1. Case 1: p = 1%; e = 15, k = 3 The settings are arranged as follows for Case 1. The probability of impulsive noise events occurrence is fixed to 1%. The length of RS redundancy is fixed to 12 given the assumed impulsive noise characteristics. In order to limit the overhead of the RS coding process,

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Fig. 5. The structure of OFDM simulation tests.

the length of codeword is fixed to a reasonable value of 15. Therefore the length of data symbol is 3 and for RS(15,k), every symbol contains 4 bits. In the first simulation, the advantage of utilizing the CCV filter on the constellation of a 16QAM demodulation process with 9 dB SNR is demonstrated. The differences between constellations of RS coded OFDM (RS-OFDM) with and without the CCV filter are shown in Fig. 6. Clearly, the effectiveness of the CCV filter in improving the desired clustering of the QAM constellation points is seen. In the second simulation, the BER performance of conventional OFDM (OFDM), OFDM with VBF filter (VBF-OFDM) [10], OFDM with CCV filter (CCV-OFDM), RS-OFDM, and RS-OFDM with CCV filter (RSCCV-OFDM) are compared. The BER simulation results are shown in Fig. 7. In these results the CCV-OFDM system shows an improved performance when compared to the VBF-OFDM system. As one can see, both the CCV filter and RS coding procedure improve the impulsive noise resistance of the OFDM system. Overall, the BER improvement of proposed RSCCV-OFDM system is the largest when compared to all other methods. 4.2. Case 2: p = 10%; e = 15, k = 3

Fig. 7. BER performance of OFDM, VBF-OFDM, CCV-OFDM, RS-OFDM, and RSCCVOFDM (p = 1%).

is fixed to 15, the length of data symbol is 3. The simulation results are shown in Fig. 8. It is seen that RS-OFDM has fairly good impulsive noise resistance and is close in performance to RSCCV-OFDM but the latter having consistently the best BER performance.

4.3. Case 3: p = 1%; e = 15, k = 3, 5, 7, 9, 11 In this case, the simulation settings are: the probability of impulsive noise events occurrence is fixed to 1%, the length of codeword is fixed to 15, the length of data symbol is varying from 3 to 11. Theoretically, if a coding scheme attempts to mitigate the effects of impulsive noise, the noise duration has to be only a small percentage of the codeword [19]. Therefore an increased size of the code block should enhance the error correcting capability but with the trade-off of more processing overhead. In this simulation, the BER performance of RSCCV-OFDM with various RS redundancies is illustrated in Fig. 9. As one can see, the results match theoretical expectations with the rate 3/15 code yielding the best performance.

In Case 2, the simulation settings are: the probability of impulsive noise events occurrence is fixed to 10%, the length of codeword

Fig. 6. Left: constellation without processing by CCV filter; right: constellation with processing by CCV filter (SNR = 9 dB, p = 1%).

Fig. 8. BER performance of OFDM, VBF-OFDM, CCV-OFDM, RS-OFDM, and RSCCVOFDM (p = 10%).

J. Jia, J. Meng / Int. J. Electron. Commun. (AEÜ) 68 (2014) 51–58

Fig. 9. BER performance of RSCCV-OFDM with various RS redundancies (p = 1%).

57

Fig. 11. BER performance of OFDM, VBF-OFDM, CCV-OFDM, RS-OFDM, and RSCCVOFDM in multipath channel.

4.4. Case 4: multipath channel: p = 1%; e = 15, k = 3 In case 4, the simulation settings are arranged as follows. The probability of impulsive noise events occurrence is fixed to 1%, the length of codeword is fixed to 15, the length of data symbol is 3. To facilitate a more realistic channel model, a timeinvariant 7-path frequency-selective channel was utilized as an example to evaluate the performance of the proposed impulsive noise suppression algorithm. The resulting channel frequency response is shown in Fig. 10. Although more difficult channel models could have been utilized, this example of a frequency-selective channel should suffice given our study focuses on point-to-point transceivers. The BER and the symbol error rate (SER) are shown in Figs. 11 and 12, respectively. From Fig. 11, it can be seen that, to achieve the same bit error condition, CCV-OFDM obtains an average 9 dB and 6 dB SNR improvement when compared to OFDM and VBF-OFDM, respectively; RSCCV-OFDM also obtains a significant SNR improvement when compared to RS-OFDM. The system SER shows similar results.

Fig. 12. SER performance of OFDM, VBF-OFDM, CCV-OFDM, RS-OFDM, and RSCCVOFDM in multipath channel.

5. Conclusion 2

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In this paper, a dual protection scheme is proposed in order to mitigate the effect of impulsive noise in OFDM systems. The CCV pre-processing filter and practical RS decoding process are theoretically analyzed and confirmed through simulation. In comparison to other existing impulsive noise suppression algorithms, RSCCVOFDM provides good resistance of impulsive noise and provides for additional performance gains over previously proposed methods. Numerous environmental regimes were tested including changes in impulsive noise rate and SNR. The following work can be included for further research. (1) In the case of a greater occurrence probability of impulsive noise, the RS codeword and redundancy extension is needed to be analyzed. RS with increased redundancy is able to correct more errors, but minimal redundancy is still needed to obtain the possibly highest code rate. (2) According to both simulation results and theoretical analysis, the decoding failure of the proposed RS decoding algorithms exists. Hence analysis of the probability of decoding failure of the proposed RS decoding algorithms with various occurrence probabilities of impulsive noise is warranted.

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[17] Wang X. NFIR nonlinear filter. IEEE Trans Signal Process 1991;39: 1705–8. [18] Stranneby D, Walker W. Digital signal processing and applications. 2nd ed. Burlington, MA, USA: Newnes; 2004. [19] Sklar B. Digital communications fundamentals and applications. 2nd ed. Upper Saddle River, NJ, USA: Prentice Hall; 2001. [20] Berlekamp JL. Algebraic coding theory. New York: McGraw-Hill; 1968. [21] Chien RT. Cyclic decoding procedures for the bose-chaudhuri-hocquenghem codes. IEEE Trans Inform Theory 1964;10:357–63. [22] Forney JD. Cyclic decoding procedures for the Bose–Chaudhuri–Hocquenghem codes. IEEE Trans Inform Theory 1965;11:549–57. [23] Tonello AM, D’Alessandro S, Lampe L. Cyclic prefix design and allocation in bitloaded OFDM over power line communication channels. IEEE Trans Commun 2010;58:3265–76. Jia Jia received his BS degree in electrical information engineering from University of Electronic Science and Technology of China, Chengdu, China, in 2005 and master degree in digital image processing from University of Bradford, England, in 2009. Currently he is pursuing the PhD degree in electrical engineering at the University of New Brunswick (UNB), Canada. His research interests include communications, digital image processing and signal processing.

Julian Meng received his master and PhD degrees in electrical engineering from Queen’s University, Canada in 1989 and 1993. Currently he is a professor in the department of electrical and computer engineering, UNB. Prior this position, he worked in various industrial positions in research areas such as LMDS wireless communications and image processing with a focus on data fusion applications. His research interests include wireless communications, distributed power generation, adaptive filtering and image processing.