Polynomial-Based Compressing and Iterative Expanding for PAPR Reduction in GFDM Zahra Sharifian 1 , Mohammad Javad Omidi 2 , Arman Farhang 3 and Hamid Saeedi-Sourck 4 1 Isfahan University of Technology, Isfahan, Iran Email: z.sharifian@ec.iut.ac.ir 2 Isfahan University of Technology, Isfahan, Iran Email: omidi@cc.iut.ac.ir 3 CTVR / The Telecommunications Research Centre, Trinity College Dublin, Ireland Email: farhanga@tcd.ie 4 Yazd University, Yazd, Iran Email: saeedi@yazd.ac.ir Abstract—GFDM (generalized frequency division multiplex- ing) is a non-orthogonal waveform that is being discussed as a candidate for the fifth generation of wireless communication systems (5G). GFDM is a multicarrier technique with circular pulse shaping that is designed in a way to address emerging applications in 5G networks such as Internet of Things (IoT) and machine-to-machine communications (M2M). The same as other multicarrier systems, GFDM suffers from a high peak to average power ratio (PAPR). To attack PAPR problem, in this paper, we propose a polynomial based companding method with iterative expansion that is called polynomial-based companding technique (PCT). Based on our simulation results, a great amount of PAPR reduction can be achieved through utilization of our proposed technique. Through simulations, we have also investigated the bit error rate (BER) performance of the system while adopting our PCT method. Our simulations reveal that there is a tradeoff between PAPR reduction and BER performance. Keywords—PCT method, GFDM, PAPR, companding. I. I NTRODUCTION Due to their robustness against multipath fading chan- nels and the ease of equalization, multicarrier modulation techniques have been widely used in communication sys- tems. In particular, orthogonal frequency division multiplexing (OFDM) has been the technology of choice for a large number of wired and wireless standards, such as asymmetric digital subscriber loop (ADSL), [1], power line communication sys- tems, [2], LTE and WiMAX, [3]. However, OFDM has some limitations such as its large out-of-band emissions which is its limiting factor for utilization of non-contiguous spectrum and its sensitivity to synchronization errors specifically car- rier frequency offset (CFO). The advent of new applications such as machine-to-machine communications (M2M), i.e., the massive wireless connectivity of machines with each other without human intervention, and Internet of Things (IoT), [4], in the fifth generation of wireless communication systems (5G) imposes some requirements to the network. For instance, in the uplink of a network with a large number of embedded devices or machines where freuency division multiple access (OFDMA) is deployed, a large amount of multiple access interference (MAI) is caused by multiple CFOs. To avoid this interference, stringent synchronization is required which imposes a large amount of overhead to the network. In order to relax the synchronization requirements and hence reduce the network overhead, the MAI problem can be tackled with a wide range of different solutions that are proposed in [5]– [8]. However, these techniques lead to a large amount of receiver complexity which makes OFDMA unattractive for such applications. Hence, waveforms with a more relaxed synchronization requirements and more localized signals in time and frequency are needed to suit the future 5G net- works without the high MAI or receiver complexity penalty. To address these aspects, the innovative multicarrier systems have been candidate, namely Filter-bank Based Multicarrier (FBMC) [9], Universal Filtered MultiCarrier (UFMC) [10], Biorthogonal Frequency Division Multiplexing (BFDM) [11], and Generalized Frequency Division Multiplexing (GFDM) [12], which is the topic of interest in this paper. Based on its appealing properties, GFDM has been recently discussed as a candidate waveform for 5G and has received a great deal of attention, [11]. GFDM is a flexible multicarrier modulation scheme that can be considered as a subset of “filtered multicarrier techniques” [13]. From filter bank point of view, GFDM is an FBMC system with circular filtering in subcarrier level rather than linear filtering which is the case in the conventional FBMC systems. In this system, a two- dimensional block comprised of data symbols spread over time-frequency resources is communicated through circular pulse shaping that is known as tail biting, [12]. Tail biting preserves circular properties across time and frequency domain in order to prevent rate loss incurred due to long cyclic prefix (CP) requirement [12]. In other words, GFDM removes the ramp-up and ramp-down of the filtered multicarrier signal, i.e., due to the transient of the prototype filter, through circular pulse shaping. One of the major drawbacks of every multicarrier system is their high peak-to-average-power ratio (PAPR). To address this problem, essential features of GFDM such as possibil- ity of reducing the number of subcarriers and changing the parameters of the pulse shaping filter, are considered in [12] and [13]. However, in any multicarrier system, reducing the number of subcarriers always leads to PAPR reduction and does not solve the issue. As a result, there still is the need for reducing the peak values to the lowest level possible while having a large number of subcarriers. Despite the large 2015 23 rd Iranian Conference on Electrical Engineering (ICEE) 978-1-4799-1972-7/15/$31.00 c 2015 IEEE 518