OFDM and FBMC Transmission Techniques - A bile High Performance Proposal for Broadband Power Line...

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OFDM and FBMC Transmission Techniques: a Compatible High Performance Proposal for Broadband Power Line Communications Maurice Bellanger Markku Renfors, Tero Ihalainen Carlos A.F.da Rocha CNAM Tampere University of Technology GPqCom/EEL/UFSC 292 rue Saint-Martin, 75141 Paris P.O. Box 553, FI-33101, Tampere 88040-900, Florianopolis-SC FRANCE FILAND BRAZIL [email protected] {markku.renfors , tero.j.ihalainen}@tut.fi [email protected] Abstract — A filter bank multicarrier (FBMC) system having a high level of compatibility with the IEEE P1901 OFDM scheme is proposed. In order to reach the level of robustness, selectivity and performance required by the broadband power line, the approach is based on near perfect reconstruction (NPR) filters combined with OQAM modulation. A key feature of the approach is the fractionally-spaced sub-channel equalizer, which is able to compensate the channel distortions and cope with residual timing offsets. The system initialization procedure and the results of OFDM are exploited by FBMC and an efficient and accurate technique is described for the derivation of the sub- channel equalizer coefficients from the OFDM frequency domain equalizer coefficients. Then, the impact of the filter impulse response on the efficiency in packet transmission is minimized. Finally, the impact of the sub-channel spacing is investigated and, in a comparison on similar basis, it appears that the proposed FBMC system can reach 228 Mbit/s in maximum bit rate, versus 197 Mbit/s for OFDM, while providing a higher level of tone protection and robustness to jammers. Keywords – Broadband PLC; compatibility; FBMC; IEEE P1901; OFDM; OQAM; equalizer I. INTRODUCTION When an OFDM (orthogonal frequency division multiplexing) system and an FBMC (filter bank multicarrier) system are both proposed for the exploitation of a transmission medium, compatibility is an important issue, particularly at initialization, because the software defined receiver has to decide reliably which scheme to implement. If the initialization procedure is common to the systems involved, the decision is much simplified, and it can be the case for OFDM and FBMC since they share a common core, namely the FFT. The above situation has arisen in the standardization group IEEE P1901, which has approved an FBMC proposal, besides an OFDM proposal and has to consider the compatibility and interoperability between them. At the beginning of a packet, the OFDM receiver has to synchronize and measure the transmission channel, in order to determine the coefficients of the frequency domain equalizers. Generally, several multicarrier symbols, called pilot symbols and grouped in a preamble, are reserved for this task and the FFT is instrumental in the process. The FBMC receiver also can rely on its FFT, subject to some constraints. First, due to the impulse response of the filter banks, a transition is needed between the pilot symbols and the data symbols. Then, while the OFDM subcarrier equalizer has a single coefficient, the FBMC sub-channel equalizer may need several coefficients in difficult environments. Moreover, it is important to have the possibility to exploit the FFT in the initialization phase without reconfiguring the terminal. The objective of this paper is to propose a high performance FBMC scheme for power line communications (PLC), with maximum exploitation of the OFDM procedures and results, in order to push compatibility as far as possible. It is based on the so-called NPR (near perfect reconstruction) scheme, particularly appropriate for PLC, because it leads to high stopband attenuation, it is robust to residual channel impairments and narrow band jammers, it provides a high level of protection of the in-band tones and it yields high bit rates. The paper is organized as follows. In section 2, the FBMC technique with NPR prototype filter and offset quadrature amplitude modulation (OQAM) is briefly reviewed. Section 3 is dedicated to the fractionally-spaced equalizer and the derivation of the coefficients from the OFDM equalizer coefficients. In section 4, a specific technique called memory preloading is introduced, so that the same filter bank structure is used for pilot and data symbols, and the efficiency in packet transmission is investigated. Section 5 is dedicated to the comparison and it appears that the FBMC scheme outperforms the OFDM proposal for IEEE P1901 in terms of maximum bit rate, while providing a high level of compatibility at initialization. To conclude, the main points are summarized and some complexity aspects are briefly discussed. II. FBMC WITH OQAM AND NPR FILTERS The FBMC and OFDM multicarrier techniques are both based on the FFT. The difference is that the FFT is complemented by a set of digital filters called polyphase network (PPN) in the FBMC approach [1], while, in the OFDM approach, a cyclic prefix is inserted after the FFT [2]. As a consequence, the signal streaming is different in the two systems during data payload transmission. However, in the initialization phase at the beginning of a packet, a number of the functions performed by OFDM can be carried over to This work was supported by the European Commission under the PHYDYAS Project (FP7-ICT-2007-1-211887) (www.ict-phydyas.org ) and partially supported by the CAPES-COFECUB Project (544/07).

Transcript of OFDM and FBMC Transmission Techniques - A bile High Performance Proposal for Broadband Power Line...

Page 1: OFDM and FBMC Transmission Techniques - A bile High Performance Proposal for Broadband Power Line Communications - Belanger

OFDM and FBMC Transmission Techniques: a Compatible High Performance Proposal for

Broadband Power Line Communications Maurice Bellanger Markku Renfors, Tero Ihalainen Carlos A.F.da Rocha CNAM Tampere University of Technology GPqCom/EEL/UFSC 292 rue Saint-Martin, 75141 Paris P.O. Box 553, FI-33101, Tampere 88040-900, Florianopolis-SC FRANCE FILAND BRAZIL [email protected] {markku.renfors, tero.j.ihalainen}@tut.fi [email protected]

Abstract — A filter bank multicarrier (FBMC) system having a high level of compatibility with the IEEE P1901 OFDM scheme is proposed. In order to reach the level of robustness, selectivity and performance required by the broadband power line, the approach is based on near perfect reconstruction (NPR) filters combined with OQAM modulation. A key feature of the approach is the fractionally-spaced sub-channel equalizer, which is able to compensate the channel distortions and cope with residual timing offsets. The system initialization procedure and the results of OFDM are exploited by FBMC and an efficient and accurate technique is described for the derivation of the sub-channel equalizer coefficients from the OFDM frequency domain equalizer coefficients. Then, the impact of the filter impulse response on the efficiency in packet transmission is minimized. Finally, the impact of the sub-channel spacing is investigated and, in a comparison on similar basis, it appears that the proposed FBMC system can reach 228 Mbit/s in maximum bit rate, versus 197 Mbit/s for OFDM, while providing a higher level of tone protection and robustness to jammers.

Keywords – Broadband PLC; compatibility; FBMC; IEEE P1901; OFDM; OQAM; equalizer

I. INTRODUCTION

When an OFDM (orthogonal frequency division multiplexing) system and an FBMC (filter bank multicarrier) system are both proposed for the exploitation of a transmission medium, compatibility is an important issue, particularly at initialization, because the software defined receiver has to decide reliably which scheme to implement. If the initialization procedure is common to the systems involved, the decision is much simplified, and it can be the case for OFDM and FBMC since they share a common core, namely the FFT. The above situation has arisen in the standardization group IEEE P1901, which has approved an FBMC proposal, besides an OFDM proposal and has to consider the compatibility and interoperability between them.

At the beginning of a packet, the OFDM receiver has to synchronize and measure the transmission channel, in order to determine the coefficients of the frequency domain equalizers. Generally, several multicarrier symbols, called pilot symbols and grouped in a preamble, are reserved for this task and the FFT is instrumental in the process. The FBMC receiver also

can rely on its FFT, subject to some constraints. First, due to the impulse response of the filter banks, a transition is needed between the pilot symbols and the data symbols. Then, while the OFDM subcarrier equalizer has a single coefficient, the FBMC sub-channel equalizer may need several coefficients in difficult environments. Moreover, it is important to have the possibility to exploit the FFT in the initialization phase without reconfiguring the terminal.

The objective of this paper is to propose a high performance FBMC scheme for power line communications (PLC), with maximum exploitation of the OFDM procedures and results, in order to push compatibility as far as possible. It is based on the so-called NPR (near perfect reconstruction) scheme, particularly appropriate for PLC, because it leads to high stopband attenuation, it is robust to residual channel impairments and narrow band jammers, it provides a high level of protection of the in-band tones and it yields high bit rates. The paper is organized as follows. In section 2, the FBMC technique with NPR prototype filter and offset quadrature amplitude modulation (OQAM) is briefly reviewed. Section 3 is dedicated to the fractionally-spaced equalizer and the derivation of the coefficients from the OFDM equalizer coefficients. In section 4, a specific technique called memory preloading is introduced, so that the same filter bank structure is used for pilot and data symbols, and the efficiency in packet transmission is investigated. Section 5 is dedicated to the comparison and it appears that the FBMC scheme outperforms the OFDM proposal for IEEE P1901 in terms of maximum bit rate, while providing a high level of compatibility at initialization. To conclude, the main points are summarized and some complexity aspects are briefly discussed.

II. FBMC WITH OQAM AND NPR FILTERS

The FBMC and OFDM multicarrier techniques are both based on the FFT. The difference is that the FFT is complemented by a set of digital filters called polyphase network (PPN) in the FBMC approach [1], while, in the OFDM approach, a cyclic prefix is inserted after the FFT [2]. As a consequence, the signal streaming is different in the two systems during data payload transmission. However, in the initialization phase at the beginning of a packet, a number of the functions performed by OFDM can be carried over to

This work was supported by the European Commission under the PHYDYAS Project (FP7-ICT-2007-1-211887) (www.ict-phydyas.org) and partially supported by the CAPES-COFECUB Project (544/07).

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FBMC and a high level of compatibility can be achieved, if the FBMC scheme is appropriately designed.

The block diagram of an FBMC system is shown in Fig.1, considering that the signal generated by the transmitter is real, which is appropriate for baseband transmission as in power line communications. The filter banks in transmitter and receiver use the conventional PPN-FFT scheme. The number of sub-channels in the system is M and, since the generated signal x(n) is real, the size of the IFFT in the transmitter, and of the FFT in the receiver, is 2M. For maximum efficiency, the filter banks are combined with OQAM modulation, according to which the rate of the filter banks is fΔ2 , twice the sub-channel spacing [3]. As a consequence, the sub-channel signals at the FFT output in the receiver are oversampled and the sub-channel equalizer is fractionally-spaced. This is a crucial property in real operation because it implies that residual timing offsets can be corrected, as well as channel distortions. At the equalizer output, the recovered signal in sub-channel with index “i”, di((m-Δ)M), is delayed by Δ multicarrier symbols, where Δ is related to the filtering characteristics as explained later on.

Fig. 1. Block diagram of the FBMC system.

The broadband power line is a challenging transmission medium and robustness to jammers and severe channel perturbations is a necessary feature, and it is brought by the filter banks in the system. Equally important is the fact that the NPR design approach yields the steep frequency transition which minimizes the bandwidth loss related to the protection of the in-band tones.

A filter bank is obtained by frequency shifts of a low-pass filter called the prototype filter. The frequency shifts are realized by the FFT and the coefficients of the prototype filter are used in the PPN. A simple approach to design a family of prototype filters is the frequency sampling technique. The generic frequency domain coefficients for the first members of the family are given in Table 1 [4]. The parameter K is called the overlapping factor, because it is the number of symbols which overlap in the time domain, and it is the ratio between the number of coefficients L and the number of filters in the bank. If the signal generated by the transmitter filter bank is real, the number of sub-channels is M and the number of filters in the bank is N=2M. Then, K=L/2M. Also given in Table 1 is the background noise power σ2 which, in fact, is the sum of the intersymbol interference and the residual intersub-channel interference due to the non-orthogonality of the sub-channels in the NPR scheme. This noise power level, which is also a signal-to-noise ratio, is controlled by the out-of-band attenuation of the prototype filter. Note that a perfect reconstruction (PR) approach has no residual interference, in

theory, when receiver and transmitter are connected back-to-back [5]. However, in the presence of the channel, the perfect reconstruction property is lost, unless a global channel equalization technique is implemented, which is complex and takes a long time to initialize at the beginning of a packet.

TABLE 1 - FREQUENCY DOMAIN PROTOTYPE FILTER COEFFICIENTS.

K H0 H1 H2 H3 σ2 (dB)

2 1 0.707 - - -35

3 1 0.911438 0.411438 - -46

4 1 0.971960 0.707 0.235147 -65

The time domain coefficients are derived from Table 1 through the expression

( )1

1

0

1 2 1 cos 2 1 1

0

Kk

i kk

kih H , i LKM

h

π−

=

⎛ ⎞= + − ≤ ≤ −⎜ ⎟⎝ ⎠

=

∑ (1)

They constitute the impulse response of the prototype filter for the parameters K=4, 2M=256 and L=1024.

The frequency responses of the prototype filters are shown in Fig. 2, where the frequency unit is the sub-channel spacing fΔ . It appears that for K=4 the attenuation in the stopband exceeds 40 dB for frequencies beyond fΔ . Therefore, the transition band between the nominal sub-channel edge and the 40 dB attenuation limit is less than

fBtr Δ−= )5.01( . (2)

Fig.2. Frequency responses of the prototype filter for K=2,3,4.

The frequency responses in Fig. 2 cross the zero axis at the integer multiples of fΔ , just like OFDM. This property is exploited in section 4 below, in the memory preloading technique, for the processing of preamble pilot symbols.

III. DESIGN OF THE SUB-CHANNEL EQUALIZER

From the measurements of the channel, OFDM systems have developed techniques to elaborate coefficients EQ(i) which are complex numbers representing frequency domain

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samples of the transmission channel equalizer, the sampling interval being the subcarrier spacing fΔ [2]. In FBMC systems, if more than one coefficient is needed, the increase to P of the number of time domain coefficients translates into an increased sample rate in the frequency domain by the factor P-1. Now, if the sizes of the FFT in OFDM and FBMC are the same, P-2 samples are missing between 2 known samples and these missing samples have to be derived from the set EQ(i) through interpolation [6]. Then, a frequency-to-time conversion provides the coefficients of the sub-channel fractionally-spaced (FS) equalizer. The design chain is sketched in Fig. 3.

Fig. 3. Sub-channel equalizer design chain.

The quality of the interpolation is crucial for the equalizer performance and the simple linear approach is insufficient for severely distorted channels. In particular, linear interpolation of the real and imaginary parts of the complex samples leads to large errors when the phase of the channel changes significantly between samples while the amplitude remains nearly constant. This situation occurs, for example, when deep fades due to reflections are present in the channel frequency response and zeros of the Z-transfer function become near the unit circle. In this case, amplitude and phase should preferably be interpolated separately and this is approximately achieved by taking the geometric mean between samples. Now, the procedure for the interpolation and the calculation of the coefficients of a P=3 tap equalizer is described. On the frequency axis, two values, namely X1 and X2, have to be calculated around EQ(i), using the adjacent samples EQ(i-1) and EQ(i+1). According to the principle of geometric interpolation of the transfer functions, they are obtained by

( ) ( ) ( )( ) 2/11 11 −−= iEQiEQiEQX (3)

( ) ( ) ( )( ) 2/12 1 iEQiEQiEQX += (4)

Similar equations can be found for any fraction of interpolation. These equations are valid for any absolute phase value, and phase differences up to ±π. For implementation, an efficient approach consists of extracting the amplitude and the phase, interpolating the phase linearly and carrying out the root extraction on the amplitude.

Next, the 3 equalizer coefficients can be derived with the help of the classical frequency sampling technique. For 3-tap FIR equalization, we use the frequency point EQ(i), and the intermediate frequency points X1 and X2.

At the receiver filter bank output, the sampling frequency for each sub-channel is fΔ2 . Considering uniform sampling,

the frequency spacing between EQ(i) and the intermediate points X1 and X2 is fΔ /2, thus, we have 2 fΔ /( fΔ /2)=4 frequency points per sub-channel. Therefore, one value is unknown, which is denoted by A. In fact, A can be found by imposing a constraint on the equalizer coefficients calculated using the 4th-order inverse Fourier transform of the ensemble {A, X1, EQ(i), X2}. Considering the ith sub-channel, the set of coefficients obtained after the IFFT is { }iiii qqqq 3210 ,,, . The central coefficient q0i is surrounded by the coefficients

ii qq 31 =− and q1i, due to the IFFT periodicity property. As we want to design an equalizer with 3 taps only, it is necessary to null the coefficient 2iq , thus we can determine the unknown A by the relation

( )( )2141

2 XiEQXAq i −+−= . (5)

Solving for the other coefficients, we get

( )( ) ( )( )122141

1 2 XXjXiEQXq i −++−±=− (6)

( )2121

0 XXq i += (7)

( )( ) ( )( )122141

1 2 XXjXiEQXqi −−+−±= , (8)

where the signs - and + correspond to the even and odd sub-channels, respectively [7]. The design for sub-channel equalizers with more coefficients can be done following the same procedure.

IV. PACKET TRANSMISSION WITH FBMC In packet transmission, the impulse response of the

prototype filter imposes transition phases at the beginning and at the end of the packet. Generally, the packet begins with a preamble consisting of one or more known symbols and, with OFDM, the preamble signal is generated by the IFFT in the transmitter and processed by the FFT in the receiver. With FBMC, it is possible to do exactly the same, provided the PPN is neutralized in transmitter and receiver and this is realized by the memory preloading technique.

The structure of the filter bank in the transmitter is shown in Fig. 4, for K=4. The PPN contains 4 memories in which the block of signal samples issued from the IFFT propagates. The system delay is related to the time this propagation takes. The output signal x(n) is obtained by a weighted summation of the memory contents.

The PPN consists of a set of 2M digital filters whose K coefficients are derived from the prototype filter impulse response through interleaving. In fact, the prototype filter impulse response is decomposed into 2M interleaved sequences of K coefficients each. A property of these sequences, due to the zeros of the frequency response as mentioned in section 2, is that the sum of the K coefficients in each interleaved sequence is unity. Thus, to neutralize the PPN, it is sufficient, instead of letting the propagation happen as in Fig. 4, to preload the memories of the PPN with the set of samples produced by the IFFT in the transmitter and with the set of received samples to be applied to the FFT in the receiver. With this, the transition phases are cancelled for the preamble.

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Fig. 4. Structure of the transmitter filter bank.

As concerns the data, however, the transition between preamble and data must be kept if the highest level of performance is sought from the very beginning of the packet on. An illustration is given in Fig. 5, where the preamble consists of 2 pilot symbols. At the end of the preamble, in the memories of the PPN, the data signals must replace the preamble signals. As a consequence, in order to transmit Nsymb data symbols, Nsymb+K-1 symbols are required. In other words, the length of the packet is increased by K-1 symbols. In practice, this overhead of K-1 symbols can be significantly reduced, considering the burst shown in Fig. 6 for K=4. Cutting half a symbol length on each side reduces the overhead from K-1=3 to 2 symbols, with a very limited impact on transmission performance. A more aggressive strategy, such

Fig. 5. Structure of the packet and preamble-data transition.

as cutting one symbol length on each side, reduces the overhead from K-1=3 to 1 symbol, while it introduces some temporary spectral leakage and a corresponding level of temporary interference with the neighboring sub-channels. It implies that the bit loading of the sub-channels in the first or the first 2 symbols must be kept below the full capacity and reduced by a few bits. An in-depth analysis of the impact of this truncation as well as simple mitigation techniques are provided in [7]. Here, we shortly review the core principles and characteristics.

0 500 1000 1500 2000 2500 3000 3500 4000 4500

-0.1

-0.05

0

0.05

0.1

(a)

0 500 1000 1500 2000 2500 3000 3500 4000 4500-1

-0.5

0

0.5

1

1.5

(b)

0 500 1000 1500 2000 2500 3000 3500 4000 4500

-0.1

-0.05

0

0.05

0.1

Sample index

(c)

y(n)

yt(n)

Lz

Lw Lw

Lz

Fig. 6. (a) Ideal burst , (b) weighting window , and

(c) truncated burst .

In the following, we analyze the impact of the pre-loading induced burst truncation, both on the symbol detection and spectral leakage performance, using a generalized weighting window model, which is illustrated in Fig. 6. Specifically, we consider a window with raised cosine (RC) shaped transitions between zero and unity weights, which can be expressed as

where boundaries , for , are defined as , , , , and

, respectively. Now, the sample sequence of the truncated burst writes . The effective reduction in the length of the burst is controlled by , the parameter defining the number of zero-weights in the window

, whereas the RC weights are used to smoothen the sharp transients introduced by the cut-off operation. The sharpness of the RC-shaped transitions (i.e. the rapidity of the change of window coefficients from 0 to 1 (pre-tail) and from 1 to 0 (post-tail)) can be adjusted by controlling the value of . Further, the length of the ideal burst (without truncation) in samples , where and denote the length of the tails and the body of the burst (carrying OQAM symbols), respectively. The effect of the truncation on the detection performance of the affected burst tail symbols is evaluated in terms of the normalized mean-squared error (MSE) expressed as

, where and denote the real-valued symbol transmitted on the

subcarrier on the OQAM subsymbol interval and the corresponding estimate at the receiver, respectively, whereas

PPN memories

data

IFFT

Σ x(n)

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stands for the average symbol power. The spectral regrowth due to burst shortening is evaluated by estimating the spectral leakage over the non-active subcarriers outsize the active band.

The cost functions and show partly contradicting behaviors over the weighting window parameters and , i.e., although both are dominantly influenced by the choice of

(showing increased level of distortion with higher values of ), there is in general an increasing MSE trend and a

decreasing out-of-band leakage trend with increasing number of RC transitions samples. Therefore, a practical optimization problem of interest is to search for such a combination of a maximum value of , , and a minimum value of ,

, that simultaneously maximizes the spectral efficiency of the FBMC burst transmission and minimizes the required processing under constraints on the maximum MSE and leakage defined by thresholds and , respectively:

Table 2 shows the results of optimization , where , for various threshold combinations

, during the first OQAM subsymbol, when out-of-band leakage is measured at subcarrier i, two subcarrier spacings from the active band.

TABLE 2 – OPTIMIZED BURST TRUNCATION PARAMETERS

, AND . SEARCH GRID

AND .

We can see that the burst tails can be truncated to less than M samples, while the MSE and spectral leakage values remain below dB and dB, respectively. Thus leaving 2M samples (one OQAM symbol) as the transition gap between bursts seems to be a natural choice.

V. A HIGH PERFORMANCE FBMC SCHEME FOR IEEE P1901

In the context of the standardization activities of the group IEEE P1901, it is proposed to compare an FBMC approach as described above for broadband PLC and the OFDM scheme which has been approved.

A specificity of broadband PLC is that a number of tones have to be protected in the used frequency band and masks have been issued, which define the corresponding stop-bands

and their attenuations, for various situations [8]. Here, the Home Plug AV mask is considered, which contains 8 stop-bands, and the attenuation objective is set to 40dB. In the FBMC transmission system, the sub-channels which overlap with the stop-bands must be left idle and the number of sub-channels which are actually used is smaller than the maximum number of sub-channels. In fact, for every specified stopband several factors contribute to the loss in bandwidth

- the width of the stopband itself, - the transition band of the prototype filter, - the positioning of the stopband with respect to the

transmission frequency grid. The latter factor is dependent on the sub-channel spacing, as illustrated in Fig.7, where the stopband width is less than fΔ .

Fig. 7. FBMC frequency pattern and stopband.

Sub-channels with indices “i” and “i+1” are impacted, but,

if the stopband is moved to the left or right on the frequency axis, a third sub-channel is affected. Therefore, in system efficiency evaluation, it is necessary to reserve a guard band which takes into account the filter transition band Btr defined in section 2 and reflects the stopband positioning. As shown in Fig.7, for each edge of the stopband, the guard band Bg is such that

fBf g Δ≤≤Δ 5.15.0 . (9)

In a global evaluation, the average is retained, that is gB f≈ Δ , which, taking into account 8 stopbands and the 2

edges of the transmission band, leads to a total loss

18gtotalB f= Δ . (10)

Through this guard band, the sub-channel spacing impacts the maximum bit rate. Considering a transmission band of 26 MHz, the aggregated width of the stop bands of 1.9 MHz, 10 bits per symbol, the maximum bit rate is given by

ffBR FBMC Δ−=×Δ−−= 18024110)189.116( . (11)

For compatibility, it is important that OFDM and FBMC have the same sampling rate, i.e. 75 MHz, and the same frequency grid. Therefore, the number of sub-channels in FBMC must be either equal to the number of carriers in OFDM, i.e. 3072, or a sub-multiple. The bit rates are shown in Fig. 8, for several such FBMC sizes. In the OFDM system, out of the 1065 available subcarriers, 917 are actually used and, considering

- 2 - 1 . 5 - 1 - 0 . 5 0 0 . 5 1 1 . 5 20

0 . 5

1

1 . 5

s to p -b a n d

s u b - c h a n n e l " i - 1 "

a m p l i t u d e

f r e q u e n c y ( u n i t = s u b - c h a n n e l s p a c i n g )

s . c ." i + 2 "

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the minimum guard time 5.56 µs and 10 bits per QAM symbol per sub-carrier, the maximum bit rate is

Fig. 8. Maximum bit rates for FBMC and OFDM.

917 10 / (5.56 3072 / 75) 197 /OFDMBR Mbit s= × + = . (12)

Now, in the decision for the FBMC size, the complexity issue must be taken into account. In order to keep the complexity similar to OFDM, while maintaining a high bit rate, the value 1024 is chosen. Then, the ratio 3 of the FFT sizes allows for a common FFT core, since the 3072-FFT can be implemented with 3 consecutive 1024-FFT’s. The system parameters are summarized in Table 3 and the gain in bit rate brought by the filter bank approach presented exceeds 15%. It must be pointed out that this is a rough estimation which has to be refined for each specific tone mask. In packet transmission, it is necessary to take into account the overhead due to the filter impulse response, which can be made very small (section 4).

TABLE 3. SYSTEM PARAMETERS.

It is interesting to figure out where the gain of the FBMC approach comes from. If there were no cyclic prefix in OFDM, the bit rate would be 224 Mbit/s. Then, the 31 Mbit/s gained by FBMC come from the absence of cyclic prefix, 27 Mbit/s, and a smaller guard band loss, 4 Mbit/s. It is worth emphasizing that a simple way to increase the maximum bit rate consists of exploiting the frequency band above 28 MHz, up to half the sampling frequency, i.e. 37.5 MHz. In the contexts where full use of this extension is possible, it would add 129 active sub-channels and boost the bit rate to 322 Mbit/s.

Regarding the number of bits per symbol per sub-channel, in QAM and in OQAM, the transmission of 10 bits with 10-7 error rate requires a signal-to-noise ratio of about 40 dB. As shown in Table 1, the background noise of FBMC with K=3,4 is compatible with this objective, with a large margin for K=4.

The initialization of OFDM can be used for FBMC. Note that, for equalization, the block diagram of Fig. 3 can be simplified with the parameters of Table 3, because interpolation is not needed if a sub-channel equalizer with 5 coefficients is used, which leads to high performance even in the presence of very distorted transmission channels. Of course, if only 3 coefficients are needed, they can be computed with the help of least squares.

VI. CONCLUSION

Filter bank multicarrier techniques are particularly well suited for broadband power line communications because of their intrinsic properties. They offer a high level of protection for the tones and they are robust to jammers. They make full exploitation of the time and the channel bandwidth. Thanks to the high performance fractionally-spaced sub-channel equalizer they are able to cope with residual misalignments and severe channel impairments. The streaming of the signals and data is regular, since there is no cyclic prefix.

Since OFDM and FBMC are multicarrier techniques, a high degree of compatibility can be obtained if the frequency pattern is the same for both approaches, particularly at initialization. They can have a common core, the FFT processor, and software defined transmitters and receivers can be efficiently implemented.

The main counterpart for the gains in maximum bit rate and robustness brought by the FBMC scheme presented is the increased computational complexity, essentially in the receiver where the filter bank is not critically sampled. In particular, the speed of the FFT, which is the major contributor to the arithmetic complexity, is doubled with respect to OFDM. However, this has to be put in perspective and appreciated with all the functionalities of the receiver, some of which have intrinsic high complexity, such as Viterbi decoders and error correction codes.

REFERENCES

[1] G. Bonnerot, M. Coudreuse and M. Bellanger, “Digital processing techniques in the 60 channel transmultiplexer”, IEEE Trans. on Communications., vol. 26, n°5, May 1978, pp. 698-706.

[2] M. Morelli, C.J. Kuo and M-O Pun, “Synchronization techniques for orthogonal frequency division multiple access (OFDMA): a tutorial review”, Proceedings of the IEEE, vol. 95, n°7, July 2007, pp. 1394-1427.

[3] P. Siohan, C. Siclet and N. Lacaille, ”Analysis and design of OFDM/OQAM systems based on filter bank theory”, IEEE Trans. on Signal Processing, vol. 48, n°11, May 2002, pp. 1170-1183.

[4] K.W. Martin, ”Small sidelobe filter design for multitone data-communication applications” IEEE Trans. on Circuits and Systems, CAS-II, vol. 45, August 1998, pp. 1155-1161.

[5] K. Izumi, D. Umehara and S. Denno,”Performance evaluation of wavelet OFDM using ASCET”, Proceedings of the conference ISPLC’07, Pisa, Italy, 2007, pp. 246-251.

[6] T. Ihalainen, T. Hidalgo Stitz, M. Rinne and M. Renfors, ”Channel equalization in filter bank based multicarrier modulation for wireless communications”, EURASIP Journal on Advances in Signal Processing, vol. 2007, article ID 49389, 18 pages, 2007.

[7] Documents D2.1 and D3.1, website www.ict-phydyas.org, July 2008.

[8] IEEE P1901 working group website: http://grouper.ieee.org/groups/1901/

FFT size

sampl.

freq. (MHz)

channel

bandw. (MHz)

s.c.

spac. (kHz)

max. nb.of

s.c.

max.

bit rate (Mbit/s)

OFDM 3072 75 2-28 24.4 1065 197

FBMC 1024 75 2-28 73.2 355 228

0 50 100 150 200 250 300180

190

200

210

220

230

240

250Bit rate

Mbit/s

sub-channel spacing - kHz

FBMC-3072

FBMC-1024

FBMC-512

OFDM-3072 (CP=5.56)

OFDM-3072 (CP=7.56)