Filtered orthogonal frequency division multiplexing for improved 5G systems

Received Dec 5, 2020 Revised Mar 29, 2021 Accepted Jun 17, 2021 Wireless communications became an integrated part of the human life. Fifth generation (5G) is the modern communication which provides enhanced mobile broadband (eMBB), ultra reliable low latency communications (URLLC), and massive machine type communication (mMTC). Thus, 5G have to provide coverage to multi-numerology devices, therefore, modulation and access schemes are suggested in the literature such as cyclic prefix orthogonal frequency division multiplexing (CP-OFDM) and filtered OFDM (f-OFDM). CP-OFDM suffers from the high out of band emission which limited the multi-numerology applications. In f-OFDM, the out of band emission can be suppressed to an accepted extent such that different numerologies can be coexisting. On the other hand, f-OFDM can be more improved by using a proper filtering approach. In this paper three different filters are suggested based windowed-sinc function; Hanning, Hamming, and Blackman. Simulation results show that the proposed filters are promising for high spectral efficiency and out of band emission rejection. Furthermore, the bit error rate, error vector magnitude, and power spectral density are further improved with respect to CP-OFDM scheme but some trade-off is present. Overall, the suggested windowed-sinc filters are outperforming the traditional CP-OFDM. As a conclusion, the suggested windnowed-sinc filters have no limitations on the modulation order or the number of subcarriers utilized in the system.


INTRODUCTION
Previous wireless generations, particularly the 4th generation (4G), is deployed worldwide. During technology development, numerous services are demanded, including internet of things (IoT) [1]. Massive machine type communication (mMTC) [2] are critical devices that demand fast data rate with sporadic transmission nature [3]. Thus, beside the traditional voice origination call, more services have to be supported; such as video streaming and virtual reality applications [4]. Long term evolution (LTE) and LTE-advanced (LTE-A) which is the technology developed for 4G wireless systems became uncapable to support these various numerologies. In fact, LTE based systems are built around cyclic prefix-orthogonal frequency division multiplexing (CP-OFDM). The subcarrier spacing in CP-OFDM is fixed, which leads to one-only numerology. The term numerology stands for subcarrier spacing, as Δf=15 kHz × 2μ, where μ is called numerology [5]. The 4G, as mentioned above, has fixed numerology which is μ=0, in other words subcarrier spacing Δf=15 kHz. To support the various services requirements, 5th generation (5G) has been designed to employ various numerologies, in which different services can be utilized.
In other words, technology continued to be developed, then novel frameworks are invented which may require access to the wireless networks. That is why extra mandated loads have to be available by the wireless network. The traditional voice origination calls and data transferring will be alongside new services, which are revealed every day. On account of this, and beyond 4G, 5G should be capable to deliver different signal forms to cover all new services. Wireless sensor networks are one of the mMTC which circumvents messages of long format, moreover IoT are another type of systems which avoids long messages [6], thus, essential modification to the traditional signal, represented by 4G LTE signals, are mandatory to tackle the coming problems [7]. Customizable waveform-shapes became obligatory to manage the vital specifications. On the other hand, additional information for synchronization is necessary in 4G, which must be released in 5G, this leading to asynchronized communication [8].
The conventional CP-OFDM, which is the modulation and access scheme employed by 4G LTE wireless system, is incompetent to cover the above necessities. In CP-OFDM, the out of band (OOB) emission is significantly effective in the time-domain leading to necessary synchronizations both in time and frequency, because the OOB emission generated interference with neighbor channels [9]. Strained synchronization emerging additional time (latency) for the system to work properly, this increased latency necessitates more power consumption, therefore, mMTC cannot be deployed with 4G system because mMTC operates with limited life-time battery [10].
On the other hand, channel estimation is worth to mention here, since it is an important part of the data recovery process at the receing end. Different optimization schemes are listed in the literature. However, two main categories for channel estimation can be said as blind and non-blind techniques. The first category does not send pilot carriers as a reference signal, while the second category does send these pilot symbols as reference signals to aid the receiver to recover the data properly. The non-blind category has further two main sub-categories, block-type and comb-type. There are other combinations in the literature, but the most famous are the block and comb types [11]. The block type is used when the channel looks like do not change the state or it is indoor behaviour. While the comb type is sending the pilot carriers with certain spacings. Optimizing these pilot carrier's location is favorable to enhance the system behaviour [12]. Aforementioned that 5G system designated to operate such that it provides services to eMBB, mMTC, and URLLC. Hence, various numerologies must be provided in order proper operation. Each one of these services has its own numerology, or signal format, signal size, overhead, for the eMBB. Specifically, Δf, cyclic prefix (CP) size/duration, and slot/subframe duration. Over gigabits/second data throughput is the part of eMBB communications, for instance, over 20 Gb/s. Smart homes/cities are examples of the mMTC. While ultra high definition streaming augmented reality, self-driving machines are sexampls of URLLC [8].
As a result, the physical layer of the new system has to be very elastic. Fortunately, signals can be formed flexibly. Thus, the literature is rich of waveforms that fits to the 5G system but with trade-offs. Namely, filter bank multicarrier (FBMC) [13], universal filtered multicarrier (UFMC), aka universal filtered OFDM (UF-OFDM) [10], generalized frequency division multiplexing [14], and the filtered OFDM (f-OFDM) [15]. These mentioned waveforms are all based on filtering operation. Industry and academia communities paid much attention for such types of waveforms, because filtering-based waveforms are outperforming the conventional CP-OFDM waveform [16]. Each of these filtering-based waveforms have its cons and pros. In particular, subcarrier filtering achieved in FBMC and GFDM have to employ the offset/staggered digital quadrature amplitude modulation (QAM), consequently, these two waveforms are not friendly with multiple input multiple output (MIMO) multiplexing schemes [17], [18]. UFMC waveform outperforms FBMC and GFDM but at the cost of filter size but not comparable to f-OFDM where the filter size is more realistic [15], [19], [20], accordingly, f-OFDM can be the promising based waveform for the 5G wireless systems.
In account of the previous discussion, filter design must be smartly designed in order to not increase latency of complexity to the system. Furthermore, waveforms based on filtering must fit the requirement which are stated previously for the 5G system. Worthy say that CP-OFDM exploits the sinc-function based filter in the frequency domain. The sinc-based filter grieves high sidelobes, which are considerably degrades the system performance. A systematic direct implementable filter can be used to originate the f-OFDM waveform [21]. This filter is called truncated-sinc filter. This filter can be generated by windowing the sincfunction with properly and smartly selected window. Thus, it was shown that windowed-sinc filter based f-OFDM outperforms CP-OFDM waveform.
Abdoli used Hanning-window [19], [22]. In another suggestion, Bazzi proposed to use Von Hann window, following the same procedure of Abdoli, however, an outperforming behavior with respect to FBMC and UFMC, but the OOB emission can be recognized significantly [23]. It is necessary and essential to avoid additional computational complexity, since the latency increased, C. An  that destroys the latency due to the additional computational complexity, where windowing/filtering is configured according to the location of the filter or the window, thus, four configurated schemes produced but at the cost of the degraded latency [24]. The Gaussian window-based filter proposed in other work aiming to reduce the OOB emission [25]. However, Gaussian based filter destroys the orthogonality between subcarriers, this loss in orthogonality produces intercarrier interference (ICI) as well as intersymbol interference (ISI). On the other hand, the finite impulse response (FIR) is another suggestion to overcome the OOB problem. It is found that the OOB problem was resolved but the computational complexity was degraded significantly [26].
In 2019, a confirmation result of [15], [19] was obtained where the OOB emission still recognized leading to loss of the synchronization [27]. The computational complexity of filtered based waveforms was suggested, which is the singular value decomposition (SVD) methodology [28]. Although the reduced complexity and OOB emission enhancements, the BER of the system was degraded.
In this paper, the physical layer of 5G wireless systems will be simulated using three different windowed-sinc filters, Hanning, Hamming, and Blackman based filters. The results will be compared fairly with the conventional CP-OFDM in terms of OOB emission rejection, BER improvement performance, error vector magnitude. Specifically speaking, the contribution of this paper is that these filters will be link level simulation and the throughput for 100ms transmission interval will be used with MIMO of eight transmitting and two receiving antennas will be employed for the downlink direction. Such link level implementation has not been achieved in the literature, at least, with the author's point of view. Thus, this paper can be a useful resource for the researchers and academia.

SYSTEM MODEL AND FILTER DESIGN
The system which will be simulated in this work can be seen in Figure 1. The difference between f-OFDM and CP-OFDM is that the filter fi(n) is not applicable in CP-OFDM, that is, both CP-OFDM and f-OFDM can be represented in Figure 1, which is the basic components to generate the physical layer for downlink link-level simulation. The binary stream of each sub-band will be first mapped to one of the QAM orders, according to the payload. Serial to parallel conversion (demultiplexing) is the next step followed by frequency-domain to time-domain conversion using the N-points inverse fast fourier transform (IFFT), then converting back to the serial form using during the parallel to serial block (multiplexing). To combat the multipath channel, the CP is inserted. The last operation is the filtering operation which will be applied only to generate the f-OFDM waveform as shown in the upper part of Figure 1. The lower part of Figure 1 stands for the receiver end, which follows the reverse operations of the transmitter. The transmitting operation can be expressed mathematically by adjusting various sub-band configurations, which are obtained using distinct numerologies, i=1, 2 … I, where I represents the number of individual sub-bands, The (1) can be seen as CP-OFDM when removing the filter fi(n). Hence, each individual sub-band is completely representing a separated CP-OFDM symbol. Accordingly, f-OFDM is flexible in its construction with different numerology. At the receiving end, matched filtering used to remove the effect of the fi(n) filter, which can be represented as, That is, removing the CP, serial to parallel achievement, time to frequency conversion using fast fourier transform (FFT), then, parallel to serial multiplexing, finally detecting the signal (de-mapping). The deployed filtering in 4G LTE signal is the sinc-function windowed by rectangular window. Hence, the sinc function is multiplied by one. Accordingly, OOB emission is recognized. On the next side, f-OFDM, in this work, made use of Hanning, Hamming, and Blackman based windowed-filters, s1(n), s2(n), and s3(n), respectively [29], where p is the window size and n=-p/2, …, -1, 0, 1, …, p/2. Accordingly, windowed-sic filter can be formulated Having described the core of the physical layer, it is worth describing the air interface structure of 5G systems and its difference with respect to 4G system. First, refer to Figure 2. There is frame structure extends to 10ms, each frame divided to 10 sub-frames, each is 1ms. Each sub-frame consists of 2-time slots, each of 0.5ms. there are 7 or 6 OFDM symbols in each time slot according to the CP length. This description is shown in Figure 2 as the time-axis. The vertical axis of Figure 2 represents the frequency-domain representing the OFDM subcarriers. Each 12-adjucent subcarriers constitute the resource block (RB) with duration of 0.5ms (one-time slot). The resource element (RE), on the other hand, is the smallest part in the resource grid (RG) shown in Figure 2, where one RE is consists of one OFDM symbol. It can be seen that there are different dimensions in the RG; this is the main con in the 5G flexible structure of the RBs. That is, according to Δf=15KHz × 2μ, the subcarrier spacing will be Δf=15KHz, 30KHz, 60KHz, 120KHz, and 240KHz [30]. In 4G systems, subcarrier spacing is fixed to 15KHz; therefore, 4G RG is not as flexible as 5G system.
The link level simulation is that the physical downlink shared channel (PDSCH) will be constructed (using properly designed toolbox in MATLAB) to determine the achieved throughput. Figure 3 depicts the link level round-trip in this work. First, binary data coded to the transport shared channel, then it will be coded to the PDSCH where the demodulation reference symbol (DM-RS) will be generated and synchronization signal (SS); primary and secondary (PSS, SSS) respectively, are also mapped in the PDSCH. Then, precoding achieved before the different numerologies employed in the construction of the CP-OFDM/f-OFDM block.
Clustered delay line (CDL) channel will be the medium to propagate the signal with additive white gaussian noise (AWGN) as shown in Figure 3. At the receiver, timing/synchronization is the first step accomplished to synchronize the transmitter with the receiver, then demodulation according to the used modulation type in the transmitter (CP-OFDM or f-OFDM). After that, channel estimation [31] is used to detect and decode the PDSCH, from which the DL-SCH transport channel can be deduced. Finally, the binary data will be outputted. However, the hybrid automatic repeat-request (HARQ) is used to find if it is required to retransmit the signal again by detecting the cyclic redundancy check code of the last transmitted signal as shown in Figure 3 [30]. In the next section, simulation results will be evaluated for a specific parameter according to the standards of the third generation partnership project (3GPP) [30].

RESULTS AND DISCUSSION
To be a fair comparison between CP-OFDM and f-OFDM, the subcarrier spacing is fixed to 30 KHz, both waveforms have the same CP length, and number of RBs=51, each consists of 12 subcarriers, two receive antennas and eight transmit antennas, consisting 8×2 MIMO system, without perfect channel estimation for the CDL propagation channel, as shown in Table 1. That is, channel estimation is accomplished using the DM-RS symbols, which are available in the PDSCH. The size of the OFDM symbol will be also fixed to both CP-OFDM and f-OFDM, N=2048 is the number of subcarriers. Number of codewords mapped in the PDSCH is one. In Figure 4 Figure 4 is based on the 64QAM constellation mapping. While Figure 5 presents the BER performance comparison of the 256QAM for the CP-OFDM and f-OFDM waveforms.
The BER curves in Figure 4 show that Hanning based signal outperforms the other waveforms, while the other waveforms are almost identical to the performance of the CP-OFDM signal. On the other hand, the BER of the waveforms shown in Figure 5, which are based on higher order constellation mapping, are all have the same performance. This shows that at higher orders of baseband mapping, the BER did not change dramatically. To a fair comparison, it is worth to examine the EVM and MER results. Thus, the peak EVM results are -10.2dB, -10.8dB, -12dB, -12.2dB for the 64QAM CP-OFDM, Hanning, Hamming, Blackman based f-OFDM waveforms, respectively. Thus, the performance of Blackman based f-OFDM is outperforming the others with respect to CP-OFDM signal. When the constellation order became 256QAM, the EVM became -11.9dB, -12.8dB, -13.1dB, -13.8dB, for the CP-OFDM, hanning, hamming, and blackman based f-OFDM waveforms, respectively. Accordingly, Blackman based waveform outperforms the others, with respect to CP-OFDM signal. The power spectral density (PSD) of the simulated signals are shown in Figure 6. It is obvious that Blackman based f-OFDM waveform has the most outperforming behavior among other f-OFDM waveforms as compared to that of CP-OFDM, where CP-OFDM has sidelobe level around -60dBW/Hz, while Blackman based signal is very low. While Hamming based signal is about -110dBW/Hz, which is higher than Blackman but still better than that of CP-OFDM signal. .  On the other hand, the system throughput can be seen in Figure 7 where a comparison between CP-OFDM, Hanning, Hamming, and Blackman based f-OFDM waveforms are drawn. It is shown that CP-OFDM performance is lower than other based f-OFDM signals. The outperformed behavior was recognized for the f-OFDM waveform based Blackman windowed-sinc, where the achieved throughput was 7.25Mbps at SNR=20dB based on 256QAM mapping, while the same waveform based on 64QAM mapping, the achieved throughput was 5.5Mbps. Other filtered waveforms are 5.8Mbps and 6.8Mbps for the 256QAM Hamming and Hanning based waveforms, respectively. While the same waveforms based on 64QAM, the accomplished throughputs are 4.2Mbps and 5Mbps, for the Hamming and Hanning based waveforms, respectively. These results confirm the performances shown in Figure 6, which is the PSD of these waveforms. That is, according to the PSD of CP-OFDM, the expected throughput should be the lowest among others, since the OOB emission was higher than other waveforms. While Blackman based waveform shows lowest level of OOB emission, where it was explained in the last paragraph that the PSD that Blackman based f-OFDM waveform has the most outperforming behavior among other f-OFDM waveforms.

CONCLUSION
In this paper it was shown that the throughput of the filtered based waveforms, particularly speaking, f-OFDM was improved with respect to that of CP-OFDM. However, it is concluded that the baseband constellation mapping did not put limitations on the f-OFDM based signals. Furthermore, the OOB emission was lower than the CP-OFDM, which is one of the main requirements for the 5G wireless systems, by which the latency has been reduced dramatically.