In OFDM multicarrier system, the frequency spectrum of the subcarriers is overlapped with the least frequency spacing and the orthogonality is attained amid the various subcarriers. In Figure 1, the input stream is subdivided into parallel data streams by means of the serial to parallel (S/P) converter, that are then passed into an inverse fast Fourier transformation (IFFT) block to produce time sequence of the streams. Consequently, by totalling a cyclic prefix (CP), the OFDM symbol time sequences are extended. The CP is a copy of the latter portion of the symbol that is added in the start of the sequence and should be greater than the network deferral spread in order to diminish the inter symbol interference (ISI) produced by the influx of various OFDM symbols with distinct delay. The resultant digital signal is transformed into analog form and transmitted over the channel [5] .

At the receiver end, the signal is reconstructed into digital form and the far Fourier transform (FFT) is achieved in the received streams after eradicating the CP [5] . Finally, the parallel streams are collected into a single stream as the original transmitted one. Some of the disadvantages of OFDM are enumerated below:

1) Decreased spectral efficiency owing to the CP employed;

2) High spectral leakage owing to the rectangular windowing;

3) Interference amid the unsynchronized signal in the neighbouring bands.

The FBMC technique overcomes the limitations of OFDM by adding generalized pulse shaping filters which delivers a well localized subchannel in both time and frequency domain. Consequently, FBMC systems have more spectral containment signals and offer more effective use of the radio resources where no CP is required. In Figure 2 it can be seen that the filterbanks on the transmitter side and the receiver side consist of an array of N filters that processes N input signals to give N outputs. If the inputs of these N filters are associated together, the system in analogous manner can be measured as an analyzer to the input signal based on each filter characteristics. In Figure 2 the filter bank used at the transmitter side is called synthesis filter bank and the filter bank used in receiver side is called analysis filter bank. As depicted in Figure 2 the input signal is first converted from serial to parallel form and then passed through synthesis filter bank and then it is converted back to serial form after coming out of synthesis bank. After this it can be seen in Figure 2 that in the receiver side after the signal passes through the channel it is converted to parallel form by serial to parallel converter and passed through analysis filter bank. Finally when the output signal is obtained it is again converted to serial form by parallel to serial converter. [7] . Hence the synthesis-analysis configuration depicted in Figure 2 is called transmulitplexer or TMUX and is applied in the MC communication systems [8] .

The TMUX system transmits OQAM symbols instead of QAM symbols. The pre-processing block, which utilizes the transformation between QAM and OQAM symbols, is shown in Figure 4. As can be seen, the first operation is a simple complex-to-real conversion, where the real and imaginary parts of a complex-valued symbol c k , l are separated to form two new symbols d k , 2 l and d k , 2 l + 1 (this operation can also be called as staggering). So the order of these original symbols depends upon the sub channel number, i.e., the conversion is distinct for even and odd numbered sub channels. The complex-to-real conversion upsurges the sample rate by a factor of 2. After this the second operation is the multiplication by θ k , n sequence [9] .

A possible choice is

θ k , n = j ( k + n ) (1)

However, it should be noted that the signs of the θ k , n sequence can be chosen arbitrarily, but the pattern of real and imaginary samples has to follow the above definition. For example, an alternative sequence

θ k , n = { 1 , j , 1 , j ⋅ ⋅ ⋅ for k even j , 1 , j , 1 ⋅ ⋅ ⋅ for k odd   (2)

The input signals are purely real or imaginary-valued after the OQAM pre-processing.

The post-processing block is shown in Figure 5 and again there are two slightly different structures depending on the sub channel number. The first operation is the multiplication by θ k , n * sequence that is followed by the operation

of taking the real part. The second operation is real-to complex conversion, in which two successive real-valued symbols (with one multiplied by j) form a complex-valued symbol c ^ k , n (this operation is also called as de-staggering). The real-to-complex conversion decreases the sample rate by a factor 2. As can be seen, the first operation is a simple complex-to-real conversion, where the real and imaginary parts of a complex-valued symbol c k , l are separated to form two new symbols d k , l and d k , 2 l + 1 (this operation can also be called as staggering). The order of these new symbols depends on the sub channel number, i.e., the conversion is different for even and odd numbered sub channels. The complex-to-real conversion increases the sample rate by a factor of 2. The second operation is the multiplication by sequence θ k , n . [9] .

A direct form SFB consists of M up samplers and M synthesis filters. As shown in Figure 3, the input signals X k ( z ) , where k = 0 , 1 , 2 , ⋅ ⋅ ⋅ , M − 1 , are first up sampled by M/2 and then filtered with synthesis filters G k ( z ) The SFB output signal Y(z) is formed when all sub signals are added together. A direct form AFB is constructed using M analysis filters and M down samplers as shown in Figure 3. The input signal Y(z) is first filtered by analysis filters F k ( z ) and these signals are then down sampled by a factor of M/2 to form output signals X k ( z ) . In the case of chosen class of complex modulated filter banks, all sub channel filters can be generated from a single real-valued linear-phase low pass prototype filter p[m] by using exponential modulation. Due to the modulation function, the resulting sub channel filters are complex-valued and therefore the useful frequency range is [ − π , π ] . Typically, two different types of channel stacking arrangements can be considered, namely, even-stacked filter banks and odd-stacked filter banks. The center frequencies of the k^th sub channel filters are w k = 2 k π / M and ω k = ( ( 2 k + 1 ) π ) / M for even stacked and odd-stacked filter banks, respectively. The k^th synthesis filter is given by

g k [ m ] = p [ m ] exp ( j 2 π k m ( m − L p − 1 2 ) ) m = 0 , 1 ⋅ ⋅ ⋅ , L p − 1 (3)

where m = 0 , 1 ⋅ ⋅ ⋅ , L p − 1 and L p is the filter length. In order to simplify notations, it is assumed that the prototype filter is designed in such a manner that there is no need for the additional scaling factor. The k^th analysis filter is simply a time-reversed and complex-conjugated version of the corresponding synthesis filter

f k [ m ] = g k * ( L p − 1 − m ) = p ( L p − 1 − m ) exp ( 2 π k m ( L p ( 1 − m − L p − 1 2 ) ) ) = p [ m ] exp ( j 2 π k M ( m − L p − 1 2 ) ) (4)

An interpretation to the above equations is that first zero-phase sub channel filters are generated from a linear-phase prototype filter and then their impulse responses are delayed by ( L p − 1 ) / 2 samples resulting in causal subchannel filters. Due to the nature of the modulation function, the m^th sub channel filter is purely real and the M/2^th is purely imaginary. However, all the sub channel filters have linear phase.

Power spectral density of the FBMC transmit signal is designed to give the low out-of-band leakage. In Figure 6 and Figure 7 the plots of the spectral densities for OFDM and FBMC schemes are compared. In Figure 6 it depicts that the FBMC has lesser side lobes. This lets an advanced utilization of the allotted spectrum, leading to advanced spectral efficiency. In Figure 7 the OFDM PSD curve has higher side lobes and out of band leakage. Hence the FBMC scheme is more advantageous in comparison to OFDM by providing higher spectral efficiency. Owing to the per subcarrier filtering, it suffers a larger filter delay (in comparison to UFMC) and also needs OQAM processing.

The computational complexity of filter bank structures can be evaluated by calculating

the number of real multiplications and additions that are necessary to compute a new length-complex-valued output sequence. However, the analysis is just based on the number of multiplications because it is a known fact that adders are considerably cheaper to implement than multipliers. So the Figure 8 depicts that the FBMC is more complex than the conventional OFDM. Here the number of real multiplications as a function of number of sub channels in the case of OFDM and FBMC has been observed. Also when using the polyphase implementations of FBMC the complexity increases as depicted in Figure 8 but decreases when FBMC is implemented without the polyphase.

The main difference between FBMC and OFDM is the choice of the prototype filter. Such that OFDM uses a rectangular window filter and FBMC using a prototype filter designed with the Nyquist pulse shaping principle, which can reduce greatly the spectral leakage problem of OFDM. This results in negligible ICI and ISI. In Figure 9 the magnitude responses of prototype filters of FBMC and

OFDM have been compared against the normalized frequency taken on the x axis.