In-phase and Quadrature Chirp Spread Spectrum for IoT Communications Ivo Bizon Franco de Almeida∗, Marwa Chafiiy, Ahmad Nimr∗ and Gerhard Fettweis∗ ∗Vodafone Chair Mobile Communications Systems, Technische Universitat¨ Dresden (TUD), Germany Email: ivo.bizon, ahmad.nimr, gerhard.fettweis @ifn.et.tu-dresden.de f g yETIS, UMR8051, CY Cergy Paris Universite,´ ENSEA, CNRS, France Email: marwa.chafi[email protected] Abstract— This paper describes a coherent chirp spread Inspired by the aforementioned works, and departing from spectrum (CSS) technique based on the Long-Range (LoRa) the LoRa PHY framework, we propose to extend it to a physical layer (PHY) framework. LoRa PHY employs CSS on coherent scheme that is able to increase the spectral efficiency top of a variant of frequency shift keying (FSK), and non- coherent detection is employed at the receiver for obtaining the (SE) (bps/Hz) and improve energy efficiency (EE). We define transmitted data symbols. In this paper, we propose a scheme this scheme as in-phase and quadrature chirp spread spectrum that encodes information bits on both in-phase and quadrature (IQCSS), since information is encoded in both in-phase (real) components of the chirp signal, and rather employs a coherent and quadrature (imaginary) components of the transmit signal. detector at the receiver. Hence, channel equalization is required The remainder of the paper is organized as follows: Section for compensating the channel induced phase rotation on the transmit signal. Moreover, a simple channel estimation technique II presents a background on chirp spread spectrum (CSS). exploits the LoRa reference sequences used for synchronization Section III describes the proposed IQCSS scheme together to obtain the complex channel coefficient used in the equalizer. with some implementation remarks. Section IV presents the Performance evaluation using numerical simulation shows that performance evaluation of the proposed scheme in terms of the proposed scheme achieves approximately 1 dB gain in terms the bit error ratio. Finally, section V concludes the paper. of energy efficiency, and it doubles the spectral efficiency when compared to the conventional LoRa PHY scheme. This is due to the fact that the coherent receiver is able to exploit the II. BACKGROUND CHIRP SPREAD SPECTRUM orthogonality between in-phase and quadrature components of the transmit signal. This section aims to give an analytical description of the Index Terms— Chirp spread spectrum, LoRa, PHY, IoT, chirp signal as well as its implementation on LoRa PHY. wireless communications. A. The chirp signal I. INTRODUCTION In CSS [9], as well as in other spread spectrum tech- ECENTLY, a lot of attention has been drawn towards niques, such as direct sequence (DSSS) and frequency hoping R long-range and low-power consuming wireless com- (FHSS), the information is transmitted using a bandwidth munication schemes [1]. Long-Range (LoRa) is a wireless much larger than required for a given data rate. Particularly communication protocol that has got preference among the in CSS, multiplication by a chirp signal is responsible for the schemes considered primary for Internet of things (IoT) energy spreading in frequency. The linear-chirp refers to the applications [2]. The main application of LoRa, and low frequency variation of the signal, which increases linearly with power wide area networks (LPWAN) in general, is to provide time. connectivity for mobile and stationary wireless end-devices The chirp waveform employed in CSS can be described by that require data rates in the order of tens of kbps up to a arXiv:2009.10421v1 [eess.SP] 22 Sep 2020 exp (j'(t)) for T=2 t T=2 few Mbps within a coverage area up to tens of kilometers. c(t) = − ≤ ≤ (1) Low energy consumption and simple design are also desirable (0 otherwise, characteristics for LPWAN devices [3]. 2 The physical layer (PHY) of LoRa has gained considerable where '(t) = π(at + 2bt), i.e., a quadratic function of time. attention of the academic community, and several papers have The chirp instantaneous frequency is defined as been published with investigations on the characteristics of 1 d'(t) LoRa PHY and MAC schemes [4], [5], [6]. v(t) = = at + b; (2) 2π dt Some authors have proposed enhancements to the LoRa PHY framework. For instance, encoding extra information bits which shows that the frequency varies linearly with time. on the phase of the chirp waveform has been proposed in Moreover, the chirp rate is defined as the second derivative of [7], and similar work makes use of pulse shaping the chirp '(t) w.r.t. t as waveform to reduce the guard-band, and thus increases the 1 d2'(t) number of channels within the available frequency band [8]. u(t) = = a: (3) 2π dt2 Wireless Up-chirp/spreading Down-chirp/despreading Channel exp jπn2/N exp jπn2/N − Sync. SF b 0, 1 Bit to symbol k kˆ ∈ { } exp (j2πkn/N) FFT arg maxf R(f) mapping × xk [n] y [n] × r[n] R(f) Frequency shift modulation Fig. 1: LoRa PHY transceiver block diagram. The up-chirp is defined when u(t) > 0, and the down-chirp In short, Fig. 1 shows the LoRa transceiver block diagram. when u(t) < 0. The code-word b contains SF bits that are mapped into one Let B (Hz) represent the bandwidth occupied by the chirp symbol k, which feeds the CSS modulator. At the receiver signal. The signal frequency varies linearly between B=2+b side, the estimated data symbol is obtained by selecting the − and B=2 + b within the time duration T (s). If the term b = 0 frequency index with maximum value. This operation can be and a = 0, the resulting waveform is the raw chirp with described as 6 starting frequency B=2 and end frequency B=2. Conversely, k^ = arg max R(f) ; (8) − f if a = 0, the complex exponential is obtained. After sampling 2K at rate B = 1=Ts, where Ts (s) is sampling time interval, the where R(f) = r[n] , r[n] represents the received signal F f g discrete-time chirp signal is given by after despreading, and the discrete Fourier transform. F {·} Luckily, this operation can be easily carried via the fast Fourier exp (j'(nTs)) for n = 0;:::;N 1 c(nTs) = − (4) transform (FFT) algorithm. (0 otherwise, A key aspect of LoRa PHY is the fact that channel estimation and equalization are not necessary, since it employs where N = T=T is the total number of samples within T . s a non-coherent FSK. However, employing coherent detection Setting b = 0, and a = B=T , the discrete-time raw up-chirp can improve the performance of LoRa. becomes 2 c[n] = exp jπn =N : (5) III. IN-PHASE AND QUADRATURE CHIRP SPREAD SPECTRUM B. LoRa PHY The synchronization preamble used in LoRa’s PHY makes Notably, LoRa PHY employs CSS in conjunction with use of 8 up-chirps for synchronization, followed by 2 down- a variant of frequency shift keying (FSK) modulation [10], chirps to indicate the start of the data symbols [11]. To make [11]. At the transmitter side, c[n] is used for spreading the further use of the information carried with the synchronization information signal within the bandwidth B via multiplication. signal, we propose to use the least squares (LS) approach The despreading operation at the receiver side is accomplished for estimating the channel gain using the already available by multiplying the received signal with a down-chirp, which structure for synchronization [12]. The received preamble can is obtained by conjugating the up-chirp. The transmit signal be modeled as can be described as E 2π yp[n] = hxp[n] + w[n]; (9) x [n] = s exp j kn c[n]; (6) k N N r where xp[n] represents the 8 raw up-chirps transmitted, w[n] where the exponential term has its frequency depending upon is additive white Gaussian noise (AWGN) with zero mean and 2 the data symbol k. LoRa PHY defines the spreading factor σw variance. Assuming that the channel presents flat-fading (SF) as the amount of bits that one symbol carriers, which within its bandwidth, the LS estimator of the complex channel ranges from 6 to 12 bits. Note that each waveform has gain is given by SF xHy N = 2 samples for having distinguishable waveforms. ^ p p h = H ; (10) The data symbols are integer values from the set K = xp xp SF 0;:::; 2 1 , which contains N elements. Es represents − where xp and yp are Np 1 vectors whose entries are the the signal energy. × H samples from xp[n] and yp[n], respectively. ( ) represents the The spreading gain, also known as processing gain, is · Hermitian operation, N = 8N is the length of the preamble defined by the ratio between the bandwidth of the spreading p in samples, and h and h^ are the true and estimated complex chirp signal and the information signal, and it can be defined channel gain, respectively. in dB as N For the case of frequency selective channels the LS ap- G = 10 log : (7) 10 SF proach can be extended, but in this case a cyclic prefix (CP) Frequency Wireless shift modulation Channel ˆ ˜ ki ki yiq0 [n] arg maxf R(f) exp (j2πkin/N) xiq0 [n] < × Remove Sync. & ˆ Add kq CP Chann. Est. arg max R˜(f) CP f = Up-chirp/spreading P Equalizer R˜(f) exp jπn2/N r˜[n] × FFT × kq 2 exp (j2πkqn/N) j exp jπn /N × − π/2 phase rotation Down-chirp /despreading Fig. 2: IQCSS transceiver block diagram. needs to be added to the synchronization chirps. Under the real part, and taking absolute value of R(f) means collecting assumption of a CP, the estimation of the equivalent channel extra noise from the imaginary part.