Effect of block size on BER performance of inverse filtering based MIMO FBMC

Filter bank multicarrier (FBMC) is a novel next-generation data transfer technique. FBMC has a large number of benefits over conventional orthogonal frequency division multiplexing (OFDM) techniques. The FBMC scheme suffers from imaginary interference, which degrades the bit error rate (BER) performance at the receiver. In the recent past, inter carrier interference (ICI)-free Alamouti-coded FBMC frame and block repetition schemes for BER improvement were discussed. However, in the analysis, various interfering terms are neglected. In this work to reduce ICI and inter symbol interference (ISI), the concept of inverse filtering is applied while considering other interfering terms. Inverse filtering can be used to reduce the negative impacts of the ICI and ISI. This is determined by mathematical modelling that includes the ICI, ISI, and other interfering parameters. The simulation is performed in MATLABR software. The obtained BER at an SNR of 15 dB is 2.3 × 10−4.The simulation results are also compared with some of the recent methods, and it has been found that the proposed scheme is better in comparison to the considered recent methods.


Introduction
The introduction of mobile communication has brought a revolution to the communication system.The current requirements of mobile phones are: high-speed Internet; good voice quality; and a good processor that requires extra bandwidth for quick transmission.These requirements of communication systems are fulfilled by OFDM [1].The major drawback with OFDM is out-of-band (OOB) emission and low spectral efficiency [2,3].All these issues related to OFDM encourage the evolution of new, improved waveforms.
Figure 1 illustrates the evolution of mobile transmission techniques.The basic principle on which 2G technology works is time division multiple access (TDMA) [4].In this technique, users send data on common frequency, and the time is divided.The 3G communication system works on Code Division Multiple Access (CDMA) [5].This method uses a coding mechanism to allow multiple users to transmit data simultaneously, which reduces delay compared to 2G technology.The 4G communication system is based on the OFDM technique with a high transmission speed of 100 Mbps.Although the implementation complexity and cost of this technique are quite high, this leads to the new technique Long Term Evolution (LTE) [6] based on OFDM and Single Carrier-FDM (SC-FDM) [7].Researchers are currently investigating 5G technology, which will have speeds between 1 and 20 Gbps.
5G standardisation and deployment are taking place all around the world.The 5G communication technology is raising communication to the next level by improving speed, effectiveness, safety, and delay [2].5G networks will improve their service in a variety of industries, including manufacturing, education, health care, transportation, and more, in the future.As a result, the next advanced network will need to service a variety of industries, each with its own set of requirements.The standard of medical care can be raised by combining 5G, the Internet of Things (IoT), and smart hospitals [8].The Internet of Things (IoT) devices can analyse the data in various industries.However, due to the limited spectrum, speed, and capacity in the current environment, IoT and wearable technology are used less frequently.It is important to investigate 5G advanced waveforms with low leakage, high data rates, and high bandwidth capabilities [8].
Currently, extensive research is going on for next-generation 5G technology.For this, FBMC [9] could be quite helpful with the least OOB emission.In this technique, information is transmitted using overlapping blocks.In FBMC, each sub-carrier has a narrow bandwidth, so the filter impulse response is long.Normally, the symbol length is th of the filter length.

FBMC basics
An alternative multicarrier transmission technique called FBMC uses high-quality filters to prevent both ingress and egress noises.FBMC can deliver faster data rates within a given radio spectrum bandwidth because it has a higher level of spectrum efficiency and makes considerably better use of the available channel capacity.In OFDM, complex symbols are transmitted and orthogonality is maintained on subcarriers.In FBMC, orthogonality is maintained using real symbols.As in FBMC, real symbols are transmitted, thus the data rate reduces to the half of OFDM.Therefore, to achieve the same data rate as in OFDM, each FBMC symbol is transmitted for half of its symbol duration, i.e., T/ 2, therefore referred to as filter bank multicarrier/offset quadrature amplitude modulation (FBMC-OQAM) (Fig. 2).It is further to note that sub carrier spacing is the same in both OFDM and FBMC-OQAM, i.e., Df, in OFDM TDf = 1 while in the case of FBMC sDf = 0.5.Therefore, information carried out by one complex OFDM symbol is achieved in FBMC with two real-valued symbols of half period duration.In general, both FBMC/OQAM and FBMC/QAM can be considered.However, FBMC/OQAM is superior to FBMC/QAM in terms of waveform localisation in time and frequency.The implementation complexity of FBMC/OQAM, however, considerably increases when we move from single input single output (SISO) to more widely used multiple inputs multiple outputs (MIMO) systems.
In FBMC/OQAM, the frequency band is split into a number of orthogonal subcarriers, each of which has a prototype filter with a suitable spectral property.The complex symbol for m th symbol on n th sub carrier is given by where, a m,n and b m,n are real and imaginary part of d m,n respectively.For real (same equation for imaginary part) part the transmitted signal can be expressed as T t e j/ m; n ð2Þ h[t] is prototype filter, T/2 is delay term and the phase term make sure that phase difference of AE p 2 between adjacent symbols, i.e., / m; n ¼ p 2 ðm þ nÞ.The phasor term is e j/ m; n ¼ e j p 2 ðmþnÞ ¼ j ðmþnÞ : ð3Þ Fig. 1 The mobile technologies generations Further, defining h m; n ½t ¼ h t À mT=2 ½ e jn 2p T t e j/ m; n .Consequently, the above equation is simplified as: where, n m.n is noise at the demodulator.Further applying orthogonality condition we get, where, I m; n is complex interference.Under the time invariant channel we have Consequently, the received symbol can be written as The imaginary interfering term in Eq. ( 7) degrades the MIMO system performance and increases the bit error rate (BER).
In this paper, detailed modelling of the FBMC-OQAM system is presented while considering various interfering terms, and it is also shown how inverse filtering is helpful in reducing the ICI and ISI.The BER results are compared with notable methods, and how block size also affects the BER performance is also discussed and simulated.
The rest of the paper is organized as follows, in Sect.2, of the paper related work, where some of the notable methods are discussed.The proposed method, along with mathematical modelling, is presented in Sect. 3 of the paper.Results are discussed in the Sect. 4 of the paper.The notable findings of the paper are discussed in Sect. 5 of the paper.

Related work
The characteristics of wireless communication channels change over time; therefore, it is impossible to exactly characterise them.However, the channel effect can be reversed using equalisers.Cyclic prefix (CP) is utilised in OFDM to minimise complexity and miximize bandwidth efficiency while reducing channel impacts.The problem with earlier MIMO-OFDM approaches was addressed by the MIMO-based FBMC technique which was introduced by Ma `rius Caus et al., [10].In the recent past, many studies have been investigated to deal with various issues and implementation details of the FBMC system.Low complexity transmitter design for FBMC was proposed by Lajos Varga & Zsolt Kollar [11].They also upgraded the transmitter design with IFFT, a polyphase filter and some computational blocks, which result in reduced computational complexity.This design could be considered an advanced version of an OFDM transmitter with some extra computational blocks.Xu et al., [12] presented a detailed examination of OFDM and FBMC while applying the Root Raised Cosine (RRC) filter, which has infinite bandwidth, and the PHYDAS filter, which was introduced by Bellanger et.al., [13].
There are many possible solutions to the ICI and ISI issues, and a few of them are presented below.He et al., [14] proposed a method where stopband energy is minimised while maintaining side-lobes and ICI/ISI suppression requirements.This is achieved by optimising the filter coefficients.You et al., [15] proposed an interference-free technique for FBMC/OQAM that works with both subband-based singular valued decomposition (SVD) precoding and codebook precoding methods.It has been discovered that these precoding techniques can effectively reduce ICI and result in significant performance improvements in terms of BER over the existing systems.In order to reduce the inherent ISI and ICI components in FBMC/OQAM, iterative interference cancellation (IC) was proposed by Yahya et.al., [16].A new FBMC system was introduced by H. Nam et al., which was based on two filters, one for real and one for imaginary symbols.This method not only fulfils the orthogonality requirements, but at the same time also enhances the spectral efficiency and reduces intrinsic interference [17].To improve BER performance, Alamouti coding cannot be applied directly due to intrinsic interference [18].Alamouti based scheme was recently proposed by designing complex transmitter and receiver designs [19].In [20], an Alamouti coded scheme was proposed, which assumes flat fading over the entire block.A FRAC (frequency reversal Alamouti coded) scheme for FBMC was proposed, and by setting phase condition, the intrinsic inter-antenna ICI (intercarrier interference) terms can be self-cancelled [21].To achieve the self-cancellation of intrinsic imaginary interference, Dejin et.al., [22] present a complex-valued symbol based FBMC/OQAM (C-FBMC/OQAM) system.The key idea is the use of a carefully designed repeating frame, in which complexvalued QAM symbols are communicated as opposed to simply real-valued symbols in the traditional FBMC/ OQAM systems.It has been proved that the C-FBMC/ OQAM systems can completely eliminate intrinsic symbol interference while still maintaining spectral efficiency even in the presence of repeated frames.Due to the inherent interference cancellation, simulation findings reveal that the proposed C-FBMC/OQAM system performs better than standard FBMC/OQAM systems.

Alamouti coding
Dejin et.al., [23] discuss the Alamouti code in FBMC/ OQAM and suggest a new block-wise Alamouti code in which a repeating block is intended to get rid of the fictitious interference among FBMC/OQAM symbols.This approach uses only one column of zero symbols as a guard interval, as opposed to two in the classical block-wise Alamouti scheme.This results in a greater spectral efficiency and an improved bit error ratio as compared to the standard method.Simulation results show that the repeating block Alamouti scheme outperforms the traditional block-wise Alamouti scheme with a much lower overhead.
In the conventional blockwise Alamouti coding scheme, the frame structure of the traditional block-wise Alamouti scheme is shown in Fig. 3, where two blocks with a block length of N are shown, with the second block using the reversion method [23].Each block needs a column of zero characters as a guard interval in order to prevent imaginary interference between the blocks.
As a result, in case of 2 9 1 multiple antenna systems the symbols for the first and second transmitting antennas at the m-th subcarrier are represented as According to Eq. ( 7), the demodulated signal at the two receivers can be written as To maintain Alamouti orthogonality we must have n .In the matrix form the Eq. ( 9) can be written as The received symbols can be expressed as âm;n bm;n

Alamouti coding based on block repetition
To deal with imaginary interference symbol reversion is used in the repeated block.Contrary to the basic Alamouti scheme (Fig. 3), no zero symbols are needed between the first and second blocks, and only one column of zero symbols is needed as a guard interval to prevent imaginary interference from the next Alamouti-coded block (Fig. 4).
The received symbols can be expressed as âm;n âm;nþ1 The above-discussed Alamouti coding schemes are developed under simplified assumptions on channel characteristics, neglecting other interfering terms like interblock interference, channel multipath effect, estimation bias error, etc.In the recent field experiment based on FBMC technology [8], BER performance is measured, but the results are not supported by mathematical modelling, which is important in characterising the interference and noise and searching for possible solutions to mitigate interference and noise.

Limitations of the state of art methods
The frequency reversal Alamouti coding can cancel ICI if the frequency reversal pair has an identical fading coefficient [21].It is not possible to achieve flat fading in an entire block or band; therefore, the band is divided into sub-bands, and on sub-bands using frequency reversal Alamouti coding the self-ICI cancellation property can be achieved.It is also notable that the peak power reduction due to DFT spreading will be less in smaller blocks, however a null carrier would be needed to separate subblocks.
The drawbacks of this scheme are.
1. Due to null subcarriers there will be data loss 2. Due to partition of blocks transmission time will be more.3.As sub-blocks increases the interference due to subblocks also increases.1. Frame will be repeated [22] 2. Block will be repeated [23] 3 Proposed method In the proposed method, detailed modelling of the FBMC-OQAM system is presented, without any assumptions.
Various interfering terms are derived, and it is shown that using inverse filtering, ICI and ISI can be eliminated, and the performance of the proposed method is superior to that of considered state-of-the-art methods in terms of BER.

Modeling of FBMC system
In the modelling, it is assumed that the system employs a fading channel that is either quasi-static or fluctuates gradually.In this case, it is reasonable to assume that the random fading coefficients are constant throughout the block and that each transmitted data block has a duration that is shorter than the channel coherence time [24].Additionally, it is also expected that the average power will not change during the block's full transmission.In Table 1, a list of symbols and their descriptions is presented; the intermediate dummy variables are not included in the table.The channel impulse response matrix's can be written as Considering, number of transmitter as N t and number of receiver as N r the above equation the l th component can be written as H l ¼ q l z 11 ðlÞ ::: z 1N t ðlÞ ::: ::: ::: z N r 1 ðlÞ ::: The received signal (r), is the sum of input signal (x) convolve with channel (H) and additive noise and can be represented (Fig. 3) where, n is Gaussian noise with mean 0 and variance r 2 .Using Eqs. ( 14) and ( 16) can be expanded as The l-tap delayed version of the input is represented by x d and b IBI is inter block interference.
The prototype filter (P) is convolved with the input signal; however, to show the filtering process, the full system should be represented in matrix form.The prototype filter matrix, with K as the overlapping factor, is defined as Considering Fig. 5, the output of the filter, which is the transmitted signal, is given by The signal received can be represented as To demonstrate the effect of multipath interference on filter distortion, we define filter as, Substituting Eq. ( 21) in Eq. ( 20), we get, The Eq. ( 22) can be represented as where, x fd ¼ P LÀ1 l¼0 q l Z l DPb ed is the filter distortion-induced interference brought on by the channel multipath effect.
The signal at the receiver is processed by a bank of filters, and in matrix form, it can be written as P H .The receive filter bank's output can be expressed as Inserting Eq. ( 23) into Eq.( 24) we get, Further defining G ¼ P H P, then Eq. ( 25) can be expressed as The output of the DFT process can be written as The term can be written as where, The Eq. ( 27) can be written as Further using, Defining, FH cir F H ¼ C is the diagonal matrix containing the frequency domain channel coefficients, and where, With following properties: DQ represents the interference coefficient matrix, which establishes the level of internal interference in the received signal block.
Using channel equalization, the received symbol can be written as Let EC ¼ b, the Eq. ( 37) can be written as The above equation has seven terms: the first term is the desired symbol, the second term is the MMSE estimation bias, and the third and fourth terms represent ICI and ISI, respectively.Multipath filter distortion is represented by the fifth term; the sixth term represents the IBI by Multipath; and noise is represented by the seventh term.

Modeling of FBMC System with inverse filtering
From the above expression Eq. (39), it is clear that the received symbol is suffering from intrinsic interference, i.e., the imaginary part of interference, along with noise and other interferences.The ICI arises due to the interference between two data streams on different channels.
The ISI arises due to the intermixing of consecutive symbols caused by multipath propagation due to the linear or non-linear frequency response of a communication channel.The intrinsic interference can be overcome by using inverse filtering (Fig. 6).The inverse filter is defined as the inverse autocorrelation of a matrix G i.e., R = G -1 [24].
In case of inverse filtering, ICI and ISI eliminated but noise and interference increases.The inverse filter is applied at the receiver only.The output of the inverse filter can be written as where, Using Eqs. ( 41) and ( 40) can be written as Taking the DFT of Eq. ( 42) we get, where, The received symbol after the equalization process can be expressed as The above equation can be further written as The first term represents the desired symbol, the second term represents the estimation bias, the third term represents the filter distortion arising due to the multipath, the fourth term represents the inter-block interference, and finally the fifth term represents the noise.
Referring, to Eqs. ( 39) and (45), it can be observed that the inverse filtering completely removes the terms, EDQ mm Cs m and P MÀ1 i¼0; i6 ¼m EDQ m;i Cs i which represents ICI and ISI respectively.The MMSE for n th modulated signal using Eq. ( 45) can be written as The estimation biased variance can be written as where N s m;n and r 2 is AWGN noise variance [25].
In case of Zero Forcing l = 0 and for MMSE l = 1.The final expression for the estimation biased can be written as The filter distortion error is give by where, Using, N½Z l Z H l ¼ 1, and r 2 s ¼ b l ed b lH ed , the Eq. ( 50) can be represented as Considering the n th diagonal element we get, where, f m;n ¼ FR m P H m a f d P m R H m F H The inter block interference error is give by The term x IBI using Eq. ( 17) can be expressed as where r p;l is interfering signal from previous block.Therefore, the term a IBI can be expanded as Considering the n th diagonal element we get, The fourth term in Eq. ( 39) is the inter-block inference term, which contributes to the inter-block interference error (r 2 IBI;m;n ).Further, considering Eqs.(49), (46), and (44), it is clear that the inter-block interference error is directly dependent on the block size, and as the block size grows, the interference error increases and thus degrades the BER performance.
The noise variance is represented by Considering the n th diagonal element we get, 4 Simulation results In the simulation, Rayleigh fading channels along with an added white Gaussian are considered.In the case of 2 9 2 spatial multiplexing, two antennas transmit bits independently.At the receiver, either zero forcing or maximum likelihood (ML) detection is assumed.It is to be noted that zero-forcing error increases noise, while ML detection is more complex.The second considered scheme is 2 9 1 Alamouti's space-time block codes.We use a 2 9 1 multiple-antenna FBMC/OQAM system, with a number of subcarriers as 2048.The modulation algorithm and multicarrier signalling method play a significant role in the FBMC technique's prototype filter selection process.Selecting a suitable prototype filter has several advantages for the system, including a reduction in OOB output, ICI, and ISI.A fitting filter can also support the improvement of the signal-to-interference-plus-noise ratio (SINR) and improved frequency localization.The PHYDAS filter fits well in the above-discussed criteria; therefore, it is considered as prototype pulse-shaping filter [16].
The time-domain impulse response of the prototype filter, which is a truncated Fourier series, can be represented as a 0 = 1, a 1 = -0.97195983, a 2 = ?0.70710681, and a 3 = -0.23514695.The performance comparisons of OFDM and FBMC under various schemes are shown in Fig. 7.The ZF detector completely eliminates interference from other symbol layers when detecting a particular symbol layer, albeit at the expense of noise-enhanced.The noise enhancement, which can lead to infinite noise power spectral densities after the equalizer, is a significant issue with the zero-forcing equaliser.ML detection is based on the mean square error and tries to minimize the error probability.The Alamouti coding scheme uses coding to minimize the errors.Here, BER at various signals to noise ratio levels for both OFDM and FBMC is similar.At the SNR level of 20 dB, comparing the BER for the OFDM scheme under the ZF, ML, and Alamouti schemes are 3.3 9 10 -2 , 1.3 9 10 -2 and 3.9 9 10 -3 respectively.Similarly, at the SNR level of 20 dB, comparing the BER for the FBMC scheme under the ZF, ML and Alamouti schemes are 3.2 9 10 -2 , 1.27 9 10 -2 and 3.8 9 10 -3 respectively.At the lower SNR levels (\ 15 dB) the noise is dominant over interfering terms, thus the BER performance of OFDM and FBMC is same.At the SNR level of 15 dB, under the Alamouti coding scheme BER is 2.6 9 10 -2 .The Alamouti scheme maintains antenna diversity, thus maximizing the symbol transfer probability, and, in turn BER.The above simulated results prove the usefulness of the Alamouti coding scheme.The BER performance of OFDM and FBMC waveforms is nearly the same, but the spectral efficiency of FBMC is much higher in comparison to OFDM [26].
As detailed above, Choi's work introduces the combination of low PAPR FBMC and FRAC methods.In Choi's work, frequency reversal scheme is used.The frequency reversal Alamouti coding can cancel the ICI if the frequency reversal pair has identical fading co-efficient.Even if the null data in the centre subcarrier is removed in FRAC-FBMC, the BER performance can be kept relatively close to the ICI-free case.In Choi's work, it is shown that a block size of 8 produces the lowest BER in terms of theoretical Alamouti coded BER.
In Fig. 8, bit error rate vs. half block size is shown.The simulation results are shown for SNRs of 15 and 21 dB.As base result, theoretical Alamouti Coded BER is shown.For SNR of 15 dB, the BER is around 10 -3 for all the schemes.This happens because the AWGN noise is dominant over other factors and the condition of being ICI-free is met in all the chosen schemes.However, as the SNR increases, the dominance of noise is suppressed and the effect of other Fig. 7 BER vs. SNR (dB) interfering terms can be observed.Under the theoretical Alamouti coding scheme, ideal conditions are assumed i.e., system is interference free, except noise all other variance terms are zero.The theoretical Alamouti-coded scheme achieves BER order is 10 -4 for SNR of 21 dB.In the FRAC-FBMC, except ICI the other variance terms are dominant so BER is relatively higher.The Choi's works, presents the generalization of the phase shift condition, which improves the BER as compared to the conventional FRAC-FBMC scheme.In the proposed work, using inverse filtering both ICI and ISI can be completely eliminated which leads to the betterment of BER.
In Fig. 9, symbol index vs.noise enhancement factor (f m,n ) is shown while blocks of sizes 14 and 64 are considered.There are three distortion terms: filter distortion error, inter-block interference, and noise variance, which depend on the noise enhancement factor.The noise distortion can be suppressed at higher SNR levels.Filter distortion can be reduced by choosing a properly designed prototype filter.Similarly, the inter-block interference can be minimized by properly choosing the block size.However, in case of inverse filtering, noise is higher as compared to without inverse filtering.Therefore, to visualize the noise enhancement factor vs. symbol index must be observed for various block sizes.The impact of the noise enhancement factor is greatest for the symbols in the middle of the FBMC/QAM data block, as shown, and it was also found that it is constant for every subcarrier in every symbol.In the Figure solid line denotes the average noise enhancement factor.For a block of size 14, the maximum noise enhancement factor is 1.55 and the average noise enhancement factor is1.36.In case of block size of 64, the inter-block interference increases thus noise also increases.The maximum noise enhancement factor is 1.68 and the average noise enhancement factor is1.49.Therefore, large block sizes should be avoided.However, with a smaller block size of 8, the average noise enhancement factor is 1.09, which is minimal.
In Fig. 10, SNR vs. BER for different block sizes while considering inverse filtering are shown.Here, three block sizes i.e., 8, 14, and 64 symbols are considered.It can be observed that as the block size increases BER also increases.This is obvious as discussed above as the block size increases, the filter distortion error, inter block interference, and noise variance increases, which in turn increases the noise enhancement factor.For comparison, considering the SNR level as 15 dB, for the block size of 8, BER is 9 9 10 -4 and for the block size of 14, BER is 1.7 9 10 -3 and finally, for the block size of 64, BER is  Finally, in Fig. 11, SNR vs. BER is shown under three schemes i.e., theoretical Alamouti coding, Choi's work and proposed method for the block sizes of 8 and 64.It can be visualized from the figure that there is a huge difference in BER for block sizes of 8 and 64.Comparing results at the SNR level of 20 dB, the theoretical Alamouti coded BER is 1.3 9 10 -4 , the BER under the Choi scheme is 1 9 10 -4 .BER under proposed scheme for a block size of 8 is 4.5 9 10 -5 but as the block size increases, BER increases drastically to 1 9 10 -3 .Therefore, the advantage of the proposed scheme is completely lost.Therefore, it can be inferred that the better BER performance is observed with a block size of 8 and the BER is comparable to the theoretical Alamouti coded for a block size of 14.Further improvement in the results may be possible using a few possible approaches.The Filtering effect i.e., distortion due to filtering can be further reduced by a specially designed filter, as discussed in [27].The other possible approach could be the use of PHYDAS filter with truncation [28].The next possible advancement is the use of coding techniques to improve the BER performance [29][30][31][32].

Comparison with notable methods
In Table 2, the compassion of notable methods is detailed.Adarsh et.al., [27], considered the design of an optimum filter to reduce ICI and ISI; for the selection of filter coefficients an algorithm was proposed and obtained BER of 1 9 10 -2 at the SNR level of 18 dB.Varlamov et al., [33] considered the self-interference compensation mechanism and obtained BER of 1 9 10 -3 at the SNR level of 22 dB.Zakaria et al., [34] considered partial interference cancellation mechanism and obtained BER of 7.8 9 10 -4 at the SNR level of 15 dB.Bedoui et.al., [35] considered the interference mitigation using deep learning mechanism and the SNR level of 12 dB obtained BER is 1 9 10 -2 .The generalisation of the phase shift condition in intrinsic ICI free Alamouti-coded FBMC was introduced by D. Na & K. Choi [21].This generalisation enables the creation of waveforms that are more advantageous and don't require null insertion into the centre subcarrier and the SNR level of 15 dB the obtained BER is 1 9 10 -3 .Dejin et.al., [22] proposed the frame repetition method and the SNR level of 15 dB the obtained BER is 3.4 9 10 -4 .Further, Dejin et.al., [23] proposed block repetition method and the SNR level of 15 dB the obtained BER is 3.0 9 10 -4 .The above discussed schemes either only consider ICI and AWGN noise in the modelling or, ICI, ISI, and AWGN noise in the  2 Comparison of recent methods simulation, while other interfering terms are neglected.In the proposed method at an SNR level of 15 dB the obtained BER is 2.3 9 10 -4 .

Conclusions
FBMC is one of the waveform techniques that can provide a competitive solution for next generation 5G mobile communication.The main issues in FBMC are high PAPR and BER.This paper addresses a comprehensive overview of FBMC technique, along-with its mathematical formulation.In this paper, to mitigate both ICI and ISI an inverse filter based approach is considered.But unfortunately, inverse filtering introduces IBI, distortion, and noise.Therefore, to limit these detrimental effects, block size is limited, as also suggested in FRAC-FBMC.However, for the faster transmission rates block size should be larger but larger block size will introduce more distortion.Therefore, optimum block sizing is important.Simulation results reveal that the proposed method has better BER performance for the block of size 8 as compared to FRAC-FBMC.It is found that with a block size of 14, BER is comparable to theoretical Alamouti coding scheme.It is also found that the obtained BER is 2.3 9 10 -4 at the SNR level of 15 dB.Hence, it can be inferred that the proposed scheme has relatively better BER performance as compared to recent notable techniques.

Fig. 2
Fig. 2 Comparison of OFDM and O-QAM symbols

Fig. 6
Fig. 6 Block diagram for FBMC under inverse filtering

Fig. 8
Fig. 8 Half block size vs. bit error rate

Table 1
List of parameters and description