1 Enhanced Orthogonal Frequency-Division Multiplexing with Subcarrier Number Modulation Shuping Dang, Member, IEEE, Guoqing Ma, Student Member, IEEE, Basem Shihada, Senior Member, IEEE, Mohamed-Slim Alouini, Fellow, IEEE Abstract—A novel modulation scheme termed orthogonal result in higher system complexity and larger device size. frequency-division multiplexing with subcarrier number modu- However, with the advancement of the Internet of Things (IoT) lation (OFDM-SNM) has been proposed and regarded as one of and machine-type communication (MTC) networks, commu- the promising candidate modulation schemes for next generation networks. Although OFDM-SNM is capable of having a higher nication nodes are miniaturized and simple, which might not spectral efficiency (SE) than OFDM with index modulation be able to afford such a high-complexity structure yielded by (OFDM-IM) and plain OFDM under certain conditions, its reli- SM and SSK [4]. ability is relatively inferior to these existing schemes, because the Subcarrier-index modulation (SIM) orthogonal frequency- number of active subcarriers varies. In this regard, we propose division multiplexing (OFDM) was proposed as the first an enhanced OFDM-SNM scheme in this paper, which utilizes the flexibility of placing subcarriers to harvest a coding gain in the attempt to extend the gist of SM to the frequency domain high signal-to-noise ratio (SNR) region. In particular, we stipulate in order to solve the aforementioned issues regarding system a methodology that optimizes the subcarrier activation pattern complexity and device size. There are two different versions of (SAP) by subcarrier assignment using instantaneous channel SIM OFDM proposed in [5] and [6], respectively. However, state information (CSI) and therefore the subcarriers with higher the former relies on a cross-layer design based on forward channel power gains will be granted the priority to be activated, given the number of subcarriers is fixed. We also analyze the error control techniques, and the latter has a lower trans- proposed enhanced OFDM-SNM system in terms of outage and mission rate, which are impractical for general cases. The error performance. The average outage probability and block first widely recognized success to transplant the gist of SM error rate (BLER) are derived and approximated in closed-form to the frequency domain refers to the OFDM with index expressions, which are further verified by numerical results gen- modulation (OFDM-IM) [7]. By OFDM-IM, a new dimension erated by Monte Carlo simulations. The high-reliability nature of the enhanced OFDM-SNM makes it a promising candidate of subcarrier index is employed for modulating extra bits in for implementing in the Internet of Things (IoT) with stationary addition to classic phase and amplitude dimensions of the machine-type devices (MTDs), which are subject to slow fading signal constellation. The proper feasibility and high efficiency and supported by proper power supply. of OFDM-IM have then drawn the attention from industry and Index Terms—Orthogonal frequency-division multiplexing academia and sparked the research enthusiasm since 2013 until with subcarrier number modulation (OFDM-SNM), subcarrier now1 [10]–[14]. Despite the feasibility in practical scenarios, assignment, reliability enhancement, outage performance analy- OFDM-IM has several drawbacks. First, by OFDM-IM, the sis, error performance analysis. number of active subcarriers in each transmission attempt is fixed to a given number, which restricts the improvement of the I. INTRODUCTION SE of OFDM-IM. Meanwhile, the codebook design of OFDM- IM depending on either a look-up table or the combinatorial ECAUSE of the saturation of base station (BS) deploy- method is of high complexity and has not fully exploited the ments in fourth generation (4G) networks, it becomes B frequency selectivity for reliability enhancement [15]. increasingly difficult to enhance the spectral efficiency (SE) arXiv:1905.00197v1 [eess.SP] 1 May 2019 In order to cope with the aforementioned drawbacks of of wireless communication by spatial optimization and fur- OFDM-IM, a novel modulation scheme termed OFDM with ther densifying networks [1]. To cope with the increasingly subcarrier number modulation (OFDM-SNM) was proposed high demand for data throughput, many researchers resort to and preliminarily investigated in terms of SE, error perfor- novel modulation schemes. In this regard, a variety of novel mance and energy efficiency (EE) in [16]. In essence, OFDM- modulation schemes were proposed. In the space domain, for SNM can be regarded as a ‘sibling’ modulation scheme multiple-input and multiple-output (MIMO) systems, spatial sharing a similar nature with OFDM-IM, which relies on modulation (SM) and space-shift keying (SSK) were intro- another set of subcarrier activation patterns (SAPs) and a duced to utilize the indices of transmit antennas to convey unique information mapping relation. Technically different additional information bits [2], [3]. Although helpful, SM and from OFDM-IM, by OFDM-SNM, the numbers of active SSK supported by a multi-antenna architecture will inevitably subcarriers in each transmission round are utilized to convey S. Dang, G. Ma, B. Shihada, and M.-S. Alouini are with Computer, extra bits, instead of the indices of active subcarriers. In this Electrical and Mathematical Science and Engineering Division, King Abdullah way, a new active subcarrier number (ASN) dimension can University of Science and Technology (KAUST), Thuwal 23955-6900, King- dom of Saudi Arabia (e-mail: fshuping.dang, guoqing.ma, basem.shihada, 1From a taxonomic viewpoint, after the concept of OFDM-IM gets well- [email protected]). known, SIM OFDM and OFDM-IM are sometimes regarded as synonyms and used exchangeably [8], [9]. 2 be employed to convey additional information. Primary results TABLE I: List of key notations used in this paper. illustrated in [16] have shown that a higher SE is achievable Notation Definition/explanation by OFDM-SNM than those of OFDM-IM and plain OFDM h(n) Channel coefficient of the nth subcarrier when binary phase-shift keying (BPSK) is in use for amplitude k Index of SAP phase modulation (APM) on individual subcarriers. Also, EE M Amplitude phase modulation order and reliability measured by error performance are shown to N Number of subcarriers be better than those of plain OFDM and comparable to those N0 Average noise power yielded by OFDM-IM. Although verified by neither analytical n Index of subcarrier nor numerical results, a hypothesis is given in [16] that there P e Average block error rate is a potential to enhance the system reliability of OFDM- Pt Total transmit power SNM by the flexibility of placing active subcarriers because pH Length of heading bit stream of the frequency selectivity. This results in an opportunity to pS (k) Length of subsequent bit stream of the kth SAP incorporate some channel-dependent adaptation mechanisms p(k) Length of entire bit stream of the kth SAP in OFDM-SNM to further enhance the system reliability, just pIM Transmission rate of OFDM-IM as for other multi-carrier system paradigms [17]–[23]. pOFDM Transmission rate of plain OFDM In this regard, we propose an enhanced OFDM-SNM p¯ Average transmission rate in bpcu scheme in this paper, which is supported by subcarrier assign- Number of active subcarriers predefined by T ment. In particular, we consider a slow fading environment and OFDM-IM the subcarriers with better quality, i.e., higher instantaneous T (k) Number of active subcarriers of the kth SAP Complex constellation symbol conveyed on the nth channel power gains will be granted the priority for use by χn the proposed enhanced OFDM-SNM scheme. Therefore, with active subcarrier the help of instantaneous channel state information (CSI), µ Average channel power gain an adaptive modulation mechanism is formed, which can Φ Average outage probability provide a dynamic codebook and enhance the performance of ξ Preset outage threshold OFDM-SNM by a coding gain. Apart from this all-important contribution, we also provide a series of in-depth performance without loss of generality. In modern multi-carrier systems, analysis and comparisons with original OFDM-SNM, aiming these N subcarriers are generated by taking the fast inverse at supplementing the primary results given in [16]. Specifi- fast Fourier transform (IFFT) with insertion of sufficiently cally, we determine the transmission rate of OFDM-SNM in long cyclic prefix (CP) and can thereby operate mutually bit per channel use (bpcu) and investigate the outage and error independently without interference and correlation [24]. We performance of enhanced OFDM-SNM by average outage denote the set of subcarriers as N . By involving OFDM- probability and average block error rate (BLER), respectively. SNM, the functionality of subcarrier is not only to convey All analytical results are derived or approximated in closed data constellation symbols, but also to provide a unique SAP form and verified by numerical results generated by Monte to transmit extra bits. Specifically, a subset of subcarriers Carlo simulations. The high-reliability nature of enhanced N (k) are selected from the full set N to be activated, where OFDM-SNM particularly suits the applications in the IoT with k denotes the index of a unique SAP, and the cardinality stationary machine-type devices (MTDs), which are subject to T (k) = jN (k)j, i.e., the number of active subcarriers is slow fading and supported by proper power supply. utilized to modulate the heading bit sequence with a fixed The rest of this paper is organized as follows. The system length pH . The relation between pH and N can be easily model of enhanced OFDM-SNM is detailed in Section II, in determined by pH = blog2(N)c, where b·c is the floor which we also present some relevant information regarding function and can be removed if and only if N is a power of transmission rate. Then, the outage and error performance two.