# Toward High Bit Rate LoRa Transmission via Joint Frequency-Amplitude Modulation
## 1 Introduction  
The Low-Power Wide-Area Network (LPWAN) has become one of the most promising solutions for achieving ubiquitous connectivity due to its long-distance and low-power characteristics. It has attracted extensive attention from industry and academia [1]. Long Range (LoRa) [2], SIGFOX [3], and NB-IoT [2] are the three commercialized wireless technologies facilitating the LPWAN development. LoRa is the most promising technology among them for IoT connectivity outdoors [4]. It is an open-source technique operating at the unlicensed ISM Sub-GHz bands without subscription fees [5, 6, 7]. Recently, the ubiquitous connection puts forward higher requirements for the maximum rate, reliability and low power consumption of the IoT device. However, the low bit rate of LoRa (37.5 Kbps) limits its potential applications [8]. In addition, serious packet collisions occur at the receiving gateway when multiple LoRa nodes transmit packets on the same frequency channel at the same time [9, 10, 11]. Even worse, the low bit rate of LoRa leads to a long packet duration, which further aggravates this problem, decreasing the network throughput and increasing the energy consumption [12]. In order to improve the data rate of the LoRa transmission, many representative efforts have been proposed. They are roughly categorized into two types: Single Chirp (SC) and Multiple Chirp (MC). For the SC schemes, ICS-LoRa [13] increases by 1-bit extradata on top of each symbol by introducing a new kind of basic chirp, which improves the information transmission rate \(\frac{SF+1}{2^{SF}}BW\), where \(SF\) is the spreading factor and \(BW\) indicates the operating bandwidth. SSK-LoRa [14] proposes a symbol scheme using the improved ICS-LoRa chirp, which overcomes the signal-to-noise ratio (SNR) loss brought by ICS-LoRa, yet keeps the same data rate as ICS-LoRa. PSK-LoRa [15] proposes to divide the information into two parts, in which one part determines the initial frequency of LoRa symbols and the other part uses PSK modulation to determine the initial phase of LoRa symbols. M-order PSK-LoRa can improve the data rate to \(\frac{SF+\log_{2}\!M}{2^{SF}}BW\). To overcome the data rate bottleneck of SC methods, MC methods are explored. \(GN(SF-\log_{2}GN)\) bits can be achieved through dividing multiple orthogonal upchirps into \(GN\) independent groups [16]. Inspired by time division multiple access, \(2 SF\) bits can be carried in a symbol by introducing a down-chirp along with an up-chirp [17] into a Time Domain Multiplexed (TDM) LoRa symbol. In addition, a dual-mode TDM is designed to enhance the data rates to \(4(SF-1)\) per symbol [18]. By deploying index modulation (IM), FBI-LoRa [19] introduces a new index modulation technology by combining multiple basic LoRa chirps. Since the number of chirp combinations is far more than the number of chirps, the data rate can be greatly improved. Most recently, layered Chirp Spread Spectrum (CSS) modulation was investigated to further improve the data rate up to \(2L(SF-1)\), where \(L\) is denoted the number of layers [20]. Additionally, ZChirp [21] proposes multiplying chirps with binary Z sequences to enable multi-user concurrent transmissions. By leveraging the low cross-correlation of Z sequences, ZChirp supports simultaneous transmissions from multiple nodes and increases data rates by encoding additional bits in Z sequence indices, achieving a \(2.0\times\) capacity gain over state-of-the-art solutions [21]. Through combining layer-based and group-based, a unified framework is defined to summarize the characteristics of most state-of-the-art modulation schemes [18]. However, data rate improvements are investigated from the perspective of either frequency or phase in the aforementioned methods. Moving beyond these traditional dimensions, recent efforts have explored alternative modulation domains to enhance LoRa's data capacity.