5G Multi-Carrier Modulation Techniques: Prototype Filters, Power Spectral Density, and Bit Error Rate Performance

: In recent years for fourth-generation wireless communication systems Orthogonal Frequency Division Multiplexing (OFDM) multi-carrier modulation (MCM) has been an excellent choice. But for the fifth-generation air interface, the choice of multi-carrier modulation remains the biggest challenge. A potential multi-carrier modulation or candidate waveforms are required for the design of the physical layer. This paper highlights the merits and limitations of new candidate waveforms for fifth-generation wireless communication system. This paper mainly reviews Orthogonal frequency division multiplexing, Filtered-OFDM (F-OFDM), Universal Frequency Division Multiplexing (UFMC), Filtered Bank Multi-Carrier Modulation (FBMC), and Generalized Frequency Division Multiplexing (GFDM). This paper mainly reviews some of the comparisons of the parameters as power spectral density and bit error rate.


Candidate waveforms system model for 5G:
This section deals with some of the new candidate waveforms that are promised as an efficient multi-carrier modulation technique for 5G. The design of multicarrier modulation techniques is depended on the tendency of spectral containment, constraint on hardware, and propagation channel [16]. The problems that are identified using previous multi-carrier modulation techniques are inclined in Table 1.

Problem Parameters Reasons
Design Complexity To suit 5G applications which require complex transceiver.

Robustness
Work against hardware and software impairments.

Spectral Efficiency
Wider bandwidth has to be divided into smaller bandwidth which provides higher data rates.

Time Localization
It enables it to efficiently use TDD with low latency.
Scalability and Flexibility To achieve localization signals both in frequency and time domain and to support asynchronous requirements.

PAPR
To provide robustness over frequency and time channel selectivity and to attain large frequencies using power amplifiers.
To attain high data rates, high spectral efficacy, low latency, increasing battery life by reducing PAPR and mMIMO compatibility [17] a new candidate waveform is required for the design of the physical layer in 5G systems architecture. The waveform modulator block diagram is shown in figure 1. The information is sent in terms of pulses that overlap in frequency and time for multi-carrier systems. This becomes a great advantage as the pulses utilize a low bandwidth. The broadband channels which are frequency selective transform into multiple subchannels that are frequency flat and have less or zero interference. This enhances the simple equalizers that uses a single tap and is related in symbol detection using maximum likelihood (ML) in a situation of gaussian noise. This also simplifies the procedure of estimating the channel, provides adaptive coding and modulation procedures that are employed in mMIMO [18]. The mathematical expression for the sent signal of a multi-carrier system in the time domain is given as ………. (1) Where , = sent symbol at subcarrier position l and time position k. It is selected from a symbol alphabet which a QAM. The transmitted basis pulse is given as Where p(t) =Prototype filter with frequency and time-shifted version T = Time spacing F = Frequency spacing or Subcarrier spacing.
As the signal is sent over a channel the obtained symbols are decoded by projecting the obtained signal onto basis pulses and is given as It maximizes the SNR in an AWGN channel. The basis pulses are chosen differently at the transceiver based on the requirement. The multi-carrier system has to fulfill some of the important properties as given below: i. Density of a symbol (Maximum) TF =1 ii. Localization on time < ∞ and Localization on frequency < ∞

iii. Orthogonality
At least one of these required characteristics has to be compromised while designing the candidate waveforms system had been stated using Balian-Low theorem.

Cyclic Prefix Orthogonal Frequency Division Multiplexing (CP-OFDM) System Model:
CP-OFDM is mostly used candidate waveform in LTE and LTE-A [19]. To form complex symbols the digital data input is mapped using M-QAM or M-PSK modulation schemes. These complex symbols are  To reduce the computational complexity, CP-OFDM uses rectangular transmitter and receiver pulses. The transmitted pulse is little more than the receiver pulse. This is used to maintain orthogonality in channels thar are selected in frequency. The transmitter prototype filter (PF) is given as The receiver PF is given as Where T0 = Time Spacing The main disadvantage of CP-OFDM is as it has no control over OOBE due to rectangular pulse. The other limitations of CP-OFDM are high PAPR and transmission overhead due to CP insertion.

Filtered-OFDM (F-OFDM) System Model:
To enhance the network data rate a larger bandwidth has to be assigned for the 5G systems [20]. For 5G networks, F-OFDM is considered as one of the efficient candidate waveforms [21][22]. The F-OFDM transceiver is shown in figure 3. also creates subband filter of an anti-image which are used to eradicate the signals that contain image. One of the limitations of F-OFDM system is the use of non-ideal filters which causes a reduction in the performance of the system [23]. Because of using low dimension DFT there will be a reduction in system complexity and the filtering operation also helps in reducing the complexity by using the up-sampling procedure. By keeping a long filter length, the OOBE and interference reduce. In uplink transmission, the DFT spreading is employed to reduce PAPR. The obtained signal by using up and down sampling of the k-th subband is given Where V= M-point matrix of IDFT (Normalized) U= Matrix with factor K (Up sampling) v= Noise matrix.
The limitation of F-OFDM is higher complexity compared to OFDM but it supports multiple users or services. In F-OFDM systems of single rate the sampling rate is kept same for all subbands and is fixed. In F-OFDM systems of multi-rate, the sampling rate is variable and it uses low complexity low dimension DFT.
So that making F-OFDM suitable for 5G systems. Just using a small modification in general OFDM system FBMC system is designed. Each of the different subcarriers is filtered to reduce side lobes which reduce interference which in turn reduces the OOBE. There is no need of adding CP so increases in achievement of attaining high data rates. FBMC and OFDM has the same symbol density but CP is not used. It works with a principle of first designing a PF with p(t)=p(-t). It is orthogonal in nature for frequency and time spacing where, Time spacing is given as T=To and Frequency spacing is given as F=2/To. A Hermite PF for FBMC is given as

Filter Bank Multi-Carrier (FBMC) System
……….. (7) The PF is proposed based on Hermite polynomials Hn(.) [24] and its coefficients ai are can be referred from [25]. There is another type of PF used for FBMC that is PHYDYAS PF [26] and is given as The coefficients of bi are referred from [27]. The second principle of FBMC is to reduce orthogonal by a factor of two for time spacing that is T=T0/2 and F=1/T0. The last principle is of shifting the induced interference to purely imaginary domain and the phase shift is given as

Universal Filtered Multicarrier (UFMC) System Model:
It is a candidate waveform that employs subcarrier filtering. The efficacy of UFMC is good in comparison to OFDM in terms of BER and sidelobe attenuation [28]. UFMC is candidate waveform is also the same as F-OFDM and FBMC candidate waveform. In UFMC a group of subcarrier modulation is done. The length of the filter and performance time is reduced based on the grouping of subcarrier. The transceiver of UFMC is shown in figure 7. The received signal Y has N length-frequency domain odd subcarrier points by eliminating even subcarrier points. To detect the sent signal equalization is performed and symbol de-mapping is performed before equalization to the exact data bits.

Generalized Frequency Division Multiplexing (GFDM) System Model:
GFDM is nonorthogonal in nature [29]. It has become one of the promising multi-carrier modulations for 5G systems. The main advantage of this GFDM is it provides low latency, low PAPR, low OOBE, and low adjacent channel leakage ratio. It has a flexible transceiver design. It provides a high degree of freedom for transceiver design which makes it to be useful in many types of applications such as cognitive radio and full-duplex radio.
GFDM based cognitive radio and full-duplex radio are good answers for spectrum management in 5G systems. The transceiver of GFDM is shown in figure 8. GFDM is a block-based candidate waveform [30]. It has K subcarriers with every transmitted M complexvalued sub symbols. The total number of transmitted signals within the block is given as The pulse shaped vector for the GFDM block is given as With the m th symbol on the k th subcarrier. The prototype of the filter is given as The transmitter sample vector is given as x = Ad …………… (16) Where A = Transmitter matrix d = GFDM block for ∈ ∁ The transmitter sample vector is given as ………… (17) Parallel to serial conversion is performed after transmitting x and CP is added with a length L which generates GFDM digital baseband transmit signal. The baseband receiver output is given as Where h= Impulse response of casual LTI system with N-tap wireless channel x= Transmitted vector w= AWGN noise vector The frequency selective multipath channel is modeled as circular convolution [31] with a combination of CP and linear convolution. Therefore, the receiver vector is obtained after removing CP, and serial to parallel conversion is performed and is given as        The comparison of a Bit Error rate of all candidate waveforms concerning SNR is shown in figure 15. The figure shows that as there is a rise in the SNR the BER of the UFMC reduces compared to other multi-carrier modulation techniques. The comparison of a Bit Error rate of OFDM and GFDM concerning SNR is shown in figure 16. The figure

Results and Discussion
shows that as the SNR value increases the BER of the GFDM reduces compared to OFDM.

Conclusion:
There is a rapid increase in connectivity of the wireless system, almost an exponential rise in wireless data. The next generation 5G WCS is been a promising technology for an increase in high data rate, QoS, and connectivity. A new application such as IoT, IoV, and smart grids are supported under the 5G WCS. There are many promising candidate waveforms for 5G WCS such as FBMC, UFMC, F-OFDM and GFDM, and many more. Compared to OFDM the other candidate waveforms are best suited for the 5G WCS. The PSD and BER performance of all multi-carrier modulation techniques is shown in this paper where a 16QAM modulation scheme is employed. As GFDM is a non-orthogonal multi-carrier modulation scheme its performance is compared only with the OFDM as it is mainly supported for the cognitive radio application.

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