 Research
 Open Access
Link performance model for filter bank based multicarrier systems
 Dmitry Petrov†^{1}Email author,
 Alexandra Oborina†^{2},
 Lorenza Giupponi^{2} and
 Tobias Hidalgo Stitz^{1}
https://doi.org/10.1186/168761802014169
© Petrov et al.; licensee Springer. 2014
 Received: 31 December 2013
 Accepted: 7 November 2014
 Published: 27 November 2014
Abstract
This paper presents a complete link level abstraction model for link quality estimation on the system level of filter bank multicarrier (FBMC)based networks. The application of mean mutual information per coded bit (MMIB) approach is validated for the FBMC systems. The considered quality measure of the resource element for the FBMC transmission is the received signaltonoiseplusdistortion ratio (SNDR). Simulation results of the proposed link abstraction model show that the proposed approach is capable of estimating the block error rate (BLER) accurately, even when the signal is propagated through the channels with deep and frequent fades, as it is the case for the 3GPP Hilly Terrain (3GPPHT) and Enhanced Typical Urban (ETU) models. The FBMCrelated results of link level simulations are compared with cyclic prefix orthogonal frequency division multiplexing (CPOFDM) analogs. Simulation results are also validated through the comparison to reference publicly available results. Finally, the steps of link level abstraction algorithm for FBMC are formulated and its application for system level simulation of a professional mobile radio (PMR) network is discussed.
Keywords
 FBMC
 SNDR
 Effective SNDR mapping
 Link performance
 PMR
Introduction
Orthogonal frequency division multiplexing (OFDM) is the dominant high data rate telecommunications physical layer (PHY) technology used by, among others, IEEE 802.11a/g (WiFi)[1], IEEE 802.16 (WiMAX)[2, 3], and 3GPP Long Term Evolution (LTE)[4]. Widespread adoption of OFDM is motivated by factors like efficient signal processing based on the fast Fourier transform (FFT), robustness in frequency selective channels, simple equalization, etc. However, OFDM might not be an optimal solution in future wireless networks due to its inherent limitations.
One of the objectives of future wireless communication systems is to utilize fragmented spectrum efficiently. Currently, professional mobile radio (PMR) networks occupy a number of narrow frequency bands (mainly allocated in the 410 to 430 MHz band in the European Union) allocated to public service and safety professionals according to the TETRA[5] and Tetrapol[6] standards. However, it would be greatly beneficial to deploy broadband data communication services within the spectrum currently devoted to the PMR network[7], making use of the advantages of cognitive radio. In order to utilize the spectrum efficiently, the multicarrier (MC) transmission scheme should be capable of identifying and exploiting unused frequency gaps, coexisting with other users or services occupying the spectrum around these gaps. Transmission of signals using such MC modulation scheme should produce only negligible interference to already operating wireless communication systems. OFDM has a poor spectral localization in frequency (13dB attenuation at the first side lobe) due to the rectangular impulse used for modulation. It results in a potentially high intercarrier interference (ICI) in nonsynchronized transmission and strong outofband emission. Hence, OFDM is not capable of fulfilling the strict interference requirements for coexistence with the PMR network, unless a lot of subcarriers are used as a guard band, which significantly reduces the OFDM spectral efficiency advantage. There are several proposals to address OFDM’s poor spectral containment, including weighted FFT, guard frequencies, application of additional windowing, etc.[8–10], trading off signal processing complexity, and loss in spectral efficiency.
Additionally to the benefits provided by FMBC, we should also mention the drawbacks of FBMC compared to OFDM. The absence of the cyclic prefix (CP) in the FBMC increases spectral efficiency but also reduces robustness to channel fades in multipath propagation scenarios, where symbol distortion, caused by ‘only real’ orthogonality of the FB basis functions, appears. This problem can be solved by utilization of advanced but more complicated channel estimation and equalization for FBMC on subcarrier level. The PHYDYAS project demonstrated FBMC performance improvements over OFDM in a WiMAXlike communication system, mainly on the link level[18, 19]. In order to assess the advantages of FBMC technology on the fragmented spectrum even further, it is necessary to evaluate its performance in PMR scenarios and compare it to an OFDM reference system on both, the link and the system levels.
The modern process of new technology development and evaluation always includes computer simulations as an important stage of the study. Modeling the whole network infrastructure, together with detailed simulation of the individual communication links, is hardly feasible and poses high computational complexity. Therefore, traditionally, a twolevel architecture is adopted for network behavior analysis, testing, and evaluation, where link level and system level simulations are performed independently. The goal of the link level simulator is to estimate the performance of PHYrelated mechanisms of transmitter and receiver under different propagation conditions. The purpose of the system level simulator is to evaluate the performance of the whole network in terms of throughput, capacity, coverage, quality of service, radio resource management, etc. In order to avoid costly link level simulations for estimating each link quality, a simplified but accurate link abstraction model has to be implemented. This model is generally realized as follows. First, extensive link level simulation campaigns are performed in order to estimate the link quality in different propagation conditions in terms of a chosen performance metric. Later, the outcome of these simulations is used to calibrate the link level abstraction model for system level simulations. The main function of the link level abstraction model is then to keep the performance characteristics sensible to the transmission mode and propagation conditions, but the link quality estimation has to be simple enough to be feasible on the system level. In this paper, the mean mutual information per coded bit (MMIB) effective signaltonoise ratio (ESNR) method is considered as the principal linktosystem mapping approach. This method has already demonstrated good performance for OFDMbased systems[20]. In particular, the SNR is used as a link quality measure in the ESNR approach on the link level. We assume that the noise component includes the interference, even though it is not simulated explicitly. On the system level, the intercell interference should be taken into account. On the system level, a link level abstraction model is used with signaltointerferenceplusnoise ratio (SINR) as an input and with the assumption of intercell interference. The first implementation results of the MMIB approach, together with several alternative link level abstractions for FBMC, have been presented in the earlier works of the authors[21, 22]. The main objective of this paper is to justify the applicability of the MMIB technique as link level abstraction for FBMC transmission in the PMR network. This paper presents the complete model of linktosystem mapping and final performance results for the FBMC transmission, including necessary calibration parameters that can be used for the whole set of channel quality indicators (CQIs) in different channel conditions. The particularity of the FBMC system is addressed by taking into account the distortion at the receiver[23] for resource quality measure estimation.
The rest of the paper is organized as follows: next section introduces the main link level abstraction methods with focus on the effective signaltonoise and interference mapping (ESM) model. In addition, the detailed mathematical derivations for the MMIB approach are provided. In the third section, we introduce the FBMC signal, describe its intrinsic interference, and provide its values for different fading channels. In the fourth section, the link level simulator is described and validated, and the received BLER simulation results for FBMC are analyzed. Section 5 summarizes the MMIB link level abstraction algorithm steps for FBMCbased systems. Conclusions are finally drawn in the 6th section.
Principles of link level abstraction
ESMbased models
where is the specified information measure function[25] and${\mathcal{I}}^{1}$ its inverse. {γ_{1},γ_{2},…,γ_{ K }} are the resource quality measures, e.g., received postprocessed SNR values, within a coded transport block for MC transmission. If scalars α_{1} and α_{2} are used, they are adjusted through the ESM principle (Equation 1) for a given modulation and coding scheme. This can be done by utilizing a least square fitting between the estimated BLERs and the simulated BLERs on the link level.
where BLER_{est} and BLER_{sim} are estimated BLERs and simulated BLERs for the set of effective data samples (Equation 2) mapped from the set of used quality measures, {γ_{1},γ_{2},…,γ_{ K }}, within a coded block of the transmission. Minimization is done over N independent channel realizations.
Then, the AMI is mapped to the BLER value under the assumption of AWGN propagation.
where E_{x,y}(·) is the expectation over {x,y}, p(yx) is the conditional probability density function (PDF) of y given x, and p(y) is the marginal PDF of y. The information gain increases with differentiation between p(yx) and p(y). Depending on the choice of the variables x and y, different MIESM methods can be built. If x is the transmitted complex quadrature amplitude modulation (QAM) symbol from a certain constellation and y is its realization at the receiver, distorted by a channel, the received mutual information rate (RMIR) ESM method can be established. This approach is invariable to different bittosymbol mappings, as only symboltosymbol channels are considered. An alternative way is to define MI on the bit channels. This approach brings us to the mean mutual information per coded bit (MMIB) ESM. In literature, it is hard to find complete derivation of the MMIB algorithm presented in a single publication on linktosystem abstraction and since the MMIB is the main model used in this paper, we present its detailed derivation in the following subsection.
Mean mutual information per coded bit ESM model
where y is the received QAM symbol.
where μ is the number of bits per QAM symbol.
Similarly, we can find LLR_{x = 1}(y).
which is a linear function of y, is normally distributed with variance${\sigma}^{2}=\frac{4}{{\sigma}_{n}^{2}}$ and its mean equals to$\frac{2}{{\sigma}_{n}^{2}}=\frac{{\sigma}^{2}}{2}$.
where a_{1} = 0.04210661, b_{1} = 0.209252, c_{1} = 0.00640081, and a_{2} = 0.00181492, b_{2} = 0.142675, c_{2} = 0.0822054 and d_{2} = 0.0549608.
Main parameter of link level simulator
Parameter description  Parameter value 

Coding  Parallel concatenated channel turbo codec 
Coding rate  Variable, Table 7.2.3.1 in[27] 
Coding block size  Variable from 40 to 6,144 bits, Table 5.1.33 in[28] 
Waveform  CPOFDM (rectangular), PHYDYAS with overlapping factor 4 
Antenna  1 transmitting and 1 receiving (SISO) 
Bandwidth  5 MHz 
Sampling frequency  7.68 MHz 
Subcarriers number  512 
Guard subcarriers  From 1 to 106 and from 407 to 512 
Subframe length  1 ms, 14 (OFDM) and 15 (FBMC) MC symbols in time 
PRB size  12 subcarriers in frequency 
Channel model  AWGN, PedB, ETU, 3GPPHT, etc. 
Carrier frequency  422.5 MHz 
Velocity  0 m/s, quasistatic channel 
Channel estimation  Ideal 
Equalizer  Zero forcing, 1 tap 
Symbol demapping  Soft, approximate LLR 
Modulation  4 QAM, 16 QAM, or 64 QAM 
However, the link level performances for FBMC and OFDM transmission in fading channel differ due to an extra intersymbol interference inherent to OFDM/OQAM based FBMC, as explained in the next section. This difference will require the modification in the channel quality measure, used as an input for the MI calculation in the MMIB linktosystem mapping algorithm.
FBMC technology and intrinsic interference
where

g[n] is the prototype filter impulse response,

L_{ g } is the prototype filter length,

$j=\sqrt{1}$,

θ_{l,m} = j^{l+m} is the phase mapping coefficient,

m ∈ {0,1,⋯,M  1} is the subcarrier index,$\frac{1}{T}$ is the subcarrier spacing,

l is the time index at FBMC real symbol rate$\frac{2}{T}$.
where ∗ denotes complex conjugation and${\delta}_{l,{l}_{0}}$ is Kronecker’s delta symbol. For filter banks with nearly perfect reconstruction, condition (Equation 11) is fulfilled approximately. Pulse shapes with even better frequency localization may be used if higher approximation is needed. Note that the imaginary part,$\mathfrak{I}\left\{\u3008{g}_{l,m},{g}_{{l}_{0},{m}_{0}}\u3009\right\}$, is not equal to zero but constitutes an extra interference after propagation through the channel with complex impulse response. For comparability purposes, an FBMC design should keep the same system characteristics as used in OFDM, such as number of subcarriers and subcarrier bandwidth. However, to transmit real information symbols, the OQAM real symbol period should be taken as$\frac{T}{2}$ to obtain the same data transmission rate as in OFDM. Finally, the prototype filter has length L_{ g }, which is usually taken as a multiple of M. Filters are overlapping not only in the frequency domain, but also in the time domain. This means that time multiplexing is observed in FBMC systems and the CP cannot be utilized.
where η[m] is complex AWGN, whose real and imaginary parts are statistically independent. It is assumed to be zeromean Gaussian with input noise power E(η[n]η^{∗}[ n]) = N_{0}. Here, the operator stands for convolution. The channel is assumed to be static during an OQAM symbol period$\frac{T}{2}$.
where${\beta}_{l,m}={e}^{j2\pi m\left(\frac{l}{2}\frac{{L}_{g}1}{2M}\right)}$, and the noise component is omitted for the sake of clarity of presentation.
Next, we are going to present the received signal as an expansion with components, whose absolute values decay as a power of M. This asymptotic approach shall permit the analytic calculation of the firstorder approximation for the FBMC interference power.
where${g}_{l,m}^{(r)}[n]={\theta}_{l,m}{\beta}_{l,m}{\left(\frac{T}{M}\right)}^{r}{g}^{(r)}\left[nl\frac{M}{2}\right]{e}^{j\frac{2\pi}{M}\mathit{\text{mn}}}$.
where the noise power${P}_{n}[m]=\frac{{N}_{0}}{{H[m]}^{2}}$. The evaluation of a link abstraction model for FBMC based on SNDR rather than on regular SNR can be done only through simulations. The next section is devoted to this topic.
Link abstraction model simulation results
We analyze the output of a MATLABbased link level simulator in order to evaluate the FBMC link performance model. The performances of both CPOFDM and FBMC PHYs are compared and validated.
Simulation scenarios
In the current study, we consider a 5MHz transmission bandwidth with a sampling frequency of 7.68 MHz and a transform size of 512 (15kHz subcarrier separation). The FBMC transmitter and receiver use the PHYDYAS project prototype filter[31], with overlapping factor K = 4. The transmission is divided into subframes of 14 MC symbols in CPOFDM and 15 MC symbols in FBMC, since the time dedicated to the CP in OFDM can be dedicated to another MC symbol in FBMC. The minimum resource allocation in the frequency domain occupies 12 subcarriers, like an LTE physical resource block (PRB). The bit error rate (BER) and BLER performances are measured on LTE physical downlink shared channel (PDSCH)like allocations spanning over 11 (12 in FMBC case) of the 14 (15 in FMBC case) MC symbols, leaving three initial MC symbols for hypothetical control information. The simulation parameters are summarized in Table1.
Each simulation scenario in our study is related to a certain modulation type and coding rate (CR). These two parameters, together with the number of PRBs and the frame structure, determine the coding block size (CBS). It is necessary to mention that we use the term CQI to specify the modulation and coding scheme (MCS), as it is explicitly defined in[27].
 1.
Generation of random bit sequence in accordance with specified physical resources and coding rate.
 2.
Turbo encoding.
 3.
Mapping of encoded bits to QAM symbols.
 4.
Generation of MC signal depending on the selected waveform (CPOFDM or FBMC). This step includes the calculation and insertion of pilots and the addition of the CP to the OFDM symbol.
 5.
Estimation of the signal distorted by the channel.
 6.
MC demodulation of the received signal.
 7.
Signal equalization. Channel estimation and synchronization from pilots are supported by the simulator, but are not utilized due to perfect channel knowledge assumption at the receiver.
 8.
Soft symbol to bit demapping. The LLR of every received bit is calculated.
 9.
Turbo decoding, where LLRs calculated at the previous step are used as an input.
 10.
Calculation of BER and decision if CB is received correctly.
Parameters for FBMC simulation scenarios
Number  CQI  Modulation  CR  PRB  CBS 

1  3  4 QAM  0.188  25  1,248 
2  7  16 QAM  0.369  25  4,864 
3  11  64 QAM  0.544  14  6,144 
Validation of simulation results
First, the results of the link level CPOFDM PHY simulations are validated via comparison of received BLER performance curves with their analogs produced by the Vienna LTE simulator[33]. The importance of such examination is emphasized by the fact that AWGN BLER curves are the reference used for BLER estimation in fading channels. In particular, they are utilized in the system level simulator for link level abstraction.
Fitting parameter of MMIBBLER curves in AWGN channel
CQI  CBS  b _{CQI,CBS}  c _{CQI,CBS} 

3  1,248  0.274  0.012 
7  4,864  0.428  0.007 
11  6,144  0.604  0.007 
FBMC performance in fading channels
where N is the total number of independent simulations.Figure14 shows that the MSE considerably decreases from 4.74 (upper graph) to 0.14 (lower graph) due to the utilization of the SNDR as channel quality measure.
MMIB link level abstraction of FBMCbased systems
We summarize here the steps of the link abstraction algorithm as follows:

The set of fitting coefficients b_{CQI,CBS} and c_{CQI,CBS} for MMIBBLER AWGN curves from Equation 18 (see Figure12) are precalculated and stored (see Table2).

SNDR values (Equation 16) are used as channel quality measures. γ_{ k } are calculated for every resource element of the subcarrier allocated for the transmission of the CB.

MMIB values are calculated according to Equations 6, 7, or 8 for each γ_{ k } depending on the modulation defined by the CQI (see Figure6).

MMIB values calculated in the previous step are averaged according to Equation 3.

The error rate of a given CB is calculated according to Equation 18 with the average MMIB value as an input.
As a result of the research presented in this paper, it can be concluded that the signaltointerference, noise and distortion ratio (SINDR) should be included into FBMCbased system level simulator as a part of the CB error estimation model. The ns3 open source LTE (Long Term Evolution)EPC (Evolved Packet Core) network simulator module LENA[38] can be considered as a promising tool for future FBMC research. The MMIBbased link abstraction model for OFDM is already realized there[39]. Fastfading samples for timefrequency instances are precalculated for the specific channel model, mobile velocity and carrier frequency.
With respect to the LTE implementation provided by ns3, modifications are needed to extend the simulator’s models to the PMR scenario. Regarding to the FBMC link performance model, the distortion samples have to be precalculated at RB resolution simultaneously with fastfading samples. The constant SINDR value for each RB has to be evaluated according to Equation 16. Link level lookup tables for MI versus SINDR and for BLER values versus MMIB in AWGN channel, for the full set of modulation and coding schemes need to be available in correct format as a simulator input. Finally, the error model has to be adapted to utilize the MMIB link level performance model for the FBMC transmission.
Conclusions
In this paper, we have presented a generic MMIBbased framework for link level abstraction of FBMCbased systems, and we have analyzed and verified it by link level simulations. The intrinsic distortion of FBMC signals in fading channels, due to the real orthogonality of the FB, is derived analytically. It can be expanded with the terms decaying as the power of$\frac{1}{M}$. The PDFs of firstorder residual error power are presented for the most commonly used channel models. Simulation results show that this distortion should be taken into account in the link level abstraction model. As a result, the quality measure of the resource element that we propose to consider for the FBMC transmission is the received SNDR.
The mean MI model via the MMIB approach has been deeply analyzed for suitability to the FBMC transmission and verified by simulations. The simulation results have shown that conditional LLR distributions do not differ for CPOFDM and FBMC transmission techniques in AWGN channel. Therefore, the same approximations of MMIB functions for 4 QAM, 16 QAM, and 64 QAM modulations can be utilized in the case of the FBMC transmission. The FBMCrelated results of the link level simulations have been compared with the corresponding CPOFDM performance. It has been confirmed that BLER performance curves for both technologies in AWGN channels are the same. Additionally, simulation results in CPOFDM scenarios have been validated, comparing them to publicly available reference results from the Vienna LTE simulator. FBMC BLER performance curves have been presented for several channel models, such as PedB, ETU, and 3GPPHT.
Finally, we conclude that the traditional MMIBbased link abstraction model cannot be used in high fading channels for the FBMC transmissions, especially with higherorder modulations. The proposed model with distortion correction is kept simple and is more accurate, and it can be efficiently used for linktosystem mapping in the FBMC case. Future work will include studying the performance of the developed link abstraction model in cases of more advanced receivers, nonideal channel estimation, and in the presence of interference. Additionally, system level simulations with the ns3 simulator in a broadband PMR network scenario applying the proposed link quality estimation are also a topic for future research.
Notes
Declarations
Acknowledgements
The authors would like to thank the anonymous reviewers and the editors for their constructive comments and suggestions to improve the manuscript, both in presentation and contents. The authors acknowledge Dr. Xavier Mestre for help in calculation and evaluation of the distortion and Dr. Stephan Pfletschinger for fruitful discussion of MIESM approach and help in soft demapping for link level simulator. We also would like to thank professor Tapani Ristaniemi for valuable advice and professor Timo Hämäläinen for the technical support. The authors acknowledge the financial support by the European Union FP7ICT project EMPhAtiC (http://www.ictemphatic.eu) under grant agreement no. 318362.
Authors’ Affiliations
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This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly credited.