Alternative Chirp Spread Spectrum Techniques for LPWANs
Ivo Bizon Franco de Almeida, Marwa Chafii, Ahmad Nimr, Gerhard Fettweis
11 Alternative Chirp Spread Spectrum Techniques forLPWANs
Ivo Bizon Franco de Almeida ∗ , Marwa Chafii † , Ahmad Nimr ∗ and Gerhard Fettweis ∗ Abstract
Chirp spread spectrum (CSS) is the modulation technique currently employed by Long-Range (LoRa), whichis one of the most prominent Internet of things wireless communications standards. The LoRa physical layer (PHY)employs CSS on top of a variant of frequency shift keying, and non-coherent detection is employed at the receiver.While it offers a good trade-off among coverage, data rate and device simplicity, its maximum achievable datarate is still a limiting factor for some applications. Moreover, the current LoRa standard does not fully exploit theCSS generic case, i.e., when data to be transmitted is encoded in different waveform parameters. Therefore, thegoal of this paper is to investigate the performance of CSS while exploring different parameter settings aimingto increase the maximum achievable throughput, and hence increase spectral efficiency. Moreover, coherent andnon-coherent reception algorithm design is presented under the framework of maximum likelihood estimation. Forthe practical receiver design, the formulation of a channel estimation technique is also presented. The performanceevaluation of the different variants of CSS is carried out by inspection of the symbol error ratio as a function ofthe signal-to-noise ratio together with the maximum achievable throughput each scheme can achieve.
Index Terms
Chirp spread spectrum, long-range communications, low energy PHY, IoT, wireless communications.
I. I
NTRODUCTION R ECENTLY, a lot of attention has been drawn towards long-range and low-power consuming wirelesscommunication schemes [1]. Long-Range (LoRa) is a wireless communication protocol that has gotpreference among the schemes considered primary for Internet of things (IoT) applications [2]. The mainapplication of LoRa, and low power wide area networks (LPWANs) in general, is to provide connectivityfor mobile and stationary wireless end-devices that require data rates in the order of tens of kbps up to afew Mbps within a coverage area up to tens of kilometers. For maximization battery life and minimizingend-device costs, low energy consumption and simple transceiver design are also desirable characteristicsfor LPWANs devices [3].The physical layer (PHY) of LoRa has gained considerable attention within the academic community,and several papers have been published with investigations on the characteristics of LoRa PHY and MACschemes [4], [5], [6]. Its modulation scheme is based on chirp spread spectrum (CSS) in conjunctionfrequency shift keying (FSK). Some authors have proposed enhancements to the LoRa PHY framework.For instance, encoding extra information bits on the phase of the spreading chirp waveform has beenproposed in [7], and similar work employs pulse shaping on top of the chirp waveform to reduce theguard-band, and thus increases the number of channels within the available frequency band [8]. Mostrecently, an approach that uses the chirp rate to carry one extra information bit has been proposed in[9]. Therefore, inspired by the aforementioned works, and departing from the LoRa PHY framework,we propose a more broad scheme that encodes multiple information bits on the discrete chirp rate. Thescheme proposed in [10] is revisited here, and while it employs coherent detection, the new scheme thatexploits the chirp rate as information carrier is able to benefit from non-coherent detection when operatingover flat-fading channels. Furthermore, maximum likelihood estimation for the transmitted data symbolsusing the classical CSS transceiver is presented. ∗ Vodafone Chair Mobile Communications Systems, Technische Universit¨at Dresden (TUD), Germany. † ETIS, UMR8051, CY Cergy ParisUniversit´e, ENSEA, CNRS, France. Emails: { ivo.bizon, ahmad.nimr, gerhard.fettweis } @ifn.et.tu-dresden.de, marwa.chafi[email protected]. a r X i v : . [ ee ss . SP ] F e b The main contributions contained in the paper are: • A detailed description of the transmission and reception of two novel modulation techniques based onCSS, namely in-phase and quadrature chirp spread spectrum (IQCSS) and discrete chirp rate keyingCSS (DCRK-CSS), which are able to increase spectral efficiency (SE) and energy efficiency (EE)when compared to the conventional LoRa PHY scheme. • A derivation of the optimum reception scheme for CSS under the framework of maximum likelihoodestimation. • A low complexity channel estimation technique that can be used with the current LoRa PHY datapacket structure.The remainder of the paper is organized as follows: Section II-A presents the mathematical foundationsof discrete-time chirp signals from its continuous-time definition, while Section II-B derives the transmis-sion and reception of CSS modulation under the framework of maximum likelihood estimation. SectionIII contain detailed description of the transceivers which employ variants of CSS. Firstly in III-A, theLoRa PHY standard [11], subsequently in III-B the recently proposed IQCSS [10], and lastly in III-C theproposed DCRK-CSS are presented. Section IV investigates the performance of the proposed schemesunder different wireless channel models. Finally, the paper is concluded in Section V with future insights,and directions on the topic of LPWANs.II. C
HIRP S PREAD S PECTRUM M AXIMUM L IKELIHOOD E STIMATION
A. The Chirp Signal
This subsection aims to give an analytical description of the chirp signal. In CSS [12], as well as inother spread spectrum techniques, such as direct sequence (DSSS) and frequency hoping (FHSS), theinformation is transmitted using a bandwidth much larger than required for a given data rate, i.e., theinformation signal is spread over the bandwidth to benefit from spreading gain. Particularly in CSS,multiplication by a chirp signal is responsible for the energy spreading in frequency. The linear-chirprefers to the frequency variation of the signal, which increases linearly with time.The chirp waveform can be described by c ( t ) = (cid:40) exp ( jϕ ( t )) for − T / ≤ t ≤ T / otherwise, (1)where ϕ ( t ) = π ( at + 2 bt ) , i.e., a quadratic function of time. The chirp instantaneous frequency is definedas v ( t ) = 12 π dϕ ( t ) dt = at + b, (2)which shows that the frequency varies linearly with time. Moreover, the chirp rate is defined as the secondderivative of ϕ ( t ) w.r.t. t as u ( t ) = 12 π d ϕ ( t ) dt = a. (3)The up-chirp corresponds to the case where u ( t ) > , and the down-chirp when u ( t ) < .Let B (Hz) represent the bandwidth occupied by the chirp signal. The signal frequency varies linearlybetween − B/ b and B/ b within the time duration T (s). If the term b = 0 and a (cid:54) = 0 , the resultingwaveform is the raw chirp with starting frequency − B/ and end frequency B/ . Conversely, if a = 0 ,the complex exponential is obtained. After sampling at rate B = 1 /T s , where T s (s) is sampling timeinterval, the discrete-time chirp signal is given by c ( nT s ) = (cid:40) exp ( jϕ ( nT s )) for n = 0 , . . . , N − otherwise, (4) where N = T /T s is the total number of samples within T seconds. Setting b = 0 , and a = M B/T , thediscrete-time raw up-chirp becomes c [ n ] = exp (cid:0) jπM n /N (cid:1) , (5)where M represents the discrete chirp rate. B. Maximum Likelihood Estimation CSS
At the transmitter side, the discrete-time chirp signal c [ n ] is used for spreading the information signalwithin the bandwidth B via multiplication. The transmit signal can be described as x k [ n ] = (cid:114) E s N exp (cid:18) j πN kn (cid:19) c [ n ] , (6)where the complex exponential term has its frequency depending upon the data symbol k , which isobtained from a bit-word b ∈ { , } SF as k = SF − (cid:88) i =0 i [ b ] i , (7)where the spreading factor (SF) represents the amount of bits in each bit-word. Note that each waveformhas N = 2 SF samples for having distinguishable waveforms. The data symbols are integer values fromthe set K = (cid:8) , . . . , SF − (cid:9) , which contains N elements. E s represents the signal energy.To explore alternative ways of generating the transmit signal, let us analyze the period of the rawup-chirp, and for the sake of brevity let us assume M = 1 . Then, exp (cid:32) jπ ( n + N ) N (cid:33) = exp (cid:0) jπn /N (cid:1) exp ( j πn ) exp ( jπN ) , (8)where the terms exp ( j πn ) and exp ( jπN ) equal the unity for all n ∈ K and N ∈ { , . . . , } .Therefore, the raw up-chirp has period N , and the LoRa transmit signal can be readily obtained via adiscrete circular time shift operation. Hence, (6) can also be written as x k [ n ] = (cid:114) E s N c [ n + k ] N , (9)where [ · ] N represents the circular shift. This equation presents simplified generation complexity whencompared to (6), since it is necessary to just store one vector corresponding to the raw up-chirp and readit circularly.The discrete-time complex-valued received signal after synchronization can be described as y [ n ] = f h ( x k [ n ]) + w [ n ] , (10)where f h ( · ) represents the equivalent channel function, and w [ n ] is assumed to be additive white Gaussiannoise (AWGN) with zero mean and σ w variance.Assuming knowledge of the equivalent channel function, the maximum likelihood estimator (MLE) forthe transmitted data symbol k is given as ˆ k = arg min k ∈ K N − (cid:88) n =0 (cid:12)(cid:12) y [ n ] − f h ( x k [ n ]) (cid:12)(cid:12) . (11)
1) AWGN Channel:
Under pure AWGN channel the equivalent function is the identity, i.e., f h ( x k [ n ]) = x k [ n ] , and (cid:12)(cid:12) y [ n ] − x k [ n ] (cid:12)(cid:12) = (cid:12)(cid:12) y [ n ] (cid:12)(cid:12) + (cid:12)(cid:12) x k [ n ] (cid:12)(cid:12) − (cid:60) { x ∗ k [ n ] y [ n ] } , (12)where ( · ) ∗ and (cid:60) {·} denote the conjugate and real part extraction operators, respectively, and note that (cid:12)(cid:12) x k [ n ] (cid:12)(cid:12) = 1 , ∀ n ∈ K . Consequently, (11) can be modified to ˆ k = arg max k ∈ K N − (cid:88) n =0 (cid:60) (cid:8) x ∗ k [ n ] y [ n ] (cid:9) = arg max k ∈ K N − (cid:88) n =0 (cid:60) (cid:40)(cid:114) E s N exp (cid:18) − j πN kn (cid:19) c ∗ [ n ] y [ n ] (cid:41) = arg max k ∈ K (cid:60) (cid:40) N − (cid:88) n =0 exp (cid:18) − j πN kn (cid:19) c ∗ [ n ] y [ n ] (cid:41) . (13)By inspecting the maximization problem in (13), one can see that the demodulation process can beefficiently executed by firstly multiplying the received signal with the conjugated raw up-chirp, hereafternamed down-chirp, secondly computing the discrete Fourier transform (DFT) of this result, and thirdlyselecting the frequency bin that maximizes the real part of the compound result. Luckily, this operationcan be efficiently carried via the fast Fourier transform (FFT) algorithm. Therefore, the MLE for thetransmitted data symbol is given by ˆ k = arg max k ∈ K (cid:60) { R ( k ) } , (14)where R ( k ) = F { r [ n ] } , r [ n ] = c ∗ [ n ] y [ n ] , and F {·} the DFT operator.
2) Flat-fading Channel:
Assuming a flat fading wireless channel, the equivalent channel functionbecomes f h ( x k [ n ]) = hx k [ n ] , where h denotes a complex-valued gain. If a channel estimation mechanismis available at the receiver side, coherent detection can be employed, and by following the same path thatled to (14), the estimated data symbol can be obtained as ˆ k = arg max k ∈ K (cid:60) (cid:110) ˜ R ( k ) (cid:111) , (15)where ˜ R ( k ) = F { ˜ r [ n ] } , ˜ r [ n ] = h ∗ c ∗ [ n ] y [ n ] . However, if non-coherent detection is implemented at thereceiver, the random phase rotation induced by the complex channel gain cannot be reverted, and (15)can be modified to ˆ k = arg max k ∈ K (cid:12)(cid:12) R ( k ) (cid:12)(cid:12) . (16)
3) Frequency Selective Channel:
Under frequency selective channel, f h ( x k [ n ]) = h [ n ] ∗ x k [ n ] , where h [ n ] represents the discrete-time channel impulse response that contains L complex-valued taps. Assumingthat channel estimation is available at the receiver, the estimated data symbols can be obtained from (11)by implementing a search over K . However, in order to derive a low complexity solution from (11),one needs to assume that a cyclic prefix (CP) is appended to the begging of the transmit signal, and N CP > L − , where N CP is the length of the CP in samples. Here a vector notation is adopted for thesake of simplicity. Let H ∈ C N × N represent the circulant channel matrix obtained from h [ n ] , y ∈ C N × and c ∈ C N × represent vectors whose entries are the samples from y [ n ] and c [ n ] , respectively. Thus, theestimated data symbol can be obtained by ˆ k = arg max k ∈ K (cid:60) { ˜ r ( k ) } , (17)where ˜ r ( k ) = F (cid:8) c H H H y (cid:9) , and ( · ) H is the Hermitian operator. Note that the channel matrix can beestimated at the received by transmitting known sequences. b ∈ { , } SF Bit to symbolmapping k exp ( j πkn/N ) Frequencyshift modulation × exp (cid:0) jπn /N (cid:1) Up-chirp / spreading x k [ n ] WirelessChannelSync. y [ n ] × exp (cid:0) − jπn /N (cid:1) Down-chirp / despreading r [ n ] FFT R ( k ) arg max k (cid:12)(cid:12) R ( k ) (cid:12)(cid:12) ˆ k Fig. 1: LoRa PHY transceiver block diagram.III. A
LTERNATIVE
CSS-
BASED M ODULATION S CHEMES
A. LoRa Physical Layer
Notably, LoRa PHY employs CSS in conjunction with a variant of FSK modulation as described above[13], [11]. It is important to note that in this case, the discrete chirp rate is set to the unity, and thereceiver employs non-coherent detection. Moreover, LoRa PHY defines the SF as the amount of bits thatone symbol carriers, which ranges from 6 to 12 bits.In short, Fig. 1 presents the discrete-time baseband LoRa PHY transceiver block diagram.The bit-word b contains SF bits that are mapped into one symbol k , which feeds the CSS modulator.The despreading operation at the receiver side is accomplished by multiplying the received signal with adown-chirp, which is obtained by conjugating the up-chirp signal. At the receiver side, the estimated datasymbol is obtained by selecting the frequency index with maximum value.The spreading gain, also known as processing gain, is defined by the ratio between the bandwidth ofthe spreading chirp signal and the information signal, and it can be defined in dB as G = 10 log (cid:18) N SF (cid:19) . (18)Larger spreading factors yield the largest spreading gains, and consequently the longer coverage range.A key aspect of LoRa PHY is the fact that channel estimation and equalization are not necessary, sinceit employs the non-coherent detection receiver. However, employing coherent detection will improve theEE performance of LoRa, since the imaginary noise component is not taken in the estimation of thereceived data symbol. Furthermore, under harsher multi-tap, i.e., frequency selective, channel conditionsthe original LoRa modulation performance can degrade significantly, as also observed in [14]. B. In-phase and Quadrature CSS
In IQCSS, information is encoded in both in-phase (real) and quadrature (imaginary) components of thetransmit signal [10]. By making use of the orthogonality between the sine and cosine waves it is possibleto transmit simultaneously two data symbols. Its transmit signal is given by x k i ,k q [ n ] = (cid:114) E s N g k i ,k q [ n ] c [ n ] , (19)where g k i ,k q [ n ] = exp (cid:18) j πN k i n (cid:19) + j exp (cid:18) j πN k q n (cid:19) , (20)where k i and k q are independent identically (uniform) distributed data symbols drawn from K , and eachcarries SF bits. Thus, the total amount of transmitted bits is doubled when compared to the LoRa PHYspecification.Fig. 3 illustrates the discrete-time baseband IQCSS transceiver block diagram. Note that the additionaloperations performed at the receiver side do not require modifications on the LoRa’s transmit signal structure, since IQCSS makes use of the already available synchronization preamble for channel estimationand subsequent coherent detection. Fig. 2 illustrates one LoRa PHY packet, where there are 14 modulatedchirps in the data payload, 10 up-chirps are available for synchronization, followed by 2 down-chirps thatindicate the beginning of the data symbols, and are named start frame delimeter (SFD) [11]. -1250125 Time (ms) F r e qu e n c y ( k H z ) Sync. preamble SFD Data symbols
Fig. 2: Spectrogram of the LoRa PHY packet structure.The received signal after equalization and despreading is given by ˜ r [ n ] = g k i ,k q [ n ] + ˜ w [ n ] , (21)where and the received data symbols are given by ˆ k i = arg max f ∈ K (cid:60) (cid:8) ˜ R ( f ) (cid:9) , (22) ˆ k q = arg max f ∈ K (cid:61) (cid:8) ˜ R ( f ) (cid:9) , (23)where ˜ R ( k ) = F { ˜ r [ n ] } .It is important to point out that IQCSS requires coherent detection to work. Therefore, for makingfurther use of the information carried with the synchronization preamble, we propose to use the leastsquares (LS) approach for estimating the channel gain using the already available preamble structure forsynchronization.Assuming that the channel presents flat-fading within its bandwidth, the received preamble can bewritten as y p [ n ] = hx p [ n ] + w [ n ] , (24)where x p [ n ] represents the 10 up-chirps transmitted at the beginning of the LoRa PHY packet, w [ n ] isAWGN with zero mean and σ w variance, and h is the complex-valued channel gain. Consequently, theLS error criterion, which is the squared difference between the received data and the signal model [15],is given by J ( h ) = N p − (cid:88) n =0 ( y p [ n ] − hx p [ n ]) , (25)where N p = 10 N is the preamble length in samples. Differentiating (25) with respect to h , and settingthe result to zero yield to ˆ h = x H p y p x H p x p , (26)where x p and y p are N p × vectors whose entries are the samples from x p [ n ] and y p [ n ] , respectively, and ˆ h is the estimated channel gain. k i exp ( j πk i n/N ) Frequencyshift modulation × exp (cid:0) jπn /N (cid:1) Up-chirp / spreading k q exp ( j πk q n/N ) × jπ/ phase rotation × P AddCP x k i ,k q [ n ] WirelessChannelRemoveCP y k i ,k q [ n ] Sync. &Chann. Est.Equalizer × exp (cid:0) − jπn /N (cid:1) Down-chirp / despreading ˜ r [ n ] FFT ˜ R ( f )arg max f < (cid:8) ˜ R ( f ) (cid:9) arg max f = (cid:8) ˜ R ( f ) (cid:9) ˆ k i ˆ k q Fig. 3: IQCSS transceiver block diagram.For the case of frequency selective channels the LS approach can be extended, but in this case, a CPneeds to be added to the synchronization chirps, thus modifying the original LoRa PHY packet structure.Under the assumption of a CP appended the beginning of each chirp, the received signal after CPremoval is given by y p = Hx p + w , (27)in vector notation. Therefore, estimation of the equivalent channel impulse response can be obtained as ˆ h = (cid:0) C H C (cid:1) − C H ¯y p , (28)where C is a N × N circulant matrix obtained from one raw up-chirp, ¯y p is a N × vector whose entriesare the averaged samples from the 10 received synchronization chirps after CP removal, and ˆ h containsthe estimated channel impulse response. It is important to note that ˆ h has in total N entries, but only thefirst L are used as an estimate of the channel taps. Furthermore, by inspecting (28), one can see that C is an orthogonal matrix, and the estimator simplifies as ˆ h = C H ¯y p , (29)which reduces considerably the estimation computational complexity.On the condition that the channel estimation and equalization modules are available at the receiver,coherent detection can be made possible. In this case, the receiver structure allows greater SE and EEwhen compared with LoRa modulation. Nevertheless, if these modules are not used, the receiver structureis equivalent to the LoRa standard. Therefore, the receiving devices (gateways) that operate using IQCSScan still decode the information transmitted using the original LoRa modulation, thus making IQCSSgateways backwards compatible. C. Discrete Chirp Rate Keying CSS
While IQCSS is able to increase the data throughput by exploiting the benefits of a coherent detectionreceiver, it is also possible to encode extra information bits on the discrete chirp rate and maintain simplernon-coherent detection. A similar approach is has been proposed in [9]. However, this approach is limitedto only one extra information bit. Hence, we propose to extend this framework to multiple extra informationbits. Hereafter, we refer to this scheme as DCRK-CSS.Let b e ∈ { , } N e denote the bit-word that will modulate the chirp rate, where N e represents the amountof extra bits encoded, and b f ∈ { , } N f denote the bit-word that will modulate the frequency of a complexexponential, N f is equivalent to LoRa’s spreading factor. The total amount of possible chirp rates is givenby P = 2 N e . Therefore, the data symbol is comprised by both bit words, i.e., b = { b f , b e } N f + N e b f ∈ { , } N f Bit to symbolmapping k b e ∈ { , } N e Bit to symbolmapping M exp ( j πkn/N ) Frequencyshift modulation × exp (cid:0) jπM n /N (cid:1) Discrete chirprate modulation x k,M [ n ] WirelessChannelSync. y [ n ] × exp (cid:0) − jπM n /N (cid:1) Discrete chirprate demodulation
FFT N ... × exp (cid:0) − jπM P n /N (cid:1) FFT N a r g m a x k , M k R p ( k ) k ˆ k ˆ M Fig. 4: Discrete Chirp Rate Keying CSS transceiver block diagram.The discrete chirp rate is selected depending upon the combination a of bits in b e , e.g., for N e = 3 bits, the defined chirp rates are given by M p = − for b e = [0 0 0] − for b e = [0 0 1] − for b e = [0 1 0] − for b e = [0 1 1]1 for b e = [1 0 0]2 for b e = [1 0 1]3 for b e = [1 1 0]4 for b e = [1 1 1] , (30)where M assumes P non-zero integer values, and p is an indexing variable. The transmit signal can bewritten as x k,M [ n ] = (cid:114) E s N exp (cid:18) j πN kn (cid:19) c p [ n ] , (31)where c p [ n ] = exp ( jπM p n /N ) .Fig. 4 illustrates the discrete-time baseband transceiver block diagram. The received signal after syn-chronization goes through a bank of dechirping modules with different chirp rates. Let the DFTs ofdespreaded signals be represented by R p ( k ) = F (cid:8) y [ n ] exp (cid:0) − jπM p n /N (cid:1)(cid:9) , for 1 ≤ p ≤ P, (32)where y [ n ] = hx k,M [ n ]+ w [ n ] considering transmission over a flat fading channel. The estimated frequency,and chirp encoded data symbols are jointly obtained as ˆ k, ˆ M = arg max k, M (cid:12)(cid:12) R p ( k ) (cid:12)(cid:12) . (33)It is important to note that the spreading chirps with different rates are not orthogonal, but they presentlow correlation, and the performance loss due to intrinsic interference becomes negligible. Furthermore,the level of intrinsic interference is inversely proportional to N , such that smaller SFs are subject tomore performance loss. To better illustrate this characteristic, Fig. 5 shows the absolute value of the innerproduct between c [ n ] and the despreading signals defined by (cid:104) c [ n ] , c ∗ p [ n ] (cid:105) = N − (cid:88) n =0 exp (cid:0) jπn /N (cid:1) exp (cid:0) − jπM p n /N (cid:1) (34) − − − − . . . M p k h c [ n ] , c ∗ p [ n ] i k SF = 6 − − − − . . . M p SF = 12
Fig. 5: Inner product between c [ n ] and different dechirping rates, considering SF = 6 and
SF = 12 .IV. P
ERFORMANCE A NALYSIS
For comparing the performance of the proposed schemes against the LoRa PHY, we resort to numericalsimulations for estimating the symbol bit error ratio (SER/BER) under three different wireless channelmodels, namely AWGN, time-variant (TV) non-frequency-selective (Rayleigh) channel, and time-variantfrequency-selective (TVFS). For the latter, the channel model chosen is ”Typical case for urban area”with 12 taps [16]. This has been chosen due to the similar operating frequency and bandwidth of LoRaand Global System for Mobile Communications (GSM) in Europe. Moreover, based on the symbol errorratio, the maximum achievable throughput is also presented for supporting the claims of increased spectralefficiency.Table I shows the simulation parameters considered.TABLE I: Simulation parameters
Parameter ValueSpreading factor SF ∈ { , , } Extra information bits N e ∈ { , } Bandwidth 250 kHzCarrier frequency 863 MHzMobile speed 3 km/hCP length 16 samplesTV channel single tap (Rayleigh)TVFS channel 12 taps ”Typical case for urban area” [16]Data frame size 30 chirpsPreamble frame size 12 chirps
A. Symbol and Bit Error Ratio Analysis1) AWGN Channel:
Fig. 6 shows the estimated BER under AWGN channel for LoRa, IQCSS andDCRK-CSS. Note that IQCSS transmits twice the amount of bits when compared with LoRa, andDCRK-CSS transmits N e extra bits. For all schemes, larger SF will result in better performance, sinceall schemes transmit data using frequency modulation, adding more symbols to the constellation doesnot reduce the minimum symbol distance. There is a gap of about 0.5 dB between the curves of IQCSSand LoRa for the same SF, whereas between LoRa and DCRK-CSS the gap increases with E b /N . Thegap between LoRa and IQCSS is observed because IQCSS collects less noise than LoRa in the processof detection, since it explores the phase information instead of making a decision based solely on the − − − − − E b /N (dB) B E R LoRaIQCSSDCRK-CSS, N e = 2 DCRK-CSS, N e = 3 SF = 12 SF = 6
Fig. 6: Average bit energy versus bit error ratio under AWGN channel. − − − − − − − − − − SNR (dB) S E R LoRaIQCSSDCRK-CSS, N e = 2 DCRK-CSS, N e = 3 SF = 12 SF = 9 SF = 6
Fig. 7: Signal-to-noise ratio versus symbol error ratio under AWGN channel.estimated energy of the frequency bins. Thus, one can use less energy to transmit more information withthe same bit error probability when employing IQCSS over LoRa. However, the gap between LoRa andDCRK-CSS is observed due to the smaller average energy bit required to maintain an equal BER, andthis gap increases as the number of extra bits encoded on the chirp slope increases. Nevertheless, notethat for the lower E b /N regime, the gap is reduced when compared with the high E b /N regime, this isobserved since the different despreading signals are not completely orthogonal to each other, but ratherpresent a significant low correlation.Fig. 7 also shows SER under AWGN channel while taking into consideration the spreading gain. Thetransmit power available is divided between the in-phase and quadrature components for IQCSS, while inLoRa DCRK-CSS and all power is used for a single component. Therefore, there is a 3 dB gap betweenLoRa and IQCSS in Fig. 7. Moreover, there is small gap between LoRa and DCRK-CSS, which is presentdue to the intrinsic interference caused by the non-orthogonality between the the different despreadingsignals. As one can see, the performance degradation is acceptable for the increased throughput providedby DCRK-CSS. It is also important to point out that for larger SFs, the this gap is reduced, since the − − − − − − − SNR (dB) T h r o u g hpu t( k bp s ) Channel capacityLoRaIQCSSDCRK-CSS, N e = 2 DCRK-CSS, N e = 3 SF = 12SF = 6SF = 9
Fig. 8: Maximum throughput achievable under AWGN channel. − − − − E b /N (dB) B E R LoRaIQCSS Known chan.DCRK-CSS, N e = 2 IQCSS Est. chan. IQCSS Est. chan. SF ∈ { , , } S F = Fig. 9: Average bit energy versus bit error ratio under flat fading channel.intrinsic interference is reduced as the SF increases.In order to quantize the advantages with respect to the maximum throughput achievable by the presentedschemes, Fig. 8 presents the maximum achievable throughput under AWGN channel. The Shannon channelcapacity is also plotted for reference. IQCSS achieves more than double the maximum throughput ofLoRa, since it encodes double the amount of bits, and it benefits from coherent detection at the receiver.DCRK-CSS is also able to increase the maximum throughput when compared to the LoRa PHY scheme.Considering
SF = 12 , there is an increase on the throughput when comparing DCRK-CSS with LoRa of16.6% and 25% for N e = 2 and N e = 3 bits, respectively. Comparatively, for SF = 6 there is an increaseof 33.3% and 50% for N e = 2 and N e = 3 , respectively. Therefore, both IQCSS and DCRK-CSS make amore efficient usage of spectrum resources. This are key aspects required for more data demanding IoTapplications.
2) Flat Fading Channel:
Fig. 9 and Fig. 10 show respectively the estimated BER and SER under time-variant flat fading channel. The same behavior observed under AWGN channel regarding the performance − − − − − − − − SNR (dB) S E R LoRaIQCSS Known chan.DCRK-CSS, N e = 2 IQCSS Est. chan. IQCSS Est. chan. SF ∈ { , , } Fig. 10: Signal-to-noise ratio versus symbol error ratio under flat fading channel.gaps can be observed between LoRa and DCRK-CSS. Moreover, there are three BER and SER curvesfor accessing IQCSS’s performance. The solid curves with circle marks represents the BER consideringan unrealistic scenario where the channel coefficient is known at the receiver, i.e., this represents thebaseline performance. Assuming that the channel coefficient remains static during the transmission ofone frame, which has 10 chirps for synchronization and channel estimation, and 30 chirps encoded withinformation, the dashed curves with asterisk marks (Est. chan. ) are obtained. These results show that theproposed channel estimation technique yields performance comparable to perfect channel estimation incases where the channel complex gain does not change during the transmission of frame. Lastly, the dotdashed curves with x marks (Est. chan. ) represent the case where the channel coefficient changes duringthe transmission of one frame. In this last case, we consider that the relative speed between transmitterand receiver is 3 km/h, carrier frequency is 863 MHz, the bandwidth occupied is 250 kHz. As a resultfrom the mobility, IQCSS suffers a performance degradation when compared with LoRa and DCRK-CSS.However, considering a low mobility scenario, this degradation might be neglected. For this particularsimulation scenario, significant performance degradation in observed for SFs greater than 10.
3) Frequency Selective Channel:
Fig. 11 shows the BER under the GSM channel model. Due tomultipath components of the channel, the DFT output from LoRa’s and DCRK-CSS’s receivers willpresent multiple peaks, and depending on the channel realization, LoRa’s receiver is not able to distinguishbetween them, but still presents a certain level of robustness. As one can see, the performance of thesetwo schemes degrades significantly under channels with long power delay profiles. However, IQCSS isable to deal with harsher multipath channels due to its more sophisticated receiver structure. Two curvesare presented for accessing IQCSS’s performance under TVFS channels. The solid curve with circlemarks is obtained considering noiseless channel estimation, whereas the dot dashed curve with x marksrepresent realistic case, and both use the LS channel estimation given by (29). As one can see, with LSchannel estimation the BER performance approaches the case of ideal channel estimation. The error flooris present since the channel impulse response changes within the frame duration. Hence, the smaller SFpresent better performance due to its shorter time duration. The mobility scenario is considered for allcurves presented in Fig. 11. For reference, a CP with length N CP = 16 samples has been employed withIQCSS.From the performance analysis presented, one can conclude that employing IQCSS in conditions wherethe wireless channel response remains static during the transmission of a data frame, and employingDCRK-CSS when it does not present significant frequency selectivity, would be advantageous for increas- − − − − E b /N (dB) B E R LoRaIQCSS Known chan.DCRK-CSS, N e = 2 IQCSS Est. chan.
SF = 12SF = 9 S F = Fig. 11: Average bit energy versus bit error ratio under frequency selective channel.ing the data throughput without sacrificing energy efficiency. Hence, for increasing the spectral efficiencyin conditions where high mobility of the transmitting units is more likely to occur when compared tofrequency selectivity, DCRK-CSS is a valid alternative to the LoRa PHY scheme. Moreover, both receiversfrom IQCSS and DCRK-CSS are designed to be backwards compatible with the current LoRa standard.It is also important to point-out that the investigation shown above considers that all modulation schemesoperate with the same transmission power. For the sporadic transmission of a large amount of PHY datapackets, the transmitting module of the device will be operating for shorter periods of time, since IQCSSand DCRK-CSS can transmit more data per unit of time when compared to LoRa. Therefore, energysaving and longer battery life can be achieved with the proposed schemes. However, an in-depth analysisof such gains is out of the scope of this paper.V. C
ONCLUSION
This paper has presented and studied novel modulation schemes inspired by the LoRa PHY for wirelessapplications that require low energy consumption and enhanced the spectral efficiency.The major advantage of IQCSS lies in the ability to double the SE, and at the same time to improveEE when compared with the conventional CSS employed by LoRa by employing coherent detection atthe receiver side. An estimation framework that uses the synchronization preamble defined by LoRa PHYto estimated the complex-valued channel gain, in flat fading channels, and an extended framework forfrequency selective channels has also been presented.On the condition of flat fading channels, the throughput can be enhanced by encoding extra informationbits on the discrete chirp rate. DCRK-CSS is able to enhance SE while maintaining the benefits of non-coherent detection.A key aspect of IQCSS and DCRK-CSS is that their receivers are still able to decode the informationtransmitted using the original LoRa modulation. Hence, gateways designed to operate with either arebackwards compatible with the conventional LoRa. Therefore, the investigations shown in this paper havedemonstrated the potential of DCRK-CSS and IQCSS as solutions for enhancing the operation of LPWAN.Nevertheless, a study on the performance the presented modulation techniques in conjunction with channelcoding remains as an interesting topic to pursue.R
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