SCIENCE CHINA Information Sciences

. RESEARCH PAPER .

February 2014, Vol. 57 022301:1–022301:13 doi: 10.1007/s11432-013-4921-7

Iterative signal reconstruction of deliberately clipped SMT signals ´ Zsolt1 ∗ , GAZDA Juraj2 , HORVATH ´ KOLLAR P´eter1 , VARGA Lajos1 & KOCUR Duˇsan2 1Budapest

University of Technology and Economics, Budapest, Hungary; 2Technical University of Koˇ sice, Kosice, Slovakia

Received July 9, 2013; accepted September 30, 2013; published online October 28, 2013

Abstract Staggered MultiTone (SMT) is a modulation technique showing significantly reduced Adjacent Channel Leakage Ratio (ACLR) resulting in a more compact Power Spectrum Density (PSD) for the transmitted signal, than the well-known and already widely adopted Orthogonal Frequency Division Multiple Access (OFDMA) scheme. However, the unique spectral properties of an SMT signal could be degraded by a non-linear element (e.g. a Power Amplifier (PA)) in the transmitter. Deliberate baseband clipping can be applied to the transmitted signal, reducing the notable high Peak-to-Average Power Ratio (PAPR). The objective of this paper is to give a brief introduction to the SMT scheme, with a special emphasis on deliberate clipping effects and their compensation. The paper introduces two receiver-oriented iterative methods aiming at the restoration of the baseband Bit Error Rate (BER) performance of a non-clipped signal. The methods are evaluated and compared based on numerical simulations. The paper concludes with the selection of a possible candidate for use in systems applying deliberately clipped SMT signals. Keywords

clipping, SMT, iterative decoding, nonlinear distortion, PAPR

Citation Koll´ ar Z, Gazda J, Horv´ ath P, et al. Iterative signal reconstruction of deliberately clipped SMT signals. Sci China Inf Sci, 2014, 57: 022301(13), doi: 10.1007/s11432-013-4921-7

1

Introduction

Orthogonal Frequency Division Multiplex (OFDM) is a modulation technique widely adopted in broadband wireless communication systems, deployed in systems including Long Term Evolution (LTE) [1] and Digital Video Broadcasting (DVB-T2)1) . Several unique properties provide OFDM a high level of robustness in real communication scenarios. Subcarrier orthogonality and Cyclic Prefix (CP) insertion enable simple one-tap channel equalization. Subcarriers could apply adaptive modulation parameters in order to maximize spectral efficiency. An OFDM signal is generated using the comparatively quick and computationally efficient Fast Fourier Transform (FFT), giving low complexity for the OFDM transceiver [2]. ∗ Corresponding

author (email: [email protected]) 1) Digital Terrestrial Television Action Group. Understanding DVB-T2. http://www.digitag.org/DTTResources/DVBT2 Handbook.pdf, 2009.

c Science China Press and Springer-Verlag Berlin Heidelberg 2013

info.scichina.com

link.springer.com

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However, shortcomings of OFDM-based transmission systems are also well-known. OFDM may find limited application in a Cognitive Radio scenario, where primary (non-cognitive) and secondary (cognitive) users transmit independently. The OFDM spectrum shows comparatively large spectral sidelobes; therefore it might not meet the leakage requirements of future mobile communication standards. Another well-known limitation of OFDM arises in case of uplink transmission, where the necessary synchronization requires additional processing steps, resulting in an increased complexity. Another problem is the significant fluctuation of the transmitted signal level (wide dynamic range), which, paired with a nonlinear electric element results in elevated out-of-band radiation. In conjunction with the large spectral sidelobes, the application of OFDM in multiple access scenarios is also complicated due to the specific filters that synthesize the OFDM subcarrier signals. These issues could be greatly suppressed if the filters that synthesize the subcarrier signals had reduced sidelobes. SMT uses filterbanks having arbitrarily low ACLR, giving a solution to the above-mentioned problems related to synchronization and multi-user scenario. The literature provides a wide range of papers on OFDM evaluation, while some papers also deal with SMT. Synchronization of SMT signals is dealt with in detail in [3,4] and references therein. Equalization of the effects of multipath propagation in SMT environment is discussed in [5–7]. The performance of available multicarrier systems including SMT, Single Carrier FDMA (SC-FDMA) and OFDM is evaluated in [8]. One should note that compared to the ongoing research interest in OFDM, only limited interest is paid to the issues related to the nonlinear amplification of an SMT signal. Such nonlinearity might completely destroy the compact PSD [9] and subsequently results in increased BER. In [8, 10] a general performance evaluation of an SMT signal undergoing nonlinear amplification is provided, concluding that nonlinear amplification severely degrades SMT performance. Various strategies are available to reduce the effects of nonlinearities introduced by the PA. Nonlinear distortion compensation methods can be implemented at transmitter or receiver side. Frequently used transmitter side solutions include clipping [11,12], active constellation extension, tone reservation [13] and selective mapping [14]. Strategies at the receiver side usually combine some form of iterative decoding [15], e.g. Turbo Codes. However, most of these techniques have been designed for OFDM-based transmission systems. Due the structure of an SMT signal, the application of the above mentioned techniques is not always straightforward. Some PAPR reduction techniques already elaborated and suitable for SMT are presented in [16, 17]. In this paper the baseband amplitude clipping method is applied for reducing the PAPR of SMT signals. The transmitted signal is clipped to match the linear range of the PA. As the PAPR of the signal is limited by clipping, nonlinear effects are introduced, degrading system performance. Clipping must therefore be compensated for in the receiver. Two receiver-oriented schemes are presented to reduce the error rate of SMT systems undergoing clipping. The techniques consist of two successive steps: estimation and compensation of nonlinear distortion introduced by clipping. The former presents the sub-optimal maximum likelihood detector using hard decisions based on the received signal vector. The latter is a modified version where soft decisions of the received signal vector are applied. Using the soft information the receiver takes full advantage of the turbo principle, yielding better BER than the hard decision based receiver. The capabilities of both schemes are evaluated prevails in Additive White Gaussian Noise (AWGN) and frequency selective scenarios. The paper shows that the system performance is significantly improved even after the first iteration, and moreover, that the soft decision based iterative receiver is capable of approaching the performance of a linear scenario where no clipping is applied. Thus, the performance of SMT systems prevails in both perspectives, BER and out-of-band radiation. The structure of the paper is as follows. The system model of the SMT modulation scheme is introduced in Section 2. Section 3 is devoted to the effects of clipping on the transmitted SMT signal. Two iterative schemes enabling the performance improvement of the clipped SMT system are introduced in Section 4. Simulation results are presented in Section 5. The conclusions are drawn in Section 6. In order to design the analog circuits aiding the transceiver chain, a deep knowledge of the statistic properties of the transmitted signal must be be acquired. Such investigations are especially important in case of the design of power amplifiers which have to work in an efficient manner while being as linear

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IFFT & polyphase structure b

Convolutional encoder

Interleaver

c

Constellation mapping

s

X IFFT & polyphase structure

Figure 1

Time staggering

Block diagram of the SMT transmitter.

as possible. A detailed investigation of such metrics for OFDM can be found in [18]. In [8] it has been shown that SMT signals have similar signal statistics as of OFDM. Nonlinearities in the transceiver chain—especially those induced by amplifiers—can severely degrade the advantageous properties (e.g. low ACLR) of SMT signals [19]. In the next section baseband clipping is introduced which can decrease the large PAPR values of the signal—without ACLR regrowth—to meet the linear range of the amplifier and can lead to more power efficient operation.

2

The SMT system

The SMT modulation scheme is a wide family of multicarrier schemes. The modulation of the subcarriers is performed via IFFT—as in OFDM systems—then each subcarrier is filtered by a uniquely designed prototype filter. A wide range of filters which can be used in SMT systems is presented in the corresponding literature [20, 21]. The key effect of this filter is that it determines the spectral characteristics of the transmitted signal. SMT applies modulated prototype filters having an impulse response of p0 . These filters fulfill the Nyquist criterion. Due to the advantageous properties of the prototype filter, SMT signals have better spectral efficiency than OFDM. First, the binary information is encoded using a convolutional encoder and then interleaved. The bits are then mapped using the complex modulation alphabet A, where each symbol X represents M bits. With the use of offset-QAM modulation, the real ℜ and imaginary ℑ parts of the complex modulation symbol X are transmitted with a time offset of half a symbol duration. Finally, prior to transmission, the symbols are overlapped such that they can be separated in the receiver. No CP is used in SMT systems to maintain orthogonality of the filters. The discrete modulated baseband SMT signal can be expressed as:   ∞ N −1  X X 2π N ejk(n−mN ) N , (1) s[n] = θk ℜ{Xm [k]}p0 [n − mN ] + θk+1 ℑ{Xm [k]}p0 n − mN − 2 m=−∞ k=0

√ π where j = −1, θk = ej 2 k , Xm [k] is the modulation value on kth subcarrier in the mth signalling time and N represents the number of available subcarriers. The overlapping ratio of consecutive symbols strongly depends on the length of the prototype filter. For simplicity and based on practical implementation the filter is designed with an impulse response of length K × N , meaning that the symbol duration is extended. To prevent data rate loss, K symbols are overlapped in the time domain. The block diagram of an SMT transmitter can be seen in Figure 1. The bitstream b is encoded to the coded bitstream c, and then the bits are mapped to complex symbols X according to the modulation alphabet A. Finally Eq. (1) is implemented computationally efficiently using an IFFT and a polyphase decomposition of the modulated prototype filters for the real and imaginary parts. Then the two output signals are time staggered and added. In order to design the analog circuits aiding the transceiver chain, a deep knowledge of the statistic properties of the transmitted signal must be be acquired. Such investigations are especially important in case of the design of power amplifiers which have to work in an efficient manner while being as linear as possible. A detailed investigation of such metrics for OFDM can be found in [18]. In [8] it has been shown that SMT signals have a similar signal statistics as of OFDM. Nonlinearities in the transceiver

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103 Real part Imaginary part

Kurtosis

102

101

100

−1

0

1

2

3

4

5

6

CR (dB) Figure 2

Kurtosis of the clipping noise in function of the CR.

chain—especially those induced by amplifiers—can severely degrade the advantageous properties (e.g. low ACLR) of SMT signals [19]. In the next section baseband clipping is introduced which can decrease the large PAPR values of the signal—without ACLR regrowth—to meet the linear range of the amplifier and can lead to more power efficient operation.

3

Baseband clipping

In this section the effects of baseband clipping on an SMT signal are investigated. Clipping is performed prior to upsampling and transmission in order to force all nonlinear distortion components to fall in the baseband, so no out-of-band radiation will appear. Clipping is the simplest way to reduce the PAPR of an SMT signal. The amplitude of the time domain SMT signal is simply limited to a threshold Amax , but the phase remains the same. As a result, the clipping model for a soft envelope limiter can be written as ( s[n], |s[n]| 6 Amax , f (s[n]) = (2) Amax ejϕ(s[n]) , |s[n]| > Amax , where ϕ(s[n]) is the phase of the complex signal s[n]. For a global characterization of such a limitation the Clipping Ratio (CR) is defined as CR = 20 log10 (γ), where γ is defined as γ=

Amax Amax = p , σ E{|s[n]|2 }

(3)

(4)

where Amax is the clipping level and σ is the square root of the average power Ps of the transmitted signal (prior to clipping). The mathematical model for clipping can be derived from Bussgang’s theorem for memoryless nonlinearities with Gaussian inputs. The cross-correlation between the input and the output signal has a shape similar to the auto-correlation of the input signal [22]. The output of the nonlinearity can be expressed as u[n] = αs[n] + d[n], (5) where α describes the attenuation and d[n] is the clipping noise, also called Bussgang’s noise, which is assumed to be uncorrelated with s[n] and normal distributed. The exact distribution of the clipping noise is dependent on the clipping ratio. The kurtosis [23] as a function of CR can be observed in Figure 2. CR = 1 dB is used in the simulations, resulting in a kurtosis of approx. 3, meaning that the distribution can be practically considered as normal.

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As it is shown in [22,24] the attenuation factor α can also be calculated using the envelope characteristic of the nonlinearity which is related to its Chebysev transform [25]. As a result α can be expressed as √ 2 π γ erfc(γ). (6) α = 1 − e−γ + 2 The output power is given by   2 Pout = 1 − e−γ Ps .

(7)

With the aid of (5) and (7), the power of the clipping noise can be expressed as   2 Pd = Pout − Pclipped = Pout − α2 Ps = 1 − e−γ − α2 Ps .

(8)

The Signal-to-Distortion Ratio (SDR) can be calculated as SDR =

Pclipped α2 . = −γ Pd 1 − e 2 − α2

(9)

The PAPR of the clipped signal will be limited by an upper bound of PAPRclipped 6

A2max γ2 . = Pout 1 − e−γ 2

(10)

In real life applications, where some carriers remain unused the technique presented in [26] should be used, where clipping is followed by an SMT demodulation with a frequency domain filtering to eliminate the effects of in-band distortion on the unmodulated subcarriers.

4

Iterative compensation in the receiver

In this section two receiver oriented clipping mitigation schemes are presented, which are suitable for restoring the performance of baseband clipped SMT signals. Please note that in the real scenario, the signal is transmitted through a multipath channel, which should also be taken into consideration when designing SMT iterative compensation schemes. The channel equalization and estimation is not straightforward for SMT systems, especially not for channels with long delay spreads as shown in [27, 28]. For relatively short channel delay spreads— compared to the symbol duration—a per subcarrier based channel equalization can be performed. The channel equalization performance of SMT matches that of CP-OFDM but with a higher data rate [29]. This assumption will be considered in the following discussion where two different schemes coping with Bussgang noise are presented. 4.1

Hard decision based iterative detector

In this section, the hard decision based Bussgang Noise Cancelation (HD-BNC) scheme will be introduced. The block diagram of the HD-BNC is depicted in Figure 3. From (5) and assuming a multipath fading channel, the decision variables at the input of the demodulation stage can be expressed as Y [k] = αH[k]X[k] + H[k]D[k] + W [k],

0 6 k < N,

(11)

where k denotes the subcarrier index, W [k] is the SMT demodulated AWGN contribution and H[k] is the frequency response of the channel at the kth subcarrier. Then, the Maximum Likelihood (ML) sequence detector must solve ˆ = arg min kY [k] − (αH[k]Al + H[k]D[k])k2 , X (12) ∀Al ∈A

where Al is any possible signal constellation point taken from the alphabet A. Obviously, solving (12) is too complex; therefore it becomes necessary to find a suboptimal solution of reduced complexity. Let us

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assume that the receiver knows D[k] and α. Then both the Bussgang noise and the attenuation factor can be compensated for in the decision variables, as ′

Y [k] =

′ 1 (Y [k] − H[k]D[k]) = X[k]H[k] + W [k], α

(13)

′

with W [k] = W [k]/α. Neither deterministic terms H[k]D[k] nor α play any role in the ML detector. As a result, Eq. (12) reduces to ˆ = arg min kY ′ [k] − Al k2 , X[k] (14) ∀Al ∈A

which by simple modifications and by considering Parseval’s theorem can be expressed as

2

Y [[k] − H[k]D[k]

ˆ

X[k] = arg min − H[k]Al

. ∀Al ∈A α

The solution to (15) is the constellation symbol Ak ∈ A that is closest to   1 Y [k] − D[k] , α H[k]

(15)

(16)

where Y [k]/H[k] is an element-wise division. In practice the receiver does have a knowledge of D[k]. However, provided it knows the transmit clipping function f (·), D[k] can be estimated from the received symbol Y [k]. This process can be done iteratively by using the following procedure: 1) Compute a hard decision of the received symbols D E ˆ (i) [k] = 1 Y [k] − D(i−1) [k] , X α

(17)

ˆ (i) [k] = Φ−1 (f (ˆ D s(i) [n]) − αˆ s(i) [n]),

(18)

ˆ (i) [k]), sˆ(i) [n] = Φ(X

(19)

where h·i denotes hard decision and i is the iteration number. Please note that the first estimation of the transmitted symbol vector is calculated directly from the received vector, without assuming prior ˆ 1 [k] = hYk /αi. knowledge of the distortion term, i.e. X (i) ˆ 2) Assuming that X [k] is the transmitted symbol, calculate the corresponding distortion term as

where −1

where Φ(·) and Φ (·) are the SMT modulation and demodulation operations and f (·) represents the nonlinear characteristics of the clipping function as presented in (2). ˆ (i+1) [k] using both the received symbol Y [k] and the estimated 3) Proceed to step 1 and calculate X (i) ˆ distortion term D [k]. This procedure could be extended in such a way that the Viterbi algorithm and channel coder are incorporated in the feedback loop. This scheme will be referred to as coded HD-BNC (Method II. in Figure 3). The conventional SMT receiver extended by the iterative detection procedure represents the novel receiver optimized for the detection of clipped SMT symbols. Following the design procedure, it can be considered to be the nonlinear iterative sub-optimal maximum likelihood receiver. In the following, it will be shown that further improvements could be reached by joint deployment of the soft detection techniques and BCJR channel decoder [30] (named after its inventors: Bahl, Cook, Jelinek and Raviv). 4.2

Soft decision based iterative detector

The basic block diagram of the soft decision based Bussgang Noise Cancelation (SD-BNC) iterative detector for SMT signals is shown in Figure 4. It is an extension of the structure presented in [31] for frequency selective channels mainly based on similar blocks as for the hard decision based detector in

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Hard BNC detector Phase compensation

Y SMT demodulation

Dˆ SMT demodulation

Y'

−

Equalizer 1/α

cˆ

Demapper

H

+ + −

dˆ

+ +

Deinterleaver

Method I.

y

Channel decoder

Coded bits

sˆ c

sˆ

Clipping

α ˆs

Xˆ SMT modulation

Mapper

Method II.

Interleaver

α

Channel decoder

Soft BNC detector Phase compensation

Y SMT demodulation

Dˆ SMT demodulation dˆ

+

sˆ c

α (i) ˆs

Figure 4

+ +

Yˆ

−

Equalizer and soft demapper

L

Deinterleaver

H

+ −

Convolutional encoder

Block diagram of the hard decision based BNC receiver for clipped SMT signals.

Figure 3

y

Information bits

Viterbi decoder

Information bits

BJCR decoder

Extrinsic information Clipping

sˆ

~ X SMT Soft mapper modulation

Interleaver

α (i)

Block diagram of the modified and extended soft decision based BNC receiver for clipped SMT signals.

Figure 3. The gray signal processing blocks are modified in accordance with soft decision making. Two main blocks are presented in Figure 4: the BNC detector and the channel decoder. The BNC detector consists of a forward and feedback signal processing path. In the following, a brief description is provided of the steps carried out by the proposed scheme. 1) The received symbols can be expressed after SMT demodulation as presented in (11). 2) The extrinsic Log-Likelihood Ratio (LLR)—soft decision for the encoded bits—for channel observation Yˆ [k] is calculated as presented in [32] as   P ˆ Al ∈A1u,v p Y [k]|Au = Al ,  L(bu,v |Yˆ [k]) = ln P (20) ˆ [k]|Au = Al p Y 0 Al ∈A u,v

where A1u,v and A0u,v , are the subsets of Au (1 < u 6 M ) . The vth bit in Au can be either 1 or 0. The conditional probability density function p(Yˆ = Al ) is given by [33] as ! ˆ [k] − αH[k]A)2 ( Y , (21) p(Yˆ [k]|A) = exp (i) N0 + |H[k]|2 PD (i)

where PD is the power of the clipping noise remaining after the ith iteration. Taking into account the large number of samples and applying the central limit theorem, the clipping noise D[k] can be modeled as a Gaussian distributed random variable independent of the channel noise W [k]. For the 0th iteration, with no feedback, Pd0 is calculated according to (8). As the receiver does not know D[k], the power of the remaining clipping noise is to be estimated as o n (i) 0 ˆ 2 . (22) − E |D[k]| PD = PD 1 0 Please note that during the 1st iteration PD = PD , as no feedback is present.

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3) After deinterleaving, the BCJR channel decoder [30] calculates the extrinsic information of the deinterleaved LLRs provided by the BNC detector. These extrinsic LLRs will be used to suppress the clipping noise in the feedback path of the BNC detector. 4) After interleaving the extrinsic LLRs provided by the channel decoder, the soft symbols are calculated as [33] M 2X −1 M−1 Y ˜ Al X[k] = P (bl,u ), Al ∈ A, (23) l=0

u=0

i.e. each symbol is weighted by the probability of the mapped bits, and then the results are summed. Using these soft symbols, a time domain estimation of the SMT signal is calculated. Then clipping is applied with a level of Amax , and the signal is converted to frequency domain. The attenuation factor α(i) must be set in accordance with the output power of the SMT modulator (e.g. the soft mapper). The √ clipping ratio for the ith iteration can be calculated as γ (i) = Amax / Psˆ. The new attenuation factor can be calculated according to (6) as √   (i) 2 π (i) α(i) = 1 − e−(γ ) + (24) γ erfc γ (i) . 2

From iteration to iteration, the attenuation factor in the feedback loop will drop from 1 to α as the estimate becomes more and more accurate. 5) Subtracting the attenuated signal from the clipped signal, the estimated SMT demodulated clipping noise can be expressed in the same way as presented in (18) and (19). ˆ is then multiplied by the channel filter coefficient and subtracted 6) The estimated Bussgang noise D from the received signal to suppress the clipping noise, as in the hard decision case.
ˆ (i) [k] + W [k]. Yˆ [k] = αH[k]X[k] + H[k] D[k] − D (25)

The modified signal can be demodulated again. The 1st iteration is considered as the case when no feedback is used, i.e. Yˆ [k] = Y [k]. As the attenuation factor α(i) is monotonously decreasing, the iteration process can stop when the change in α(i) is smaller than a given threshold between consecutive iterations. • Convergence analysis. The EXtrinsic Information Transfer (EXIT) chart was developed and published in [34]. It is used to investigate the iteration behavior of a turbo loop based on the exchange of mutual information. Using the EXIT chart for the BNC receiver the mutual information exchange between the BNC detector and the channel decoder can be traced over the iterations. The EXIT function of the BNC detector is a function of the a priori mutual information IA provided by the channel decoder and also of Eb /N0 as IE1 = f (IA1 , Eb /N0 ). The EXIT function of the channel decoder only depends on the a priori LLRs provided by the BNC detector as IE2 = f (IA2 ). Using the EXIT functions of the BNC detector and the channel decoder, the iteration steps of the turbo loop can be visualized. The output of the channel decoder becomes the input of the BNC detector, and the output of the detector will be the new input of the decoder in the next iteration. To observe the mutual information transfer of the turbo loop, the EXIT chart is constructed from the two EXIT functions. The EXIT function of the channel decoder is plotted with swapped x-y axes on top of the BNC detectors to visualize the iteration trajectory. Iteration trajectories are shown in Figure 6 for Eb /N0 = 4 dB and Eb /N0 = 12 dB with a channel decoder rate of 1/2. In turbo receivers, the EXIT function of both decoders must be monotonously increasing to achieve convergence. It can be observed in Figure 5 that the monotony of the BNC detector is satisfied. As the input mutual information IA1 is increasing, an increasing output mutual information IE1 can be observed. 4.3

Comparison

The basic idea of the HD-BNC and SD-BNC receivers is similar, and the main difference is in the required information and signal processing complexity. Most of the signal processing blocks are the same for both techniques, as depicted in Figures 4 and 3. To compare the techniques, the signal processing complexity of the gray boxes have to be closely investigated.

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1.0 IE1 BNC detector/IA2 channel decoder

1.0

IE1 BNC detector

0.8

0.6

0.4 Exit function of the original BNC detector, Eb/N0=4 dB Exit function of the original BNC detector, Eb/N0=12 dB

0.2

Exit function of the modified BNC detector, Eb/N0=4 dB Exit function of the modified BNC detector, Eb/N0=12 dB

0

0

0.2

0.4

0.6

0.8

1.0

IA1 BNC detector

0.6

0.4 Exit function of the channel decoder Exit function of the BNC detector, Eb/N0=4 dB

0.2

Exit function of the BNC detector, Eb/N0=12 dB Decoding trajectory

0

0

0.2

0.4

0.6

0.8

1.0

IA1 BNC detector/IE2 channel decoder

Figure 5 EXIT functions of the original (constant α) and the modified (adaptive α(i) ) soft BNC detector for Eb /N0 = 4 dB and Eb /N0 = 12 dB values with CR = 1 dB. Table 1

0.8

Figure 6 EXIT chart with iteration trajectories of the BNC turbo receiver for SMT with an R = 1/2 rate channel decoder with Eb /N0 = 4 dB and Eb /N0 = 12 dB values with CR = 1 dB.

Computational complexity of the HD- and SD-BNC in function of the number of iterations (i)

Signal processing block

HD-BNC (Method I.)

HD-BNC (Method II.)

SD-BNC

Equalization and demapping

i × O(Hard demapping)

i × O(Hard demapping)

i × O(Soft demapping)

Decoder

O(Viterbi)

i × O(Viterbi)

i × O(BCJR (logmap))

Mapper

i × O(Hard mapper)

i × O(Hard mapper)

i × O(Soft mapper)

First, the equalization and demapping is analyzed. In case of hard decision, the equalizer/demapper requires a multiplication with the channel coefficient and a minimum Euclidean distance calculation over the constellation alphabet A to demap the modulation value. In case of the soft demapper the noise variance of the AWGN term is required and Eq. (20) has to be evaluated for each bit. As presented in [32], the complexity is exponentially growing with the size of A. Secondly, the decoder/coder is analyzed. For hard decisions the coded bits can be calculated with the smallest Hamming distance, meanwhile for soft decision the BCJR [30] decoder or the simplified logmap decoder [35] has to be applied. For hard BNC using Method I. only a single Viterbi decoder is required since it uses the rough demapped bits in the feedback loop. Finally the complexity mapping process of the hard and soft mapper is to be investigated. For hard mapping—based on the incoming bits—the constellation points can be easily determined. For the soft mappers, all constellation points must be weighted with the bit probabilities and then summed, as presented in (23). Nevertheless, for the SD-BNC decoder the attenuation factor α in the feedback-loop has to be recalculated for every iteration, but for HD-BNC α remains constant throughout the iterations. The calculation complexity comparison of the HD-BNC and SD-BNC is summarized in Table 1. A detailed computational complexity analysis of these blocks can be found in [36].

5

Simulation results

This section illustrates the performance improvement of both schemes. AWGN and frequency selective scenarios are considered in the simulation setup. IEEE 802.22 B channel model [37] is used as reference. The parameters of the IEEE 802.22 B channel model can be seen in Table 2. Please note that new channel realizations are considered for each SMT signal realization in order to model a block-stationarity behavior. Perfect channel estimation is assumed in the simulation setup, while joint effects of imperfect channel estimation due to the clipping are not considered. This is a reasonable assumption, as e.g. in

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Table 2

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Excess delay and relative amplitude for IEEE 802.22 B channel profiles

Profile B

Path 1

Path 2

Path 3

Path 4

Path 5

Path 6

Excess d. (µs)

−3

0

2

4

7

11

Rel. amp. (dB)

−6

0

−7

−22

−16

−20

the Long Term Evolution (LTE) uplink, the pilot (reference) signals are periodically inserted to the subcarriers in a time-multiplexed manner, in a so-called block-type pilot arrangement. The reference signals are generated using Zadoff-Chu sequences that imply a low fluctuation of the transmitted signal envelope and thus, negligible effect of clipping. Therefore the effects of the clipping and channel fading are not mixed together and can be separated in the receiver. A similar procedure could be applied for SMT modulated signals to overcome the problems of blending the channel effects and effects of the clipping. An additional solution for the above mentioned problem for OFDM based transmission systems is introduced in [38], with potential of being reformulated to SMT. The binary data are encoded with a code rate of 1/2, using a 4-state recursive systematic convolutional encoder with polynomials (1, 5/7)8 in octal notation. The interleaved bits are mapped according to a 16-QAM constellation with Gray mapping. From the available N = 1024 subcarriers Nc = 768 were used for data transmission. The clipping level (CR) is set to 1 dB. For the prototype filter of the SMT system, the coefficients presented in [39] are applied. The system bandwidth and overlapping factor are set to B = 8 MHz and K = 4, respectively. For decoding of the received bits in the SD-BNC the BCJR decoder is suggested, but due to arithmetic overflow issues, the log-map decoder [35] is used. The SNR is calculated using normalized bit energy as     Pout N Pb = 10 log10 , (26) SNRdB = 10 log10 N0 N0 M RNc where Pb is the bit power, N is the number of the available subcarriers and Nc is the number of subcarriers used. M is the number of bits transmitted by one subcarrier and R is the code rate. Assuming a normalized symbol duration of T , the bit energy can be expressed as Eb = Pb T = Pb . Figures 7 and 8 show the Error Vector Magnitude (EVM) of the constellation at the input of the demapper at SNR = 10 dB. EVM can be used to characterize the influence of the nonlinearity (i.e. clipping) on the signal constellation. Please note that lower EVM means a less distorted signal constellation ˆ i and Xi denote the constellation point at the output of the receiver and better BER performance. Let X and the ideal transmitter constellation points, respectively. EVM is calculated as ! ˆ i − X i |2 } E{|X EVM = 10 log10 , (27) PA where PA is the maximum power of the constellation set A. As can be seen from Figures 7 and 8, a noticeable EVM reduction with respect to conventional receivers is achieved at low and moderate CR. From the application point of view, it should be noticed that the employment of the presented iteration schemes is meaningful for the CR < 4 dB. If the CR is higher than this threshold, the effects of the clipping are negligible and the iteration schemes do provide only minor additional performance. Figure 9 presents the BER performance improvement capabilities of the HD-BNC iterative scheme. It can be seen that the performance of the conventional receiver is heavily impacted by the baseband clipping. Nevertheless, the HD-BNC and coded HD-BNC receivers are capable of improving the performance compared to the conventional case. It should be also noted that the coded HD-BNC receiver delivers higher performance gain, however requires higher computational complexity. In fact, most of the performance improvement is achieved by just three iterations. The reason is that the estimated nonlinear distortion in the feedback loop improves only slightly after the third iteration. Figure 10 presents the performance results for the SD-BNC receiver. As can be observed, the 1st iteration provides significant performance improvements and the 2nd iteration reaches an almost linear stage. Thus, we can conclude that the nonlinear effects of the investigated SMT system are efficiently alleviated.

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0 EVMiterative − EVMconventional (dB)

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Figure 8 EVM reduction of SD-BNC receiver with respect to conventional SMT receiver as a function of γ at SNR = 10 dB.

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Figure 7 EVM reduction of HD-BNC receiver with respect to conventional SMT receiver as a function of γ at SNR = 10 dB.

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Figure 9 BER results of the HD-BNC receiver for clipped SMT signals.

Figure 10 BER results of the SD-BNC receiver for clipped SMT signals.

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Eb /N0 (dB) Figure 11 BER results of the HD-BNC receiver for clipped SMT signals—Channel B.

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Eb /N0 (dB) Figure 12 BER results of the SD-BNC receiver for clipped SMT signals—Channel B.

Figures 11 and 12 present the results of the coded HD-BNC and SD-BNC receiver over frequency selective channel modeled by IEEE 802.22 B channel profile. As can be observed the BER performance

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is significantly improved using the above given iterative procedures, nevertheless, SD-BNC again shows superior performance. The main advantage of the proposed schemes is the high flexibility in terms of application. Based on the requirements of the service, the base station (in case of uplink transmission) can dynamically adjust the receiver scheme to fulfill the BER requirements and in parallel allowing power efficient operation. In case of not so challenging BER requirements the base station may pick the conventional receiver scheme. Provided that BER performance is of more importance for the given service, HD-BNC receiver scheme or SD-BNC receiver scheme could be potentially chosen. While doing so, complexity requirements of these receiver schemes should also be taken into account.

6

Conclusion

In this paper, compensation of nonlinear effects caused by baseband clipping of the transmitted SMT signal have been investigated. To cope with the BER increase due to the signal clipping, three iterative schemes applied in the receiver side have been introduced, namely HD-BNC, coded HD-BNC and SDBNC. For all iterative schemes, only the knowledge of the CR is required in the receiver. The iterative schemes show different computational complexity and performance improvement. The EVM results presented in this paper demonstrate that for low SNR the HD-BNC is not converging and provides rather limited results compared to the coded HD-BNC and SD-BNC schemes. On the other hand, for high SNR and high CR, the performance of the HD-BNC could be sufficient, provided the computational complexity is the major system requirement. To address this issue, the computational requirements of the presented schemes are also discussed in the paper. The performance improvement of the presented schemes has been evaluated in both AWGN and frequency selective channels. It has been verified that the receiver-based iterative strategies are capable of improving BER degraded by clipping and only few iterations are needed to recover the transmitted signal.

Acknowledgements The research leading to these results was partially derived from the European Community’s Seventh Framework ´ Programme (FP7) under Grant Agreement Number 248454 (QoSMOS) and partially supported by TAMOP4.2.2.C-11/1/KONV-2012-0001 Project. This work was supported by the European Union, co-financed by the European Social Fund.

References 1 Dahlman E, Parkvall S, Sk¨ old J. 4G: LTE/LTE-Advanced for Mobile Broadband. Elsevier Ltd., 2011 2 Fazel K, Kaiser S. Multi-Carrier and Spread Spectrum Systems. 2nd ed. Wiley, 2008 3 Medjahdi Y, Terre M, Le Ruyet D, et al. Performance analysis in the downlink of asynchronous OFDM/FBMC based multi-cellular networks. IEEE Trans Wirel Commun, 2011, 10: 2630–2639 4 Premnath S, Wasden D, Kasera S K, et al. Beyond OFDM: best-effort dynamic spectrum access using filterbank multicarrier. In: 4th International Conference on Communication Systems and Networks, Bangalore, 2012. 1–10 5 Baltar L G, Schaich F. Computational complexity analysis of advanced physical layers based on multicarrier modulation. In: Future Network & Mobile Summit, Warsaw, 2011. 1–8 6 Datta R, Fettweis G, Koll´ ar Z, et al. FBMC and GFDM interference cancellation schemes for flexible digital radio PHY design. In: 14th Euromicro Conference on Digital System Design, Oulu, 2011. 335–339 7 Hu S, Wu G, Li T, et al. Preamble design with ICI cancellation for channel estimation in OFDM/OQAM system. IEICE Trans Commun, 2011, E93.B: 211–214 8 Koll´ ar Z, Horv´ ath P. Physical layer considerations for cognitive radio: modulation techniques. In: IEEE 73rd Vehicular Technology Conference, Budapest, 2011. 1–5 9 Skrzypczak A, Siohan P, Javaudin J P. Power spectral density and cubic metric for the OFDM/OQAM modulation. In: IEEE International Symposium on Signal Processing and Information Technology, Vancouver, 2006. 846–850 10 Khodjet-Kesba M, Saber C, Roviras D, et al. Multicarrier interference evaluation with jointly non-linear amplification and timing errors. In: IEEE 73rd Vehicular Technology Conference, Budapest, 2011. 1–5

Koll´ ar Z, et al.

Sci China Inf Sci

February 2014 Vol. 57 022301:13

11 Li X, Cimini L J. Effects of clipping and filtering on the performance of OFDM. IEEE Commun Lett, 1998, 2: 131–133 12 Xiao Y, Bai W L, Dan L L, et al. Performance analysis of peak cancellation in OFDM systems. Sci China Inf Sci, 2012, 55: 789–794 13 Deumal M, Behravan A, Eriksson T, et al. Constrained clipping for peak reduction of multicarrier systems by tone reservation. In: IEEE 65th Vehicular Technology Conference, Dublin, 2007. 2195–2199 14 Dan L L, Xiao Y, Cheng P, et al. A low-complexity multiple signal representation scheme in downlink OFDM-CDMA. Sci China Ser F-Inf Sci, 2009, 52: 2433–2444 15 Chen H, Haimovich A H. Iterative estimation and cancellation of clipping noise for OFDM signals. IEEE Commun Lett, 2003, 7: 305–307 16 Koll´ ar Z, Varga L, Czimer K. Clipping-based iterative PAPR-reduction techniques for FBMC. In: OFDM-Workshop 2012, Esssen, 2012. 139–145 17 Yuen C H, Amini P, Farhang-Boroujeny B. Single carrier frequency division multiple access (SC-FDMA) for filter bank multicarrier communication systems. In: Proceedings of the IEEE 5th International Conference on Cognitive Radio Oriented Wireless Networks & Communications, Cannes, 2010. 1–5 18 Gazda J, Drot´ ar P, Kocur D, et al. Joint evaluation of nonlinear distortion effects and signal metrics in OFDM based transmission systems. Acta Electrotech Inf, 2009, 9: 55–60 19 Koll´ ar Z, Horv´ ath P. Modulation schemes for cognitive radio in white spaces. Radioengineering, 2010, 19: 511–517 20 Viholainen A, Ihalainen T, Stitz H T, et al. Prototype filter design for filter bank based multicarrier transmission. In: Proceedings of the 17th European Signal Processing Conference, Glasgow, 2009. 1359–1363 21 Amini P, Farhang-Boroujeny B. Isotropic filter design for MIMO filter bank multicarrier communications. In: IEEE Sensor Array and Multichannel Signal Processing Workshop, Kibbutz, 2010. 89–92 22 Rowe E. Memoryless non-linearities with Gaussian inputs: elementary results. Bell Syst Tech J, 1982, 61: 1519–1525 23 Abramowitz M, Stegun I A. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. 9th printing. New York: Dover, 1972 24 Minkoff J. The role of am-to-pm conversion in memoryless nonlinear systems. IEEE Trans Commun, 1985, 33: 139–144 25 Blachman N M. Detectors, bandpass nonlinearities, and their optimization: inversion of the Chebyshev transform. IEEE Trans Inform Theory, 1971, 17: 398–404 26 Armstrong J. Peak-to-average power reduction for OFDM by repeated clipping and frequency domain filtering. Electron Lett, 2002, 38: 246–247 27 Ihalainen T, Stitz H T, Renfors M. Efficient per-carrier channel equalizer for filter bank based multicarrier systems. In: IEEE International Symposium on Circuits and Systems, Kobe, 2005. 3175–3178 28 Koll´ ar Z, P´ eceli G, Horv´ ath P. Iterative decision feedback equalization for FBMC systems. In: Proceedings of IEEE First International Conference on Advances in Cognitive Radio, Budapest, 2011 29 Baltar L G, Nossek J. Multicarrier systems: a comparison between filter bank based and cyclic prefix based OFDM. In: OFDM-Workshop 2012, Essen, 2012. 6–10 30 Bahl L R, Cook J, Jelinek F, et al. Optimal decoding of linear codes for minimizing symbol error rate. IEEE Trans Inform Theory, 1974, 20: 284–287 31 Koll´ ar Z, Gazda J, Horv´ ath P, et al. Iterative compensation of baseband clipping in SMT transceivers. In: Radioelektronika 2012, Brno, 2012. 205–208 32 ten Brink S, Speidel J, Yan R H. Iterative demapping and decoding for multilevel modulation. In: Global Telecommunications Conference, Sydney, 1998. 579–584 33 D´ ejardin R, Colas M, Gelle G. On the iterative mitigation of clipping noise for COFDM transmissions. Eur Trans Telecommun, 2008, 19: 791–800 34 ten Brink S. Designing iterative decoding schemes with the extrinsic information transfer chart. AEU-Int J Electron Commun, 2000, 54: 389–398 35 Bauch G. Turbo-equalization and transmit antenna diversity with space-time-codes in mobile communication (in German). VDI Verlag GmbH, 2001 36 All´ en M, Levanen T, Marttila J, et al. Iterative signal processing for mitigation of analog-to-digital converter clipping distortion in multiband OFDMA receivers. J Elect Computer Eng, 2012, 2012: 1–16 37 Sofer E, Chouinard G. WRAN channel modeling. IEEE 802.22-05/0055r7, 2005 38 Xiao Y, Li S, Lei X, et al. Clipping noise mitigation for channel estimation in OFDM systems. IEEE Commun Lett, 2006, 10: 474–476 39 Bellanger M. Physical layer for future broadband radio systems. In: Proceedings of the IEEE Radio and Wireless Symposium, New Orleans, 2010. 436–439