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Frequency-Shift Chirp Communications with Index Muhammad Hanif, Senior Member, IEEE, and Ha H. Nguyen, Senior Member, IEEE

Abstract—This paper introduces a novel frequency-shift chirp quadrature phase-shift keying (DQPSK) to encode the infor- spread spectrum (FSCSS) system with index modulation (IM). mation bits. Similarly, the authors in [10] employ quadrature By using combinations of orthogonal chirp signals for message (QAM) instead of DQPSK for encoding representation, the proposed FSCSS-IM system is very flexible to design and can achieve much higher data rates than the the information bits in both the initial phase and amplitude of conventional FSCSS system under the same bandwidth. The a linear chirp. However, these techniques come at the expense paper presents optimal detection algorithms, both coherently of increased receiver complexity and signalling overhead since and non-coherently, for the proposed FSCSS-IM system. Fur- the phase and/or amplitude of the received chirp needs to be thermore, a low-complexity non-coherent detection algorithm is estimated. also developed to reduce the computational complexity of the receiver, which is shown to achieve near-optimal performance. One approach to reduce the receiver complexity is to embed Results are presented to demonstrate that the proposed system, the information in the initial frequency of the linear chirp while enabling much higher data rates, enjoys similar bit-error instead of its initial phase [2], [4], [5]. Such a modulation performance as that of the conventional FSCSS system. scheme is aptly named as frequency-shift chirp modulation Index Terms—Chirp-spread spectrum modulation, LoRa mod- (FSCSS modulation) [5] and is also known simply as CSS ulation, index modulation, permutation modulation, non-coherent when used in the context of LoRa [2], [4], [11]. detection. FSCSS modulation enjoys low-complexity thanks to the fast Fourier transform (FFT) [5]. However, I.INTRODUCTION due to a limited number of orthogonal frequency-shift chirps available in given bandwidth and symbol duration, FSCSS HE modulation scheme in a chirp spread spectrum (CSS) modulation suffers from a low data rate, especially when communication system uses linear frequency-modulated T the available bandwidth is limited [12]. As such, different chirps to represent message symbols. Due to its robustness standards that employ CSS modulation have provisions for against narrow-band interference, constant envelope and re- other modulation schemes to attain a higher data rate than sistance against multi-path fading and Doppler effect, CSS what is achievable with the CSS modulation. For example, modulation has been adopted in various low-power wide-area LoRa chips have two modulation schemes implemented in (i.e., long-range) wireless applications [1]–[5]. For example, them: the LoRa (FSCSS) and the frequency-shift keying the IEEE 801.15.4a standard [1] has provisions for CSS (FSK) modulation schemes. The data rate provided with LoRa modulation along with the burst-position modulation scheme. modulation depends primarily on two factors, the spreading More recently, LoRa technology has been introduced for factor (SF) and the occupied bandwidth. The highest data rate Internet-of-Things (IoT) applications, which is also based on is kbps when the smallest value of SF, that is , frequency-shift chirp modulation and more commonly referred 37.5 SF = 7 and the maximum bandwidth of kHz are selected1. For to as LoRa modulation [2]–[5]. 500 applications that require higher data rates, LoRa chips have an Historically, linear chirps have been used in continuous- FSK transceiver, but it can achieve data rates up to 50 kbps arXiv:2102.04642v2 [cs.IT] 19 May 2021 wave frequency-modulated radars due to their good autocorre- only [4]. lation properties [6]. In digital communications, CSS was first Although implementing multiple transceivers in a device introduced in a simple form of binary modulation, in which can increase the achievable data rate, it consumes more two linear-frequency modulated chirps with opposite sweep hardware and software resources, especially at the reception directions, i.e., up chirp and down chirp, are used to represent side. As such, there have been active research efforts to an information bit. Such a scheme is also known as slope-shift increase the data rate of the conventional frequency-shift CSS keying [7], [8]. Although the up and down chirps are nearly communication systems. For example, the authors in [13], [14] orthogonal to each other, they are not completely orthogonal. have proposed to increase the data rate by embedding addi- As a consequence, the lack of complete orthogonality affects tional bits in the initial phase of an up chirp. Unfortunately, the bit-error-rate (BER) performance of slope-shift keying. carrying additional information in the phase requires channel For non-binary transmission, only one linear chirp is used estimation at the receiver side, which increases the receiver in [9], but its initial phase is modified using differential complexity, not to mention the sensitivity of these schemes to M. Hanif is with the Department of Engineering and Applied Sci- synchronization errors [15]. ence, Thompson Rivers University, Kamloops, BC V2C 0C8 (email: [email protected]), and H. H. Nguyen is with the Department of Electrical 1In general, with LoRa modulation, the higher the data rate is, the lower and Computer Engineering, University of Saskatchewan, Saskatoon, SK S7N the receiver sensitivity, i.e., the shorter the transmission range to achieve a 5A9, Canada, (e-mail: [email protected]). given level of bit error rate. 2

In [12], the authors propose to use interleaved chirps along IM principle to select spreading codes to represent a part of with linear up chirps to double the number of chirp signals, information bits. These techniques are fundamentally different hence increasing the data rate by 1 bit per each symbol from the proposed CSS modulation technique, which uses (message). However, similar to binary slope-shift keying, the chirps to represent the information bits instead of spreading BER performance of the interleaved FSCSS modulation is codes. degraded due to the non-orthogonality between the added The rest of the paper is organized as follows. Section II interleaved chirps and the original set of orthogonal up chirps. reviews the conventional FSCSS system. Our proposed FSCSS Another approach is recently introduced in [15] in which with index modulation (FSCSS-IM) scheme is detailed in down chirps are used instead of the interleaved chirps to Section III. The optimal and suboptimal detection algorithms double the size of the signal set. It was demonstrated in [15], for the proposed FSCSS-IM scheme are developed in Section via correlation and error-rate analysis, that using down chirps IV. Performance results and comparison to the conventional instead of interleaved chirps reduces the peak correlation FSCSS system are presented in Section V. Section VI con- between the added signal set and the original signal set, cludes the paper. hence improving the BER performance. Nevertheless, by only doubling the original signal set, the data rate improvement II.CONVENTIONAL FSCSSSYSTEM attained by the two schemes in [12], [15] is quite marginal, namely only one extra bit per modulated symbol. Similar to In a conventional FSCSS system, a set of linearly- [15], both up and down chirps are used for data transmission independent up chirps are used for representing information in [16]. However, instead of increasing the data rate as in bits. In particular, a set of M orthogonal chirps are used, [15], the authors in [16] leverage the near orthogonality of which are all generated from one linear up chirp, also referred the up and down chirps to improve the performance of LoRa to as the basic chirp in the sequel. The complex baseband- communications under packet collisions. equivalent form of the basic chirp has the following discrete- In this paper, by making use of the concept of permutation time representation [14], [42]: modulation (PM) introduced in [17], we develop a different πn2 approach to increase the data rate of the conventional FSCSS x [n] = exp j , (1) 0 M modulation scheme. Specifically, an important class of per-   mutation modulation that uses binary permutation vectors, where n = 0, 1, ,M 1, and M is the number of known as index modulation (IM) [18], is applied to the set orthogonal chirps used··· in the− conventional FSCSS modulation of orthogonal up chirps. scheme. The other orthogonal chirps are related to x0[n] as It is pointed out that IM has been employed in conventional [14] frequency-shift keying (FSK) modulation [19], as well as in orthogonal frequency-division (OFDM) systems xm[n] = x0[n + m], (2) [20]–[24]. The technique of IM appears in other names in where 0 n, m < M. Observe that other applications, such as parallel-combinatory (PC) spread- ≤ spectrum modulation [25], spatial modulation (SM) for multi- π(n2 + m2 + 2nm) antenna systems [26]–[29], space-shift keying [30], [31] multi- xm[n]= exp j M tone FSK [32], etc. The interested reader is referred to [33]–   2πm [36] for a comprehensive review of index modulation and its = x [m]x [n] exp j n . (3) 0 0 M applications.   To the best of our knowledge, this paper is the first work As such, the instantaneous (digital) frequency of the mth chirp on the application of IM in chirp spread spectrum com- differs from that of the basic chirp by m . 2 M munications . A somewhat related technique to increase the In the conventional FSCSS modulation, each chirp is associ- data rate is suggested in [10], [38] by transmitting multiple ated with a message symbol. Specifically, let b0, b1, , bΛ 1 chirps together. In particular, time-delayed basic up chirps be a group of Λ information bits associated with a··· message− are added to the basic up chirp, and the information bits symbol, and m be the corresponding decimal number, i.e., are represented in the phase and/or amplitude of the basic Λ 1 i m = i=0− bi2 . The transmitted signal corresponding to mes- chirp and its time-delayed versions, while no information sage m, denoted by sm[n], is simply given by sm[n] = xm[n]. is represented in the initial delay of the added time-shifted P Λ Note that Λ = log2 M, or M = 2 . This means that in a basic chirp. Such a technique is markedly different from conventional FSCSS modulation, such as in LoRa modulation, the index modulation technique in which the information is the number of chirps is selected to be a power of 2. embedded in the indices of the added signals. As shall be Assuming perfect synchronization, the received signal, de- seen, for the FSCSS modulation, those indices are related to noted by y[n], is given as the initial delays or the initial frequencies of the up chirps. Other techniques, such as, code index modulation or OFDM- y[n] = hxm[n] + w[n], (4) IM spread spectrum and their variants [39]–[41] apply the where m is an arbitrary transmitted symbol, h denotes 2The main idea and inventions in this paper are protected by a US patent the channel gain, and w[n] is a zero-mean circularly- #10,778,282 [37]. symmetric white Gaussian noise with variance N0. Since 3

M 1 2 − x [n] = M, the average signal-to-noise ratio (SNR) (PAPR) of the resultant transmitted signal. The optimal and n=0 | m | of the received symbol, denoted by Es/N0, is given by low-complexity detection algorithms for the proposed scheme P are developed in Section IV. ME h 2 Es/N0 = | | = Mγ,¯ (5) In the proposed scheme, the transmitter assigns a unique N0  and distinct combination of orthogonal chirps to every value 2 Λ where E h is the expected value of the squared absolute of m between 0 and 2 1. Let m denote the index set of − I | | E[ h 2] the chirps corresponding to message m. Then the transmitted value of the channel gain, and γ¯ = | | is the average   N0 signal corresponding to message m is constructed as channel SNR. For an additive white Gaussian noise (AWGN) channel, the channel gain is h = 1, and the instantaneous and 1 sm[n] = xl[n]. (9) average channel SNRs are both equal to 1/N0. m l m Detection of the transmitted symbol m works as follows [5], |I | X∈I p [14]. First the received signal in (4) is multiplied with the com- As a simple example, consider M = 8 and K = 2. This means that a total of 8 = 28 different messages can be plex conjugate of the basic chirp to produce r[n] = y[n]x [n]. 2 0∗ sent using the following combinations for index sets : Then the discrete-Fourier transform (DFT) is applied on r[n]  Im M 1 j 2πl n 0, 1 , 0, 2 , , 0, 7 , 1, 2 , 1, 3 , , 1, 7 , 2, 3 , to obtain R[l] = − r[n]e M , l = 0, 1, ,M 1. n=0 − {2, 4}, { , }2,···7 , {3, 4}, {3, 5}, { , }3,···7 , {4, 5}, {4, 6}, For coherent detection, i.e., when the channel··· gain− h is { }, ··· { , } { , } { . Then} ··· the{ message} { } { } available at the receiver,P the ML estimate of the transmitted 4, 7 5, 6 5, 7 6, 7 m = 0 {corresponds} { to} { } { and} can be sent using the signal symbol can be found by 0 = 0, 1 s [n] = 1 (xI[n] +{ x [}n]), whereas massage m = 15 0 √2 0 1 mˆ = argmax h∗x∗[m]R[m] . (6) corresponds to = 2, 5 and can be sent using the signal < 0 15 m s [n] = 1 (x I[n] + x{ [n])}, and so on.  15 √2 2 5 For an AWGN channel, (6) further simplifies to Since the total number of distinct combinations of M chirps used for transmission can far exceed M, the data rate of the mˆ = argmax x0∗[m]R[m] . (7) m < proposed scheme can be significantly higher than that of the  conventional FSCSS modulation scheme. To be specific, if all When h is not available at the receiver, the optimal non- 3 coherent detection of FSCSS signals amounts to simply iden- combinations of K chirps out of M chirps are used, where tifying the index of the peak absolute value of the DFT output. 1 K M/2, the number of bits that are mapped to (i.e., ≤ ≤ M That is, carried by) one symbol is given as Λ = log2 K . As an example, for M = 128 and K = 2, we have Λ = 12 bits. 2 j k mˆ = argmax R[m] . (8) In contrast, with the conventional FSCSS modulation (which m corresponds to K = 1), Λ = 7 bits only. This means that

III.PROPOSED FSCSS WITH INDEX MODULATION the data rate for M = 128,K = 2 is almost 1.7 times higher than what{ is achieved with the} conventional FSCSS The proposed scheme exploits index modulation to increase modulation using M = 128 orthogonal chirps. the data rate of the conventional FSCSS system. In particular, Table I tabulates the number of bits that a symbol can carry instead of transmitting only one chirp at a time, multiple chirps in the proposed scheme for different values of M when a are transmitted simultaneously. This results in a significant fixed number of chirps are selected for transmission. Here, we expansion of the signal set, which allows embedding more bits have selected values of M that are typically used in LoRa to one transmitted symbol, thus increasing the achievable data modulation [43], [44]. Note that, in the conventional FSCSS rate. However, increasing the size of the signal set results in modulation scheme, = 1, and as such, a total of log M interference among transmitted symbols as the orthogonality m 2 bits are transmitted per|I symbol.| Table I also tabulates the data among the transmitted symbols is not preserved in the enlarged rate improvements by the proposed scheme. For example, with signal space. This, in turn, results in deterioration of the M = 27 and = 4, one symbol can convey a total of BER performance of the resultant scheme. Additionally, the m 23 bits instead|I of| only 7 bits as in the conventional FSCSS receiver’s complexity generally increases since the receiver scheme. These numbers translate to 3.29 times higher data has to estimate the transmitted symbol from a larger signal rate achieved by the proposed FSCSS-IM scheme. Observe set. that, for LoRa chips, this gain implies that the maximum Fig. 1 depicts the block diagram of the transmitter and achievable data rate can be 123 kbps instead of 37.5 kbps, receiver for the proposed FSCSS-IM system. Among the which is also significantly higher than 50 kbps achievable by depicted blocks, the pulse shaping, interpolation, inphase- the FSK transceiver implemented in LoRa chips. The table also quadrature modulation and digital-to-analog conversion, are lists the very modest data rate improvements by the schemes present in the transmitter of a typical communication system. in [12] (abbreviated as ICS-LoRa) and [15] (abbreviated as Likewise, the receiver of a typical communication system SSK-LoRa). has an analog-to-digital converter, inphase-quadrature demod- Before closing this section, we provide the worst-case PAPR ulator, synchronizer and a matched filter. The rest of the analysis of the transmitted signals produced by the proposed blocks are specific to the proposed scheme. In this section we describe how the proposed scheme is implemented in the 3 M M  We keep K M/2 since K = M K , hence selecting K > M/2 transmitter and also analyze the peak-to-average-power ratio does not result in≤ increased data rate. − 4

x0[n] Transmitter x1[n] x2[n] x3[n] x4[n] Pulse Shaping I/Q Modulator + + Channel Interpolation D/A P 1 xM 3[n] − √ m xM 2[n] |I | − m xM 1[n] − I Mapper m

Receiver I/Q Demodulator + x0∗[n] A/D R[0] R[1]

ˆm M-Point r[n] y[n] Synchronization mˆ I S/P + DFT Matched Filter Detection Algorithm Demapper R[M 1] −

Fig. 1. Block diagram of the proposed FSCSS-IM scheme.

TABLE I NUMBER OF BITS THAT CAN BE TRANSMITTED IN A SYMBOL OF DIFFERENT MODULATION SCHEMES AND DATA-RATE IMPROVEMENT IN PERCENTAGE.

FSCSS ICS-LoRa [12] Proposed FSCSS-IM

m = 1 SSK-LoRa [15] m = 2 m = 3 m = 4 |I | |I | |I | |I | M = 27 7 8 114% 12 171% 18 257% 23 329% M = 28 8 9 112% 14 175% 21 263% 27 338% M = 29 9 10 111% 16 178% 24 267% 31 344% M = 210 10 11 110% 18 180% 27 270% 35 350% M = 211 11 12 109% 20 182% 30 273% 39 355% M = 212 12 13 108% 22 183% 33 275% 43 358% scheme. As noted, the significant data-rate improvements of Consequently, the PAPR of the transmitted signal in the the proposed scheme (as presented in Table I and discussed proposed scheme can be upper bounded as earlier) result from adding multiple chirps together. Adding PAPR . (13) chirps together, however, does not preserve their constant m ≤ |Im| envelope, which increases the PAPR. Note that, for the conventional FSCSS systems, = 1. In In the following, we compare the PAPR of the proposed m that case, the PAPR is exactly equal to its upper|I bound,| i.e., scheme with that of the conventional FSCSS scheme. To this PAPR = 1. On the other hand, using a higher value of end, the PAPR defined for the transmitted signal in complex m m achieves a larger data-rate improvement, but at the expense|I of| baseband-equivalent form is a higher PAPR of the transmitted signal. However, the PAPR

2 as defined in (10) never exceeds m , while m is typically maxn sm[n] 2 |I | |I | PAPRm = | | = max sm[n] , (10) a small number in the proposed scheme. For example, in LTE M 1 2 n − sm[n] /M | | systems, the target PAPR is between 6 dB and 8 dB. This n=0 | | range translates to 6, which can still result in huge P m where the last equality follows from (15). Moreover, (9) data rate improvements|I | (see ≤ Table I). implies that

2 1 IV. DETECTION ALGORITHMSFORTHE PROPOSED max sm[n] = max xl[n]xp[n]∗. (11) n | | m n FSCSS-IMSCHEME l p |I | X∈Im X∈Im In this section we develop the detection algorithms for the Using ai ai , we arrive at proposed FSCSS-IM scheme. We will first present the optimal | i | ≤ i | | detection algorithms (both coherent and non-coherent), then P P 2 1 a suboptimal non-coherent detection algorithm to reduce the max sm[n] max xl[n]xp[n]∗ = m . (12) n | | ≤ m n | | |I | l p computational complexity of the receiver. |I | X∈Im X∈Im 5

Similar to the conventional FSCSS system in Section II, the B. Optimal Non-Coherent Receiver received signal in the proposed FSCSS-IM system is given as When the receiver does not have the knowledge of h, which is the case of practical interest, the ML receiver estimates m by y[n] = hsm[n] + w[n], (14) maximizing the likelihood function f(m y) = E[f(m y, h)], where, as before, m is an arbitrary message symbol, h denotes where the expectation is carried over| the distribution| of the channel gain, and w[n] is a zero-mean circularly-symmetric h. For a Rayleigh fading environment, h is a circularly- white Gaussian noise with variance N0. Since the chirps xl[n] symmetric Gaussian random variable [45, Section 3.2]. That are orthogonal to one another, we have is, h = hR + jhI , where both hR and hI are independent and M 1 M 1 identically distributed zero-mean Gaussian random variables γN¯ − 2 1 − 2 with variance 0 . In order to compute f(m y), we first note sm[n] = xl[n] = M. (15) 2 | | | m | | that n=0 |I | l m n=0 X X∈I X 2 1 ∞ ∞ h 2+2 h∗β |h| Therefore, the average SNR in the proposed system is exactly −| | <{ }− σ2 2 e dhrdhi the same as that in the conventional FSCSS system. πσ Z2−∞ Z−∞ 2 2 2 σ 2 − σ σ 2 2 β h 2 β 2 β e 1+σ | | ∞ ∞ 1+σ e 1+σ | | = e− σ2/(1+σ2) dh dh = , (20) A. Optimal Coherent Receiver πσ2 r i 1 + σ2 Z−∞ Z−∞ The maximum likelihood (ML) estimate of the trans- where the last equality follows from the fact that the area under mitted message aims to maximize the log-likelihood a probability-density function is unity. function. Given the observed signal samples y = Consequently, it is not hard to verify that f(m y) is given y[0] y[1] y[M 1] and channel information h, the by | ··· − likelihood function of message m is given by the multi-variate   M 1 2 complex Gaussian density function as [45, Eq. (5.24)] γN¯ 0 − f(m y) = C0 exp y[n]s∗ [n] , (21) | 1 +γN ¯ m M 1 2  0 n=0 ! 1 n=0− y[n] hsm[n] X f(m y, h)= exp | − | | (πN )M − N where the constant C0 is 0 P 0 ! PM−1 y[n] 2 M 1 exp n=0 | | 2 h∗ n=0− y[n]sm∗ [n] N0 = C exp <{ } , (16) C0 = − . (22) N (πN )M (1 +γN ¯ ) P 0 ! 0 0 where denotes the real part of a complex number, and Using (9), the ML estimate of m can be found as <{·} M 1 2 the constant C is − 2 M 1 2 mˆ = argmax y[n]sm∗ [n] 1 M h + − y[n] m C = exp | | n=0 | | . (17) n=0 M X (πN0) − N0 ! M 1 2 P 1 − = argmax y[n]xl∗[n] . (23) Taking logarithm of both sides and using (9), the ML estimate m m l m n=0 of the message symbol, denoted by mˆ , can be found as |I | X∈I X Lastly, using x [n] = x [l]x [n] exp j 2πl n , we obtain M 1 l 0 0 M h∗ − mˆ = argmax y[n] x [n] . (18) M 1 2 l∗ 1 −  m < ( m ) j2πnl/M |I | n=0 l m mˆ = argmax x0∗[l] r[n]e− X X∈I m m l m n=0 Finally, using (3), we getp |I | X∈I X 1 2 M 1 = argmax x∗[l]R[l] , (24) h∗ − 2πl 0 j M n m m mˆ = argmax x∗[l] y[n]x∗[n]e− l m 0 0 |I | ∈I m < ( m ) X l m n=0 |I | X∈I X where r[n] = y[n]x∗[n], and R[l], l = 0, 1, ,M 1, is the 0 ··· − ph∗ discrete Fourier transform (DFT) of r[n]. = argmax x0∗[l]R[l] , (19) m < m ( l m ) Remark 2. When the index sets have the same cardinality for |I | X∈I all messages, the optimal ML estimate of can be found as where R[l], l =p 0, 1, ,M 1, is the discrete-Fourier m ··· − 2 transform (DFT) of r[n] = y[n]x0∗[n] evaluated at the lth index. In other words, the optimal coherent ML receiver first mˆ = argmax x0∗[l]R[l] . (25) m l m correlates the received signal with a basic down chirp (x0∗[n]), X∈I then performs the DFT operation on the correlated output and Remark 3. For the conventional FSCSS modulation, estimates the transmitted message by maximizing a weighted m = m . Since x0∗[m] = 1, the detection rule in (24) sum of the DFT values. becomesI {(8),} as it should| be.|

Remark 1. For the conventional FSCSS modulation, m = In the general case when more than one chirp are combined m . As such, the ML estimate of the transmitted messageI and used for signal transmission (hence increasing the data simplifies{ } to (6). rate), the above optimal receiver would require a search over 6 all the patterns used at the transmitter to find mˆ that maxi- Algorithm 1 Proposed Suboptimal Receiver for the Complete 2 Codebook 1 mizes x∗[l]R[l] . As such, the optimal receiver m l m 0 Input: m , y[n] for n = 0, 1, ,M 1 |I | ∈I |I | ··· − requires large computational effort and memory. In the sequel, Output: ˆm P I we develop a suboptimal detection scheme that significantly 1: Compute r[n] = y[n]x∗[n] for n = 0, 1, ,M 1 0 ··· − reduces both the computational complexity and memory. 2: Compute R = DFT( r[0] r[1] r[M 1] ) ··· − 3: Compute Y [l] = x∗[l]R[l] for l = 0, 1, ,M 1 0  ··· −  4: 0, 1, ,M 1 C. Proposed Suboptimal Non-Coherent Receiver S ← { ··· − } 5: ˆl = argmax Y [l] The proposed low-complexity detection algorithm estimates 1 l ∈S m in a recursive manner. Once the set m is found, the 6: ˆ ˆl I I Im ← { 1} message m can be determined from m by using the com- 7: ˆl I S ← S \ { 1} binatorial method described in [20, Sect. III], i.e., without the 8: for k = 2, , do ··· |Im| need to store any lookup tables. In particular, the proposed ˆ k 1 ˆ 9: lk = argmaxl Y [l] + m−=1 Y [lm] algorithm estimates the elements of one at a time. In order ∈S Im to conveniently illustrate the proposed detection algorithm, we 10: ˆ ˆ ˆl P Im ← Im ∪ { k} first consider a case when all messages are represented by two 11: ˆl S ← S \ { k} chirps, i.e., = 2. Let = l , l . Then the proposed 12: end for |Im| Im { 1 2} detection algorithm first estimates l1 as

2 TABLE II ˆl1 = argmax R[l] . (26) l | | m ALONGWITH m AND p CORRESPONDINGTO 2 OUTOF 8 SELECTED I INDEXES. Note that (26) estimates l1 exactly the same way as is done for the conventional FSCSS modulation (see (8)). Once is m m p m m p m m p m m p l1 I I I I estimated, can be estimated using (24) as 0 0, 1 1 7 1, 2 10 14 2, 4 20 21 3, 7 31 l2 { } { } { } { } 1 0, 2 2 8 1, 3 11 15 2, 5 21 22 4, 5 37 2 { } { } { } { } ˆ ˆ ˆ 2 0, 3 3 9 1, 4 12 16 2, 6 22 23 4, 6 38 l2 = argmax x0∗[l1]R[l1] + x0∗[l]R[l] . (27) { } { } { } { } l 3 0, 4 4 10 1, 5 13 17 2, 7 23 24 4, 7 39 { } { } { } { } 4 0, 5 5 11 1, 6 14 18 3, 4 28 25 5, 6 46 For m > 2, the proposed detection rule is carried out sim- { } { } { } { } |I | 5 0, 6 6 12 1, 7 15 19 3, 5 29 26 5, 7 47 ilarly. In particular, the elements of m = l1, l2, , l { } { } { } { } I { ··· |Im|} 6 0, 7 7 13 2, 3 19 20 3, 6 30 27 6, 7 55 are detected recursively as { } { } { } { } ˆ l1 = argmax x0∗[l]R[l] = argmax x0∗[l] R[l] l l Table II also tabulates a number p along with the index 2 = argmax R[l] , (28) set m corresponding to message m. For a given m = l l , I , l , where l < < l , p is calculatedI as 1 m 1 m and { ··· |I |} ··· |I | m 1 k 2 |I |− m i ˆ ˆ ˆ p = li+1M |I |− . (30) lk+1 = argmax x0∗[l]R[l] + x0∗[lm]R[lm] , (29) i=0 l m=1 X X for k = 1, 2, , 1. Observe that there is a one-to-one relationship between m m I A pseudo··· code|I of| − the proposed detection algorithm is (or equivalently, m) and p, and p increases as m increases and described in Algorithm 1. The code assumes that all com- vice versa. As such, m m0 is equivalent to p p0, where M ≤ ≤ binations of the chirps (that is of them) are used for p0 is the number corresponding to m0 . For example, m 15 K I ≤ transmission. In practice, however, a total of 2Λ codewords corresponds to p 21 for the codewords in Table II.  ≤ are used, where Λ is the number of bits represented by each To work with the reduced codebook, Algorithm 1 needs to symbol. The most common case is when Λ = M . This incorporate the condition m 2Λ 1, which is equivalent to b K c ≤ − means that Algorithm 1 can produce catastrophic results when incorporating the condition p p0, where p0 is computed  ≤ the estimated m does not belong to the codebook used at the for 2Λ 1. To this end, we add an extra condition while I − transmitter [20].I In order to avoid such catastrophic results, we determining the last index in the estimated in the proposed Im introduce Algorithm 2 and explain how it works and differs detection scheme presented in Algorithm 1. The modification from Algorithm 1 in the following. is incorporated in Algorithm 2, where we use a function To elaborate the difference between Algorithm 1 and Algo- FINALINDEX to determine the range of the last index, ˆl . |Im| rithm 2, we consider Table II, which lists all 28 combinations The function FINALINDEX is given in Algorithm 3. It takes for M = 8 and m = 2. Algorithm 1 assumes that all three inputs: the estimated , the final index set , and the combinations are used|I | for message transmission, whereas Al- cardinality of . Elements ofI both sets are in ascendingF order. gorithm 2 only considers the first 16 codewords, corresponding In the following,F we explain the operations carried out by the to m = 0, 1, , 15, for messages. function FINALINDEX by considering the codebook of Table ··· 7

Algorithm 2 Proposed Suboptimal Receiver for a Reduced for general and K. Depending on the first (and the min- Codebook imum) elementsF of both sets, we have three cases: (1) < I Input: m , y[n] for n = 0, 1, ,M 1, LastCode (1), (1) > (1), and (1) = (1). When (1) < (1), |Iˆ | ··· − F I F I F I F Output: m we return M 1. On the other hand, when (1) > (1), I − K 1 i K I1 F i 1: Compute r[n] = y[n]x0∗[n] for n = 0, 1, ,M 1 we return − − to ··· − (1) + i=1 (i + 1)M − i=1 (i)M − 2: Compute R = DFT( r[0] r[1] r[M 1] ) F F − I ··· − ensure that the number p corresponding to is less than or 3: Compute Y [l] = x∗[l]R[l] for l = 0, 1, ,M 1 P PI 0  ··· −  equal to p0. Last, when (1) = (1), finding the maximum 4: 0, 1, ,M 1 I F S ← { ··· − } possible value of the last index becomes equivalent to finding ˆ the maximum possible value of the last index of (2 : K). 5: l1 = argmaxl Y [l] I ∈S As such, we call FINALINDEX() to determine the maximum 6: ˆ ˆl Im ← { 1} limit of the last index of in Algorithm 3. 7: ˆl I S ← S \ { 1} 8: for k = 2, , 1 do ··· |Im| − D. Computational Complexity and Memory Requirements ˆ k 1 ˆ 9: lk = argmaxl Y [l] + m−=1 Y [lm] ∈S The optimal detection algorithms determines the index set by searching over the entire codebook. Since the codebook 10: ˆm ˆm ˆlk P M m I ← I ˆ∪ { } length is of the order of = M |I | , the com- 11: lk m S ← S \ { } |I | O 12: end for putational complexity and the memory requirements of the  m  13: Sort ˆ in ascending order optimal algorithm are both M |I | . On the other hand, the Im O 14: z FINALINDEX(ˆ , LastCode, ) proposed suboptimal detection algorithm does not require the ← Im |Im|  1 codebook to be saved, which results in a huge memory saving. 15: ˆ |Im|− ˆ l m = argmaxl ,l z Y [l] + m=1 Y [lm] |I | ∈S ≤ Furthermore, the proposed suboptimal detection algorithm determines the index set by finding the maximum of a metric 16: ˆm ˆm ˆl P I ← I ∪ { |Im|} for a total of m times. Since the complexity of finding the maximum from|I a| list of size M is (M), the computational O II. For convenience, we denote the kth elements of and complexity of the proposed suboptimal detection algorithm I F is only (M ), i.e., linear in both and M and by (k) and (k), respectively. O |Im| |Im| ForI the codebookF of Table II, = 2, 5 . We consider four much lower than the computational complexity of the optimal values of ˆl , i.e., ˆl = 0, 2, 4, 6.F Note{ that } = ˆl . Now, for detection algorithm. 1 1 I { 1} (1) = ˆl1 = 0 < (1), ˆl2 can be as large as M 1 = 7. For I(1) = ˆl = 2 = F(1), the maximum value of ˆl −is 5. Finally, V. PERFORMANCE RESULTS AND COMPARISON I 1 F 2 the maximum value of ˆl2 is 2 when ˆl1 = 4 and is 1 when In this section, we present simulation results to depict the ˆl = 6. Observe that, in the last two case, (1) > (1), and BER performance of the proposed FSCSS-IM system under 1 I F the maximum value of ˆl2 can be determined by ensuring that both optimal and suboptimal detection algorithms. The BER the number p corresponding to must not exceed p = 21. performance is also compared to that of the conventional I 0 This can be done by satisfying ˆl2 M +ˆl1 (1) M + (2). FSCSS system. × ≤ F × 1 F Solving the inequality yields ˆl2 (1)+ (2) M − (1) Fig. 2 depicts the BER of the proposed FSCSS-IM system 1 ≤ F F × −I × M − . in an AWGN channel when two chirps are selected for repre- senting a message symbol. Here, the BER performance of the Algorithm 3 Final Index Range Finder optimal non-coherent detection rule in (24) and the proposed 1: function FINALINDEX( , , K) I F low-complexity suboptimal detection algorithm described in 2: if K = 1 then Section IV-C are plotted. A total of 109 Monte-Carlo trials 3: return (1) F were used to generate the plots. 4: end if A couple of interesting observations can be made from 5: if (1) < (1) then I F the plotted curves. First, the proposed suboptimal detection 6: return M 1 − algorithm enjoys near-optimal performance for the whole 7: else Es/N0 Eb/N0 range, where Eb/N0 = Λ is the signal-to-noise 8: if (1) > (1) then ratio per bit, and for all values of M. This is despite the I F K 1 i 9: p0 (1) + i=1− (i + 1)M − fact that the proposed scheme is highly memory efficient and ← FK 1 iF 10: p − (i)M − significantly less computationally intensive than the optimal ← i=1 I P 11: return p0 p algorithms, as mentioned in Section IV-D. P − 12: else Second, similar to the conventional FSCSS modulation, the 13: return FINALINDEX( (2:K), (2:K), K-1) performance of the proposed FSCSS-IM scheme improves I F 14: end if as the number of orthogonal chirps increases. This improve- 15: end if ment in the BER performance comes at the expense of the 16: end function achievable data rate. For example, for the same occupied bandwidth, an FSCSS-IM symbol for M = 256 is two times Now, we describe the operations of FINALINDEX( , ,K) longer than a FSCSS-IM symbol corresponding to M = 128. I F 8

-1 -1 10 10

-2 10 -2 10

-3 10 -3 10 -4 10 Bit-Error Rate Bit-Error Rate -4 10 -5 10 Proposed, M = 128 FSCSS (M = 128) Optimal, M = 128 FSCSS-IM (M = 128, m = 2) Proposed, M = 256 -5 |I | -6 10 FSCSS-IM (M = 128, m = 3) 10 Optimal, M = 256 FSCSS (M = 256) |I | Proposed, M = 512 FSCSS-IM (M = 256, m = 2) Optimal, M = 512 FSCSS-IM (M = 256, |I | = 3) -7 -6 m 10 10 |I | 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 0 1 2 3 4 5 6 Eb/N0 [dB] Eb/N0 [dB]

Fig. 2. BER comparison of the optimal and proposed suboptimal non-coherent Fig. 3. BER comparison of the conventional FSCSS and proposed FSCSS-IM detection algorithms for the FSCSS-IM system when M = 128, 256, 512, systems for M = 128, 256. and m = 2. |I |

rate than the conventional FSCSS modulation scheme while Consequently, for m = 2, the maximum achievable data rate slightly improving the BER performance. Specifically, con- for M = 256 is 1|I/2 | 14/12 0.583 times the maximum × ≈ sider the BER performance of the conventional FSCSS mod- data rate achievable for M = 128. But, on the other hand, ulation scheme for M = 128 and the proposed FSCSS-IM FSCSS-IM with M = 256 shows a performance gain of 0.5 scheme for M = 256 and m = 3. The figure depicts 5 |I | dB over FSCSS-IM with M = 128 at the BER of 10− . that the proposed FSCSS-IM scheme has slightly better BER Fig. 3 shows the BER performance of the conventional performance than the conventional scheme. Note that the FSCSS system for M = 128 and M = 256 in an AWGN symbol duration of the conventional FSCSS modulation for channel. A total of 109 Monte-Carlo trials were used to M = 128 is half of the symbol duration of the proposed generate the plots. A similar trend is observed in this figure, FSCSS-IM scheme for M = 256. Also, each transmitted i.e., the lower the data rate of a scheme is, the better it symbol conveys a total of Λ = 21 bits in the proposed performs in terms of BER. This trend is evident from the slight FSCSS-IM scheme. On the other hand, in the same symbol degradation in BER performance of FSCSS-IM when m duration, the conventional FSCSS scheme can transmit a total |I | increases from 1 to 3 for both values of M. Such performance of 2 7 = 14 bits. That is, the proposed FSCSS-IM scheme, degradation can be intuitively explained from the fact that in while× performing slightly better than the conventional FSCSS the conventional FSCSS scheme ( m = 1), the index sets modulation scheme, can also achieve a data rate of 1.5 times |I | are non-overlapping, whereas they generally overlap in the that of the conventional FSCSS modulation scheme. proposed FSCSS-IM scheme ( m > 1). This overlap results In Fig. 4, the symbol-error-rate (SER) performance of both |I | in slight degradation of the bit-error-rate performance. the conventional FSCSS and proposed FSCSS-IM schemes are Another interesting observation can be made from Fig. 3. plotted against the channel SNR, γ¯, in an AWGN channel. For each M, the bit-error rates for = 2, 3 are only Observe that the lower the data rate of a scheme, the better |Im| slightly worse than that for = 1, which corresponds the scheme is in terms of SER, and vice versa. In the figure, |Im| to the conventional FSCSS modulation scheme. On the other for example, (M, m ) = (256, 1) scheme has the lowest SER hand, the maximum data rates achieved with = 2, 3 are for a given channel|I SNR,| while (M, ) = (128, 2) has the |Im| m significantly higher than that with the conventional FSCSS highest SER. At the same time, the first|I scheme| has the lowest modulation. For instance, the maximum data rate achieved data rate, whereas the latter has the highest data rate. The with = 2 and = 3 for M = 128 are Λ/ log (M) = (M, ) = (128, 1) and (M, ) = (256, 2) schemes have |Im| |Im| 2 m m 12/7 1.7143 and Λ/ log (M) = 18/7 2.5714 times the same|I | data rate and have almost|I | the same SER performance ≈ 2 ≈ the maximum data rate achieved by the conventional FSCSS against the channel SNR. That is, the proposed FSCSS-IM modulation, respectively. So the proposed FSCSS-IM system scheme and conventional FSCSS modulation scheme have can improve the achievable data rate significantly with only similar reception sensitivity for the same data rate. slight degradation in the bit-error rate. The data rate can Next, Fig. 5 compares performance of the proposed FSCSS- further be improved by using more chirps for transmission IM scheme with the SSK-LoRa scheme introduced in [15]. and reception, i.e., by using m > 3. The plots are generated using a total of 109 Monte-Carlo trials |I | On a difference comparison, Fig. 3 actually shows that (i.e., 109 FSCSS-IM or SSK-LoRa symbols are simulated for the proposed FSCSS-IM scheme can achieve a higher data each SNR value). Fig. 5 depicts that the BER performance 9

0 10

-1 10

-1 10

-2 10

-2 10 -3 10

-3 10 Bit-Error Rate -4 10 Symbol-Error Rate SSK-LoRa -4 FSCSS 10 -5 10 Proposed ( m = 2) (M = 128, m = 1) |I | |I | K-Max ( m = 2) (M = 256, m = 1) |I | |I | Proposed ( m = 3) (M = 128, m = 2) |I | -5 K-Max ( m = 3) 10 |I | -6 (M = 256, m = 2) 10 |I | |I | 0 1 2 3 4 5 6 -16 -15 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 Eb/N0 [dB] γ¯ [dB]

Fig. 5. BER comparison of the FSCSS-based modulation schemes under Fig. 4. SER comparison of the conventional FSCSS modulation and proposed different detection schemes for M = 256. FSCSS-IM schemes for M = 128, 256 and m = 1, 2. |I | of SSK-LoRa modulation is better than the BERs of both the conventional FSCSS and proposed FSCSS-IM schemes. -1 10 On the other hand, the proposed FSCSS-IM scheme per- forms slightly worse than the conventional FSCSS modulation scheme when the receiver of Algorithm 2 is used. In terms of data rate, although the SSK-LoRa modulation scheme also achieves higher data rates than the conventional FSCSS -2 modulation scheme, the data-rate improvements are marginal. Bit-Error Rate 10 In particular, for M = 256, the data-rate improvement is only 12.5%. In contrast, the proposed FSCSS-IM scheme achieves significant improvements in the data rate while performing Optimal Coherent only slightly worse than the conventional FSCSS modulation Optimal Noncoherent Proposed scheme. The data-rate improvements for the proposed scheme, 10 -3 0 5 10 15 20 25 as given in Table I, are 75% and 163% for m = 2, and |I | Eb/N0 [dB] m = 3, respectively. Finally, the figure also depicts the performance|I | of the proposed FSCSS-IM scheme when using a non-coherent detection algorithm similar to that proposed in Fig. 6. BER performance of the proposed FSCSS-IM with different detection schemes for M = 128, m = 2 over a Rayleigh fading channel. [23] for OFDM-IM and [46] for multi-tone FSK modulation |I | (labeled as “K-Max” in the figure’s legend). In particular, in the K-max algorithm, the indexes of the largest values of |Im| coherent reception. Again, this comparison clearly demon- x0∗[l]R[l] (or equivalently, R[l] , since x0∗[l] = 1) constitute |the estimated| index set. Observe| | that our| proposed| detection strates the efficiency and effectiveness of the proposed low- scheme results in much better performance than the scheme complexity non-coherent detection for the FSCSS-IM scheme. of [23]. Finally, Fig. 6 shows the performance of the proposed VI.CONCLUSION scheme over a Rayleigh fading channel. A total of 106 Monte- In this paper, we introduced index modulation into the Carlo trials were used for each SNR to generate the plot. conventional FSCSS system to improve the achievable data The figure displays the performance of the optimal detec- rates for different system parameters. We have also developed tion schemes along with the proposed suboptimal detection optimal coherent and non-coherent detection algorithms for the scheme. As expected, because the optimal coherent proposed FSCSS-IM scheme under fading channels. Moreover, makes use of the channel-state information, it shows the best a suboptimal non-coherent detection algorithm was also pro- performance. The optimal non-coherent detection incurs a posed that eliminates memory requirement and significantly SNR degradation of about 0.8 dB as compared to the coherent reduces the computational complexity of the optimal algo- detection, whereas the proposed suboptimal reception shows rithm, while performing almost equally well. The proposed almost identical performance as that of the optimal non- FSCSS-IM scheme is very flexible to design and can achieve 10

much higher data rates than the conventional FSCSS system [18] M. Wen, X. Cheng, and L. Yang, Index Modulation for 5G Wireless (under the same bandwidth) with only slight degradations in Communications. Springer International Publishing, 2016. [19] H. L. Schneider, “Data transmission with FSK permutation modulation,” the bit-error rate performance. The Bell System Technical Journal, vol. 47, no. 6, pp. 1131–1138, Jul. Although the conventional FSCSS system uses orthogonal 1968. chirps, the concept of index modulation can also be applied for [20] E. Bas¸ar, U.¨ Aygol¨ u,¨ E. Panayırcı, and H. V. Poor, “Orthogonal frequency division multiplexing with index modulation,” IEEE Trans. a set of non-orthogonal chirps. As discussed in the paper, using Signal Process., vol. 61, no. 22, pp. 5536–5549, Nov. 2013. both up and down chirps, and even together with interleaved [21] M. Wen, B. Ye, E. Basar, Q. Li, and F. Ji, “Enhanced orthogonal chirps can increase the highest achievable data rate of the frequency division multiplexing with index modulation,” IEEE Trans. Wireless Commun., vol. 16, no. 7, pp. 4786–4801, Jul. 2017. conventional FSCSS modulation scheme. Moreover, applying [22] M. Wen, Q. Li, E. Basar, and W. Zhang, “Generalized multiple-mode the concept of index modulation on top of such an expanded OFDM with index modulation,” IEEE Trans. Wireless Commun., vol. 17, set of (non-orthogonal) chirps can further improve the data no. 10, pp. 6531–6543, Oct. 2018. [23] J. Choi, “Noncoherent OFDM-IM and its performance analysis,” IEEE rate. Developing optimal and low-complexity suboptimal re- Trans. Wireless Commun., vol. 17, no. 1, pp. 352–360, Jan. 2018. ceivers and performing theoretical analysis of the bit-error [24] R. Fan, Y. J. Yu, and Y. L. Guan, “Generalization of orthogonal rate performance for such a novel scheme (as well as for the frequency division multiplexing with index modulation,” IEEE Trans. Wireless Commun., vol. 14, no. 10, pp. 5350–5359, Oct. 2015. proposed FSCSS-IM for that matter) is an interesting topic [25] S. Sasaki, J. Zhu, and G. Marubayashi, “Performance of parallel com- and is left as a future research topic. binatory spread spectrum multiple access communication systems,” in IEEE Int. Symp. Personal, Indoor and Mobile Radio Commun., Sep. 1991, pp. 204–208. CKNOWLEDGEMENT A [26] Y. A. Chau and S.-H. Yu, “ on wireless fading This work is supported by the NSERC/Cisco Industrial channels,” in IEEE Veh. Technol. Conf., vol. 3, Oct. 2001, pp. 1668– 1671. Research Chair in Low-Power Wireless Access in Sensor [27] R. Y. Mesleh, H. Haas, S. Sinanovic, C. W. Ahn, and S. Yun, “Spatial Networks. modulation,” IEEE Trans. Veh. Technol., vol. 57, no. 4, pp. 2228–2241, Jul. 2008. REFERENCES [28] A. Younis, N. Serafimovski, R. Mesleh, and H. Haas, “Generalised spatial modulation,” in Asilomar Conf. Signals, Syst. Comput., 2010, [1] E. Karapistoli, F. Pavlidou, I. Gragopoulos, and I. Tsetsinas, “An pp. 1498–1502. overview of the IEEE 802.15.4a standard,” IEEE Commun. Mag., [29] J. Wang, S. Jia, and J. Song, “Generalised spatial modulation system vol. 48, no. 1, pp. 47–53, Jan. 2010. with multiple active transmit antennas and low complexity detection [2] U. Raza, P. Kulkarni, and M. Sooriyabandara, “Low power wide area scheme,” IEEE Trans. Wireless Commun., vol. 11, no. 4, pp. 1605–1615, networks: An overview,” IEEE Commun. Surveys Tuts., vol. 19, no. 2, Apr. 2012. pp. 855–873, 2nd quarter 2017. [30] J. Jeganathan, A. Ghrayeb, L. Szczecinski, and A. Ceron, “Space [3] SemTech, “AN1200.22: LoRa Modulation Basics,” May 2015. shift keying modulation for MIMO channels,” IEEE Trans. Wireless [4] ——, “AN1200.13: SX1272/3/6/7/8: LoRa Designer’s Guide,” Commun., vol. 8, no. 7, pp. 3692–3703, Jul. 2009. Jul. 2013. [31] J. Jeganathan, A. Ghrayeb, and L. Szczecinski, “Generalized space shift [5] L. Vangelista, “Frequency shift chirp modulation: The LoRa modula- keying modulation for MIMO channels,” in Int. Symp. Pers. Indoor tion,” IEEE Signal Process. Lett., vol. 24, no. 12, pp. 1818–1821, Dec. Mobile Radio Commun., 2008, pp. 1–5. 2017. [32] C. Luo, M. Medard, and L. Zheng, “On approaching wideband capacity [6] J. R. Klauder, A. C. Price, S. Darlington, and W. J. Albersheim, “The using multitone FSK,” IEEE J. Sel. Areas Commun., vol. 23, no. 9, pp. theory and design of chirp radars,” The Bell Syst. Tech. J., vol. 39, no. 4, 1830–1838, Sep. 2005. pp. 745–808, Jul. 1960. [33] N. Ishikawa, S. Sugiura, and L. Hanzo, “50 years of permutation, spatial [7] D. S. Dayton, “FM “chirp” communications: Multiple access to disper- and index modulation: From classic RF to visible light communications sive channels,” IEEE Trans. Electromagn. Compat., vol. EMC-10, no. 2, and data storage,” IEEE Commun. Surveys Tuts., vol. 20, no. 3, pp. pp. 296–297, Jun. 1968. 1905–1938, 3rd Quarter 2018. [8] A. Berni and W. Gregg, “On the utility of chirp modulation for digital [34] M. Wen, B. Zheng, K. J. Kim, M. Di Renzo, T. A. Tsiftsis, K. Chen, signaling,” IEEE Trans. Commun., vol. 21, no. 6, pp. 748–751, Jun. and N. Al-Dhahir, “A survey on spatial modulation in emerging wireless 1973. systems: Research progresses and applications,” IEEE J. Sel. Areas [9] A. Springer, W. Gugler, M. Huemer, R. Koller, and R. Weigel, “A Commun., vol. 37, no. 9, pp. 1949–1972, Sep. 2019. wireless spread-spectrum communication system using SAW chirped [35] E. Basar, M. Wen, R. Mesleh, M. Di Renzo, Y. Xiao, and H. Haas, delay lines,” IEEE Trans. Microw. Theory Techn., vol. 49, no. 4, pp. “Index modulation techniques for next-generation wireless networks,” 754–760, Apr. 2001. IEEE Access, vol. 5, pp. 16 693–16 746, Aug. 2017. [10] P. Zhang and H. Liu, “An ultra-wide band system with chirp spread [36] S. D. Tusha, A. Tusha, E. Basar, and H. Arslan, “Multidimensional spectrum transmission technique,” in 6th Int. Conf. ITS Telecommun., index modulation for 5G and beyond wireless networks,” Proc. IEEE, Jun. 2006, pp. 294–297. vol. 109, no. 2, pp. 170–199, Feb. 2021. [11] B. Reynders and S. Pollin, “Chirp spread spectrum as a modulation [37] M. Hanif and H. H. Nguyen, “Methods for improving flexibility and technique for long range communication,” in Symp. Commun. Veh. data rate of chirp spread spectrum systems in LoRaWAN.” Technol., Nov. 2016, pp. 1–5. [38] T. Yoon, S. Ahn, S. Y. Kim, and S. Yoon, “Performance analysis of an [12] T. Elshabrawy and J. Robert, “Interleaved chirp spreading LoRa-based overlap-based CSS system,” in Int. Conf. Adv. Commun. Technol., vol. 1, modulation,” IEEE Internet Things J., vol. 6, no. 2, pp. 3855–3863, Apr. Feb. 2008, pp. 424–426. 2019. [39] G. Kaddoum, M. F. A. Ahmed, and Y. Nijsure, “Code index modulation: [13] R. Bomfin, M. Chafii, and G. Fettweis, “A novel modulation for IoT: A high data rate and energy efficient communication system,” IEEE PSK-LoRa,” in IEEE Veh. Technol. Conf., Apr. 2019, pp. 1–5. Commun. Lett., vol. 19, no. 2, pp. 175–178, Feb. 2015. [14] T. T. Nguyen, H. H. Nguyen, R. Barton, and P. Grossetete, “Efficient [40] G. Kaddoum, Y. Nijsure, and H. Tran, “Generalized code index modula- design of chirp spread spectrum modulation for low-power wide-area tion technique for high-data-rate communication systems,” IEEE Trans. networks,” IEEE Internet Things J., vol. 6, pp. 9503–9515, Dec. 2019. Veh. Technol., vol. 65, no. 9, pp. 7000–7009, Sep. 2016. [15] M. Hanif and H. H. Nguyen, “Slope-shift keying LoRa-based modula- [41] Q. Li, M. Wen, E. Basar, and F. Chen, “Index modulated OFDM spread tion,” IEEE Internet Things J., vol. 8, no. 1, pp. 211–221, Jan. 2021. spectrum,” IEEE Trans. Wireless Commun., vol. 17, no. 4, pp. 2360– [16] Z. Xu, S. Tong, P. Xie, and J. Wang, “FlipLoRa: Resolving collisions 2374, Apr. 2018. with up-down quasi-orthogonality,” in IEEE Int. Conf. Sens. Commun. [42] M. Chiani and A. Elzanaty, “On the LoRa modulation for IoT: Wave- Netw. (SECON), 2020, pp. 1–9. form properties and spectral analysis,” IEEE Internet Things J., vol. 6, [17] D. Slepian, “Permutation modulation,” Proc. IEEE, vol. 53, no. 3, pp. no. 5, pp. 8463–8470, Oct. 2019. 228–236, Mar. 1965. 11

[43] SemTech, “AN1200.26: LoRa and FCC Part 15.247: Measurement Ha H. Nguyen received the B.Eng. degree from Guidance,” May 2015. Hanoi University of Technology (HUT), Hanoi, [44] ——, “SX1276/77/78/79 - 137 MHz to 1020 MHz Low Power Long Vietnam, in 1995, the M.Eng. degree from the Asian Range Transceiver,” Aug. 2016. Institute of Technology (AIT), Bangkok, Thailand, [45] A. Goldsmith, Wireless Communications. Cambridge, U.K.: Cambridge in 1997, and the Ph.D. degree from the University University Press, 2005. of Manitoba, Winnipeg, MB, Canada, in 2001, all in [46] C. Luo and M. Medard, “Performance of single-tone and two-tone electrical engineering. He joined the Department of frequency-shift keying for ultrawideband,” in Asilomar Conf. Signals, Electrical and Computer Engineering, University of Syst. Comput., vol. 1, Nov. 2002, pp. 701–705. Saskatchewan, Saskatoon, SK, Canada, in 2001, and became a full Professor in 2007. He currently holds the position of NSERC/Cisco Industrial Research Chair in Low-Power Wireless Access for Sensor Networks. His research interests fall into broad areas of Communication Theory, Wireless Communi- cations, and Statistical Signal Processing. Dr. Nguyen was an Associate Editor Muhammad Hanif received the Ph.D. degree in for the IEEE Transactions on Wireless Communications and IEEE Wireless electrical engineering from the University of Victo- Communications Letters during 2007-2011 and 2011-2016, respectively. He ria, Canada, in 2016. He was a Post-Doctoral Fellow currently serves as an Associate Editor for the IEEE Transactions on Vehicular with the University of Alberta, Canada, from 2016 Technology. He served as a Technical Program Chair for numerous IEEE to 2018, and with the University of Saskatchewan, events. He is a coauthor, with Ed Shwedyk, of the textbook ”A First Canada, from 2018 to 2019. He is currently an Course in Digital Communications” (published by Cambridge University Assistant Professor at Thompson Rivers University, Press). Dr. Nguyen is a Fellow of the Engineering Institute of Canada (EIC) Canada. His research interests are in the general area and a Registered Member of the Association of Professional Engineers and of signal processing and wireless communication Geoscientists of Saskatchewan (APEGS). systems, including cognitive radio networks, mas- sive MIMO systems, polar codes, and machine-to- machine communications.