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\title{BER Performance Analysis of OFDM, W-OFDM and F-OFDM for 5G Wireless Communications}
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             \author[1]{MD.Hasan  Mahmud}

             \author[2]{Mirza Abir  Mahmud}

             \author[3]{MD.Hafizul  islam}

             \author[4]{MD. Maruf  Hosain}

             \affil[1]{  Pabna University of Science and Technology.}

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\date{\small \em Received: 12 December 2019 Accepted: 5 January 2020 Published: 15 January 2020}

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\begin{abstract}
        


Orthogonal Frequency Division Multiplexing (OFDM) is a pertinent multi-carrier modulation approach that is more immune to frequency selective fading. In the 5G waveform, in order to reduce the traffic in OFDM based on technology, it is important to re-size the bandwidth. Consequently, a spectrally localized waveform technology called Filtered Orthogonal Frequency Division Multiplexing (F-OFDM), which is primarily an approach to sub-band based filtering is introduced. Windowed-OFDM (W-OFDM), which is basically a classical OFDM scheme where each symbol is windowed and overlapped in the time domain. Each of the different subbands can be processed according to the traffic scenario.

\end{abstract}


\keywords{OFDM, F-OFDM, W-OFDM, relay, MIMO, BPSK, QAM, BER, ISI.}

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\let\tabcellsep& 	 	 		 
\section[{Introduction}]{Introduction}\par
fter years of discussions through the industry and academia, the requirements and expectations for the 5th generation (5G) cellular networks have been made clear. Whilst the millimeter wave is expected to deliver short-range with high-speed radio access by tens of Gbps the lower frequency bands (e.g., those are currently used by the 4G long-term evolution networks) will continue to provide ubiquitous and reliable radio access, but with an improved spectrum efficiency \hyperref[b13]{[1]}. To this end, the air interface, mainly the underlying waveform, should be revisited. Next-generation cellular networks present the most challenging issues for researchers and engineers.\par
The main aim is to improve the actual LTE performance, in order to meet the growing data demand from the newly provisioned technologies and services \hyperref[b14]{[2]}. For instance, increasing the data rate by a factor 100 with respect to LTE, while decreasing the latency from the actual 15 ms down to as low as approximately, 1 ms. Massive MIMO Enabling new technologies and services, such as Device-to-Device communications (D2D), Wireless Software Defined Networking (WSDN), Millimeter Wave communications and network Densification, are being utilized in order to reach 5G's goals  {\ref [3] [4]}.\par
In this paper, we deal with problems concerning Radio Access techniques. As stated earlier, new services in 5G require high data rates with large spectral efficiency. For this reason, we focus on the spectral efficiency problem of a legacy the Orthogonal Frequency Division Multiplexing (OFDM) system, which has to improve its performance to achieve the required goal. As is well known, OFDM is the most important transmission technique of the recent past, largely used in LTE standards \hyperref[b16]{[5]}. The principle of OFDM based on sub-carrier the division has been well studied and performed during the years and the first advantage of this scheme is its simplicity of implementation. Moreover, OFDM allows for simple modulation and demodulation and is highly MIMO friendly. On the other side, OFDM suffers from high PAPR (Peak-to-Average Power Ratio) and most of high Out-Of-Band (OOB) emissions. The required Cyclic Prefix (CP) and strict bounds for synchronization are other disadvantages of OFDM. Indeed, in a 5G scenario, it is desirable to use sub-bands that do not need to be perfectly synchronized with each other due to the different requirements of the multitude of devices on the network. In fact, in 5G we will have different kinds of devices that rarely connect to the network \hyperref[b16]{[5]}  \hyperref[b17]{[6]}. For instance, an IoT (Internet of Things) device needs to send a few control bytes on rare occasions, and several kinds of devices will have a very short battery life. For these causes, it may be desirable to use a waveform with relaxed synchronization requirements \hyperref[b18]{[7]}.\par
This article attempts to summarize benefits and disadvantages of these two schemes currently being considered by 3GPP (Third Generation Partnership Project) for 5G applications, namely F-OFDM (Filtered OFDM) and W-OFDM (Windowed OFDM) based one BER, PSD and signal to noise ratio using BPSK, QPSK, 16-PSK, QAM, 8-QAM and 16-QAM modulation, we consider standard OFDM sub-bands, without using any strategy to reduce OOB emissions \hyperref[b19]{[8]}. In the F-OFDM schemes, we consider low-pass filters in order to attenuate the OOB emissions and have an efficient sub-II. Ofdm (Orthogonal Frequency-Division Multiplexing)\par
OFDM means Orthogonal frequency-division multiplexing. OFDM scheme requires N number of subcarriers to transmit the number of data streams. Each of these carriers is orthogonal to other and centered at multiples of frequencies. These serial data streams are converted to N parallel data streams and then they are digitally modulated using appropriate modulation techniques like BPSK, QAM, PSK and others \hyperref[b1]{[11]}. The constellation mapper or Lookup Table is used for the special purpose that is the modulation. For the superimposition of the modulated data on the orthogonal sub-carriers, it demands N sinusoidal oscillators tuned with N orthogonal frequencies that are parallel to each other. The output of the sinusoidal oscillators is added up together that results to produce an final OFDM signal. These oscillators and the summer are replaced with an IFFT block that was recommended by Weinstein and Ebert to scale down the complexity of OFDM  {\ref [11] [12]}. From the IFFT output, the OFDM symbol samples are attained. The IFFT block switches the signal from frequency domain to time domain. Fig. \hyperref[fig_0]{1} above shows the OFDM Architecture.\par
The Inter-symbol-Interference (ISI) imposes a negative impact on the OFDM which is induced by the specific delay spread. Delay spread occurs since multiple copies of the transmitted signals are received at different intervals of time rather than a single time. But the ISI results when the delay spread goes beyond the symbol time duration. The ISI can be eliminated by the use of the cyclic prefix \hyperref[b2]{[12]}. The cyclic prefix is a manner of adjoining some portion of the OFDM symbol at the beginning of the OFDM symbol. The Inter-carrierinterference (ICI) can also be eliminated by the proper use of the cyclic prefix. The channel portion adds AWGN (Additive White Gaussian noise) to the received signal. The reverse operation of transmitter section appears at the receiver side. At the receiver section, the transmitted signal is converted from analog to digital and then removes the cyclic prefix portion. The receiver has to perform synchronization (both channel timing and frequency), channel estimation, demodulation, and decoding systems. The output from FFT and the input of the IFFT are same range \hyperref[b3]{[13]}  \hyperref[b4]{[14]}. Finally, the original signal can be recovered by reassembling all data streams from the individual carrier. 
\section[{III.}]{III.}\par
Windowed Ofdm (W-ofdm)   In this section, we illustrate time domain windowing strategy. Since, the signal high frequency components are generated by the discontinuities between adjacent OFDM symbols, softening these singularities with a proper transition lowers the OOB emissions \hyperref[b21]{[10]}.  The OFDM symbols must be elongated with the insertion of CP, prefix and suffix, then windowed and finally concatenated (by partially overlapping two consecutive symbols) according to fig. \hyperref[fig_1]{2}. W-OFDM Architecture model is denoted by fig. \hyperref[fig_2]{3}.\par
emissions are reduced by smoothing the symbol transitions with a time domain window applied on each sub-band. Other results on f-OFDM can be found in the \hyperref[b21]{[10]}, which gives a closed form for ISI (Inter-Symbol Interference), ICI (Inter-Carrier Interference) and ACI (Adjacent-Channel Interference). Suggests a filter-bank version of f-OFDM, while discusses PAPR reduction in F-OFDM. samples of the (i+1) ??? ) W-OFDM symbol. The windowed symbol ?? ?? is obtained from the extended symbol x via equation \hyperref[b13]{(1)}.?? ?? = ?? ð??"ð??" . ?? ð??"ð??" (1)\par
Where, ?? ð??"ð??" represents the window of length ?? ð??"ð??" (?? ) . We use a window defined via equation \hyperref[b14]{(2)}.?? ð??"ð??" = ? 0 (?? ??ð??"ð??" ??? ????ð??"ð??" /2 ) . 1 (?? ð??"ð??" +?? ð??"ð??"ð??"ð??" ??? ????ð??"ð??" +1) . 0 (?? ??ð??"ð??" ??? ????ð??"ð??" /2 ) . ?\textbf{(2)}\par
Where, 0 ?? represents a column vector of L elements filled by zeros, likewise 1 ?? is the similar type of vector filled by ones. The parameter ?? ??? represents the window transition length, i.e. the number of samples the window spends to go from zero-to-one and from one-tozero, ?? ??ð??"ð??" is the transition length in the ð??"ð??" ??? of sub-band.\par
IV. 
\section[{Filtered Ofdm (f-Ofdm)}]{Filtered Ofdm (f-Ofdm)}\par
The transmission chain for f-OFDM is similar to that for the CP-OFDM, with an additional low-pass filter introduced Clearly, the structure of the transmitter low-pass filter is numerous important for reducing OOB emissions and possible interference. we want a filter perfectly flat in pass-band and zero outside this band, with null transition bands  {\ref [17] [18]}. This kind of filter is unrealizable but can be approximated by truncating and windowing the ideal sinc (.) impulse response. This operation introduces the new element in this framework, the filter transition bands. It is important to note that the transition bands are completely independent of frequency guard bands. Obviously having the transition band contained in the guard band could guarantee better performances. The filter has to be as flat as possible in the pass-band with tight transition bands section. To achieve this specific goal we have chosen a windowed-sinc filter with ideal impulse response?? ð??"ð??" (n) = Sinc (Î?"ð??"ð??" ð??"ð??" (?? ??ð??"ð??" + 2?? ð??"ð??" ) ?? ?? ð??"ð??" ? ) (3) For -[?? ð??"ð??" /2] ? n ? [?? ð??"ð??" /2],\par
Where ?? ð??"ð??" represents the filter order and Î?"ð??"ð??" ð??"ð??" ?? ð??"ð??" the transition band in one side. p i (n) doesn't represent our final filter, it is only a truncated based sinc. The Role of transition bands of the filter is given below by the fig. \hyperref[fig_4]{5}.  Where, n is bounded as in equation. The filter impulse response contains 2?? ð??"ð??" +1 samples, that causes a signal extension in the time domain by 2 ?? ð??"ð??" samples. Fortunately, this kind of filter has the major part of its energy concentrated in the Sinc lobe, so the elongation is important just for a small time period during the CP of the symbol \hyperref[b9]{[19]}. For this reason, it is not necessary to choose Li to be very small, specifically ?? ð??"ð??" can be larger than ?? ð??"ð??"ð??"ð??" (length of the cyclic prefix). symbol, as typically done for CP-OFDM \hyperref[b5]{[15]}. The first ?? ??ð??"ð??" samples are denoted as "prefix", while the remaining ?? ð??"ð??"ð??"ð??" are denoted by CP. The W-OFDM symbol is then further extended by copying the first ?? ??ð??"ð??" + 1 samples of the native OFDM symbol at the end of the new W-OFDM symbol, as shown in the Figure  {\ref .} Native OFDM symbols in each sub-band may have different lengths; hence the parameter ?? ??ð??"ð??" is used to denote the prefix or suffix parameter for the ð??"ð??" ??? subband. At this point the W-OFDM symbol that is denoted as ?? ð??"ð??" contains ?? ð??"ð??" ?? =?? ð??"ð??" + ?? ð??"ð??"ð??"ð??" + 2?? ??ð??"ð??" + 1 samples \hyperref[b6]{[16]}. However, prefix and suffix both will be smoothed with a windowing operation, and then the suffix of the ð??"ð??" ??? W-OFDM symbol will be overlapped with the first ?? ??ð??"ð??" +1\par
The first operation is to extend the OFDM symbol by copying the last ?? ð??"ð??"ð??"ð??" samples of the native OFDM symbol at the beginning of the new W-OFDM the different modulation techniques such as BPSK, QPSK, 16-PSK, QAM, 8-QAM and 16-QAM. The signals are encoded via orthogonal space time block codes for transmission over the Rayleigh fading channel. Five independent antennas links are formed, out of which four are served as transmitting antennas and the remaining four are acting as receiving antennas. During the transmission through the channel, IDWT transformation is performed after the OSTBC encoding. For W-OFDM transmission, the information is first grouped and mapped according to the modulation and hen, is sent to inverse discrete wavelet transform (IDWT), which converts frequency domain signal into time domain signal and also provides orthogonality similarly for F-OFDM. The simulation adds white the Gaussian noise at the receiver process. Then, it combines the signals from both receive antennas into a single stream for the demodulation. Afterward, DWT is applied at the receiver side to reconstruct the signal in frequency domain. Total of 192 Samples per frame have been taken. Bits per symbol considered for the simulation is 100. W-OFDM and F-OFDM symbol rates are 10Ksps and the symbol period is 10-6s. The system is designed over four transmitting antennas and four receiving antennas (4 x 4) employing an independent Rayleigh fading for transmission of data.\par
V. The MIMO incorporated OFDM, W-OFDM and F-OFDM-WOFDM systems are modeled using Orthogonal Space Time Block Coding (OSTBC) technique, having symbol wise maximum likelihood (ML) decoding, to attain the high diversity gains in order to obtain higher data rates. The proposed system model is demonstrated in Fig. \hyperref[fig_6]{6}. For simulation, the random binary signal is created and modulated by employing         
\section[{System Model}]{System Model} 
\section[{Results and Analysis}]{Results and Analysis} 
\section[{PSD -40 dB}]{PSD -40 dB} 
\section[{Conclusions}]{Conclusions}\par
In this paper, the performance of MIMO-WOFDM system and its assessment with MIMO-OFDM, MIMO-WOFDM and MIMO-FOFDM systems by means of various modulations techniques is presented in this work. The SNR requirements for higher order PSK schemes are more to the acceptable range of BER over the simulated channel. It is also noteworthy that the higher orders of the QAM scheme have a little bit of significant influence over the performance of the both simulated systems. Moreover, QAM requests lesser SNR as contrast to PSK for suitable BER for both the systems. To analyze BER, PSD and signal to noise ratio with BPSK, QPSK, 16-PSK, QAM, 8-QAM and 16-QAM modulation it can be concluded that among three multiplexers (OFDM, W-OFDM, and F-OFDM) F-OFDM provides high performance and bandwidth efficient in the wireless system.\begin{figure}[htbp]
\noindent\textbf{1}\includegraphics[]{image-2.png}
\caption{\label{fig_0}Figure 1 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{2}\includegraphics[]{image-3.png}
\caption{\label{fig_1}Figure 2 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{3}\includegraphics[]{image-4.png}
\caption{\label{fig_2}Figure 3 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{4}\includegraphics[]{image-5.png}
\caption{\label{fig_3}Figure 4 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{5}\includegraphics[]{image-6.png}
\caption{\label{fig_4}Figure 5 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{6}\includegraphics[]{image-7.png}
\caption{\label{fig_6}Figure 6 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{}\includegraphics[]{image-8.png}
\caption{\label{fig_7}Global}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{7}\includegraphics[]{image-9.png}
\caption{\label{fig_8}Figure 7 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{8910111213}\includegraphics[]{image-10.png}
\caption{\label{fig_9}Figure 8 :Figure 9 :Figure 10 :Figure 11 :Figure 12 :Figure 13 :}\end{figure}
     \begin{figure}[htbp]
\noindent\textbf{1} \par 
\begin{longtable}{P{0.425\textwidth}P{0.425\textwidth}}
Parameter\tabcellsep Considerations for Simulation\\
Modulation Scheme\tabcellsep BPSK,QPSK,16-PSK,QAM,8QAM, and 16-QAM\\
Channel\tabcellsep Rayleigh Fading Channel\\
Multiplexing\tabcellsep OFDM, W-OFDM, F-OFDM\\
Samples per frame\tabcellsep 192\\
No. of transmitting \& receiving antennas\tabcellsep 4*4\\
Signal to Noise Ratio\tabcellsep 0 to 25dB\end{longtable} \par
 
\caption{\label{tab_0}Table 1 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{2} \par 
\begin{longtable}{}
\end{longtable} \par
 
\caption{\label{tab_1}Table 2 :}\end{figure}
 			\footnote{Year 2020 ( ) E © 2020 Global Journals BER Performance Analysis of OFDM, W-OFDM and F-OFDM for 5G Wireless Communications} 			\footnote{© 2020 Global Journals BER Performance Analysis of OFDM, W-OFDM and F-OFDM for 5G Wireless Communications} 		 		\backmatter  			  				\begin{bibitemlist}{1}
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