Performance comparison of multicarrier communication systems over doubly-selective channels

To mitigate the effect of 5G wireless channel, new multicarrier with robust features and waveform needs to replace the conventional OFDM system. In this study, three adopted multicarrier systems are employed and compared with OFDM including FBMC, FOFDM and UFMC over 5G channel. The BER performance, PAPR and PSD are compared with OFDM system. One tap frequency domain equalizer is used with all multicarrier systems and test the performance over 5G channel. The consequences show that, FBM has the best BER at high Doppler spread and has lowest PSD. In the other side, FBMC has highest PAPR comparing with other multicarrier system.

where the number of subcarriers is act by N, N g is the number of guard samples. Also, a QAM detection symbols is obtained at the reception using Fast Fourier Transform (FFT). The recovered sequence after removed the cyclic prefix signal is a. OFDM transmitter system b. OFDM receiver system

FBMC/OQAM system
The transceiver scheme of FBMC/OQAM is plotted in Figure 2. At the transmitter side, the information bits is passing through QAM mapping and the k-th subcarrier of the l-th time, ( ), is obtained. To obtain offset QAM (OQAM) signal, OQAM pre-processing stage is required. The complex signal ( ) is converted to real signal using complex-to-real conversion and separated to new two signals ( ) and ( + 1). The complex to real transform is different for even and odd numbered sub-channels and can be written as where Re (.) and Imag (.) are real and imaginary part of the signal, respectively. The signal ( ) is multiplied by ( ) = + to obtain the orthogonal symbols. The OQAM signal, ( ), is expressed as ( ) = ( ) ( ) (5) In this case the sampling rate of ( ) is double that of an OQAM signal. The synthesis filter bank of FBMC is implemented with efficient design using polyphase filter branches. The OQAM signal is multiplied by the phase ( ) and then taking IFFT transform. The transmitted signal of a FBMC/OQAM modulation is written as [6], [19] ( where M is the sub-channel number, ( ) is the k-th subcarrier and n-th time of the phase multiplier which is expressed as [21]: Also, L p is the prototype filter length, p(m) is prototype filter. There are different prototype filters, the best one is Hermite filter that depends on Hermite polynomials H n (·) [20] ( ) = where the parameters are 0 =1.412692577, 4 = −3.0145 · 10−3 8 =−8.8041 · 10−63 12 =−2.2611 · 10−9, 16 =−4.4570 · 10−15, , 18 =1.8633 · 10−16 . Hn( ) of order n can be calculated from the recursive relations [14]: H 0 ( )=1, H n+1 ( )=2e H n ( )-́( ), where ́( ) is the derivative of H n ( ) with respect to e. T 0 is a time-scaling parameter that based on subcarrier spacing. All the operations is reversed in the receiver side as shown in Figure

FOFDM communication system
The block diagram of FOFDM transceiver system is illustrated in Figure 3. It is clear that the FOFDM system is identical to OFDM system except that the FOFDM transmitted signal, (m), is obtained by convolve the transmitted OFDM sequence, s(m), with a filter sequence f(m) as [11]: where * is the convolution function and f(n) is a FIR filter and is written as: where ( ) is the ideal linear phase filter and w(m) is window function. Different window functions can be used such as Hamming, Hanning, Kaiser, Chebyshev or Blackman window [11]. In this paper Hanning window is used. a.

UFMC Communication System
UFMC has the features of OFDM, FBMC, and FOFDM in which blocking a full range of OFDM system into sub-bands without needing to cyclic prefix. The scheme of transceiver UFMC system is illustrated in Figure 4 [15]. At the transmitter, the input data is converted to B sub-blocks, QAM mapping is used to convert the data bits into symbol level, , , = 1, . . , , k=0,..,N-1 . Each output of sub-block is passed through N point IFFT representing with , , = 1,2, . . , , = 0, . . , − 1. The output of IFFT will be serialized and passing through filter representing with , , i=1,..,B, k=0,..,N-1. The filter used in this paper, is Dolph-Chebyshev window filter with order L [9], in this work 60 dB side lob attenuation is used. The transmitted signal of UFMC is expressed as [15]: At the reception side, the received signal is passing through FFT function and then one tap frequency domain equalizer is taken for each subband. Finally, QAM demapping is used to detect the original bits. a.
UFMC transmitter system b.
UFMC receiver system

One-Tap channel equalizer
In multicarrier transmissions, the reception sequence of the -th time and k-th subcarrier is decomposed by: Since the imaginary interference is orthogonal to the desired sequence, it has no effect on the performance. Then, a simple one-tap Zero-Forcing (ZF) equalizer obeyed by nearest-neighbor-detection is represented by [21] ̂, = , ℎ ,

Simulation results
In this simulation, OFDM, FBMC, FOFDM, and UFMC modulations are investigated and compared using MATLAB 2018. The comparison is made using BER, PAPR, and PSD measures. Two types of 5G channel are used: vehicular channel model A that is the fast fading channel and pedestrian channel model B that is slow fading channel. The channel Model parameters is listed in Table 1. Table 2 shows the main parameters of the simulation. It can be seen that the behavior of FBMC, FOFDM and UFMC are approximated identical and outperform the performance of OFDM in slightly. Also, increase the order of QAM will degrade the BER performance of the systems. Figure 6 shows the BER comparisons between MC systems over Vehicular-A channel with subcarriers 200, 64 QAM and different velocities. From this figure, the BER of FOFDM and UFMC systems are approximated the same of that OFDM. At low velocity (10 km/h), FBMC appears to be the worst one comparing with others but with high velocity FBMC BER becomes the best. In high velocity, one tap equalizer becomes inefficient and need another stronger equalizer. Figure Figure 9 shows the CCDF comparisons for different subcarriers. From these figures, it can be seen that FBMC has the largest PAPR and OFDM has the lowest PAPR. FOFDM has approximately the same PAPR as OFDM. UFMC has lower PAPR than FBMC. Increasing either the order of QAM or subcarrier number will increase the PAPR value for all MC systems. Figure 10 shows the PSD comparisons between different MC systems with 64 QAM and 24 subcarrier number. It can be seen that, FBMC has the lowest PSD comparing with other systems.

Conclusion
In this paper, the comparisons and parametric investigations between different multicarrier systems including OFDM, FBMC, FOFDM and UFMC are carried out across 5G channels. The comparisons is made using BER performance, PAPR and PSD analysis. Two channels are taken that are Vehicular-A and Pedestrian-B channel with different scenarios and parameters. The results show that FBMC has the best BER at high velocities and the best PSD comparing with other MC systems. Also, FBMC has the worst PAPR than other MC systems.