Anti-Multipath Performance Improvement of an M-ary Position Phase Shift Keying Modulation System

Transcription

1 sesors Article Ati-Multipath Performace Improvemet of a M-ary Positio Phase Shift Keyig Modulatio System Haiyua Wag ad Hogxia Tia * School of Electroic ad Iformatio Egieerig Beijig Jiaotog Uiversity, Beijig 44, Chia; 722@bjtu.edu.c * Correspodece: hxtia@bjtu.edu.c; Tel.: Received: 7 March 29; Accepted: 22 April 29; Published: 25 April 29 Abstract: Low-Power Wide-Area Network (LPWAN) is the techology that the Iteret-of-Thigs (IoT) uses i log-distace, wide-coverage scearios. As oe of the ultra-arrowbad (UNB) modulatio techiques, M-ary positio phase shift keyig (MPPSK) modulatio ca provide high coverage ad high reliability for LPWAN. This paper proposes a multipath separatio method based o MPPSK modulatio, which aims to elimiate the ifluece of multipath o the mai path without icreasig the spectrum overhead ad system complexity. Specifically, the modulatio parameter of the system is adjusted accordig to the delay value, so that the phase jump of the multipath sigal falls outside the phase jump of the mai path symbol to achieve separatio of the multipath from the mai path. Moreover, a ormalized symbol joit decisio method is proposed i order to reduce the itroduced oise while usig multipath iformatio for decisios. The simulatio results idicate that the multipath separatio coditios give i this paper ca meet the requiremets of multipath separatio of MPPSK sigals. Compared with the existig maistream decisio scheme, the ormalized symbol joit decisio improves the demodulatio performace of the system. Keywords: M-ary positio phase shift keyig; multipath; joit judgmet. Itroductio The Iteret-of-Thigs is a ew cocept that is icreasigly attractig the attetio of researchers ad idustries []. It is expected that by 22, there will be 2 billio commuicatig objects i the world [2]. I order to meet the demad of so may coectec devices, LPWAN that ca realize log-distace trasmissio ad reduce commuicatio power cosumptio is proposed [3]. Ultra-arrowbad modulatio with high spectral efficiecy as the physical layer techology of LPWAN ad ca meet the large coverage ad high reliability requiremets of LPWAN [2,4 8]. I order to achieve very high spectral efficiecy without excessively reducig power efficiecy, modulatio of M-ary Positio Phase Shift Keyig (MPPSK) is proposed based o Exted Biary Phase Shift Keyig (EBPSK) modulatio [9 ]. As a multi-bad form of EBPSK modulatio, it is a efficiet ad flexible modulatio method. The receiver ca achieve demodulatio by extractig tiy modulatio iformatio usig a extremely arrow pass bad filter called a digital impactig filter (DIF). I [2,3], the special mechaism of DIF is explaied i detail. MPPSK ca flexibly select modulatio schemes, chage bit rate, power efficiecy ad spectrum efficiecy by chagig modulatio parameters. Compared with traditioal modulatio methods, MPPSK also has the advatages of high badwidth efficiecy ad lie spectrum elimiatio. Therefore, it has importat theoretical ad practical sigificace. High-speed digital mobile commuicatio is affected by frequecy selective fadig caused by multipath with various time delays [4]. Iter-symbol iterferece caused by frequecy selective fadig Sesors 29, 9, 938; doi:.339/s

2 Sesors 29, 9, of 7 affects the correct demodulatio of the demodulator, thereby limitig the maximum trasmissio data rate. I order to combat multipath fadig, techiques such as diversity ad equalizatio ca be employed. The multipath separatio techique is based o spread spectrum commuicatio. Usig the good autocorrelatio property of the Pseudo-Noise Sequeces, the receiver separates the multipath sigal by correlatig the multipath sigal with multiple correlators [5,6]. However, the spread of the sigal spectrum reduces the spectrum utilizatio ad the demodulator complexity is high. I [7], a multipath separatio method based o the EBPSK modulatio system is proposed. This scheme is oly applicable to biary EBPSK modulatio, ad there are fewer scearios available. Whe sub-path iformatio is used to participate i the decisio, the multipath separatio scheme based o EBPSK modulatio itroduces all sub-path oise. I order to further improve the frequecy bad utilizatio, it is very importat to study the ati-fadig of multi-ary modulatio techology i efficiet modulatio. I this paper, based o the waveform characteristics of MPPSK modulatio, a multipath separatio method based o MPPSK modulatio is proposed ad the multipath separatio coditios are give. The modulatio parameters are adjusted by the multipath delay value to achieve the separatio of the multipath ad the mai path, thereby reducig the iter-symbol iterferece of the multipath sigal to the mai path sigal ad improvig the ati-multipath iterferece ability of the sigal. Compared with the scheme of separatig multipath by sigal spread spectrum, this scheme reduces the spectrum overhead. Compared with the multipath separatio scheme proposed i [7] for biary ultra-arrowbad sigals, the multipath separatio method proposed i this paper is applicable to the M-ary MPPSK sigals with higher trasmissio rate. By usig the ormalized symbol joit decisio proposed i this paper, the receiver reduces the itroduced oise while utilizig multipath iformatio, thereby reducig the bit error rate of the system. The rest of this paper is orgaized as follows. Sectio 2 itroduces the chael model, MPPSK modulatio ad demodulatio scheme. Sectio 3 itroduces multipath delay estimatio, modulatio parameter desig ad ormalized symbol joit decisio. Sectio 4 presets the simulatio results. Fially, Sectio 5 cocludes the paper. 2. System Descriptio 2.. Mppsk Modulatio MPPSK is a high spectral efficiecy techique ad a member of the sie-like modulatio family [8]. MPPSK modulatio is a modulatio method exteded from EBPSK to multi-ary modulatio, which uses M-ary symbol to cotrol the phase hoppig positio of siusoidal carrier i each symbol period. Sice MPPSK makes full use of the positio chage of the phase jump i the symbol, the iformatio trasmissio rate is icreased by log 2 M times uder the same badwidth coditio, thereby further improvig the spectrum utilizatio rate. The expressio of MPPSK modulatio i a symbol period [, NT] is give by Asi2π f c t t < NT, k = f k (t) = Asi2π f c t t < (k )KT Bsi(2π f c t + θ) (k )KT < t < (k r g )KT, k M Asi2π f c t (k r g )KT t < NT where A is the carrier amplitude of the symbol ad the o-zero symbol o-phase modulatio iterval, B is the carrier amplitude of the o-zero symbol phase modulatio iterval, k =,, 2,..., M is the actual trasmitted symbol with M 2 values, T = ( ) 2π wc () is the carrier period, N is the umber of carrier cycles i the symbol period, T s = NT is the symbol period, ( r g )K is the umber of carrier cycles that the phase jump cotiues, < θ π is the agle of the phase jump, ad r g ( r g < ) is the Guard Iterval factor. I order to meet the requiremets of differet applicatio idicators, differet modulatio sigal badwidths, trasmissio rates, ad system demodulatio performace

3 Sesors 29, 9, of 7 ca be obtaied by adjustig the values of modulatio parameters A, B, M, N, K, θ ad r g. The MPPSK sigal i the specific case A = B =, r g =, N =, K = 2, θ = π ad M = 4 are depicted i Figure. symbol symbol Samplig poit symbol 2-5 Samplig poit symbol Samplig poit - 5 Samplig poit Figure. The MPPSK Waveforms Mppsk Demodulatio Special impactig filter is a special class of ifiite impulse respose (IIR) filters [9]. I very arrow passbads, Special impactig filter (SIF) has otch ad select frequecy characteristics. While filterig out oise, SIF ca covert the phase jump of the MPPSK modulated sigal ito a amplitude impactig. Therefore, the modulatio symbol ca be demodulated by detectig the positio of the impact at the demodulatio termial, which greatly simplifies the demodulatio difficulty of the MPPSK system. The trasfer fuctio of SIF is give by H(z) = L b(i)z i i= + J (2) a(i)z i i= This paper takes the filter havig two cojugate poles ad oe zero poit, where b = b 2 = ; b = , a = , a 2 = , a 3 = , a 4 = The desiged filter is suitable for MPPSK sigal whose samplig frequecy is 2 times of carrier frequecy. -frequecy respose ad phase-frequecy respose of the SIF are show i Figure 2.

4 Sesors 29, 9, of 7 Figure 2. The MPPSK Waveforms. I this paper, the demodulatio method based o amplitude itegral decisio is adopted. MPPSK system structure is show i Figure 3. Iformatio Source MPPSK Modulatio Chael received MPPSK sigal SIF Low pass filter itegral decider itegral decider2.... itegral deciderm- 2 M- Output Figure 3. MPPSK system structure. The received MPPSK sigal ca trasform phase jump ito amplitude impact after passig through the impactig filter, ad the evelope of the sigal ca be extracted after passig through the low pass filter for decisio. The evelopes of M phase hoppig positios are sampled ad itegrated over the symbol period to fid the maximum value of the itegral ad the associated slot. If the maximum is below the threshold level, the decoder outputs a zero value. Otherwise, the decoder allocates the symbols represeted by the time slots correspodig to the largest itegrated value [8]. The threshold level of the symbol is the average of the itegral value at the phase jump of the symbol ad the itegral value at the correspodig positio of the symbol. The waveform of MPPSK system is show i Figure 4. 4 Symbol MPPSK sigal sigal after SIF sigal after low-pass filter Samplig poit Figure 4. Waveform of MPPSK system.

5 Sesors 29, 9, of High Frequecy Multipath Chael HF chaels are ostatioary i both frequecy ad time, but if cosideratio is restricted to bad-limited chaels (for example, khz) ad sufficietly short times (for example, mi), most chaels are early statioary ad ca be adequately represeted by a statioary model [2]. The chael model is show i Figure 5. Iput Sigal tapped delay lie τ τ i τ a a i a Output Sigal Figure 5. Chael Model. Where is the umber of paths, τ is the delay of each path, ad a is the gai of each path. The iput sigal is subjected to a fiite order delay. Each order of the sigal has a appropriate order gai to amplitude ad phase modulate it. The modulated sigal is summed at the output [2]. I this paper, whe simulatig the multipath effect, the multipath is regarded as the waveform of the mai path delay. The received sigal ca be represeted by superimposig the mai path sigal ad the mai path sigal delayed for a certai time. It is assumed that the received expressio of the trasmitted MPPSK modulated sigal is ag(t). After trasmissio over a multipath chael, the received sigal is give by r(t) = a i g(t τ i ) (3) i= where a i is the amplitude fadig caused by the gai of each path chael, ad τ i is the delay of each path relative to the mai path. 3. The Scheme of Multipath Delay Estimatio ad Normalized Symbol Joit Decisio To reduce the iterferece of multipath to the sigal, it is ecessary to estimate the delay value of the multipath, ad the desig the modulatio parameters of the sigal to achieve the purpose of separatig the multipath. At the demodulator ed, ot oly the multipath iformatio is used for the decisio, but also the oise itroduced by the multipath iformatio is reduced, so that the demodulatio performace ca be improved. 3.. Multipath Delay Estimatio Geeralized cross-correlatio (GCC) is oe of the covetioal methods for fidig the time differeces but it requires a priori statistics of the received sigals i order to obtai accurate delay estimates [2]. I practical applicatios, these priori kowledge are ofte difficult to obtai or icomplete, which will affect the actual performace of this methods. O the other had, due to the possible relative motio betwee the trasmitter ad the receiver, the time delay will chage over time. These two problems will cause the GCC method to estimate the delay iaccuracy. Compared to the above method, the least mea square time delay estimatio(lmstde) method does ot rely o statistical prior kowledge of the iput sigal ad oise, ad it ca costatly adjust its parameters durig the iterative process. I additio, the adaptive filter i the LMSTDE method

6 Sesors 29, 9, of 7 is simple i desig, low i computatioal complexity, ad easy to implemet. The block diagram of LMSTDE is show i Figure 6 with â fixed at uity [22]. x(d) α P W z = w i z i i= P e(d) + y(d) Figure 6. Block diagram of LMSTDE. Where x(d) ad y(d) are the two sigals received by the receiver. The basic idea of LMSTDE method is to estimate the delay through a adaptive ocausal FIR filter i the form of W(z) = P i= P w i z i. The delay value foud with the least mea square error compared with the referece sigal is the time delay estimate. The filter weight vector coefficiets that are iterated accordig to the LMS algorithm are give by w i (d + ) = w i (d) + µ w e(d)x(d i) (4) where the error e(d) = y(d) P i= P w i (d)x(d i), µ w is a positive scalar to cotrol the covergece rate ad stability of the iteratio. Whe the adaptive filter coverges, a time delay estimate ca be obtaied from the weight vector peak coordiates of the adaptive filter. The delay ˆD w (d) is give by [23] where sic( ) = siπ( ). π( ) 3.2. Modulatio Parameter Settig ˆD w (d) = arg max t { P i= P w i (d)sic(t i)} (5) Assume that the delay of the sub-path relative to the mai path is τ. First, the iteger part value m of τ T is obtaied, ad m represets the umber of symbol periods i which the sub-path is delayed from the mai path. The the parameter τ-mt is calculated, which is a specific positio of sub-path i the (M + )-th symbol period of mai path. I order to separate the mai path ad the sub path sigal, the coditio is that the phase jump of the sub path after the delay caot overlap with the phase jump of the mai path. I this paper, takig oly two paths of multipath as a example, accordig to the waveform characteristics of the MPPSK sigal, the separatio coditios of the mai path ad the sub path ca be obtaied.. Whe < τ mt < (M r g )KT, the mai path delays m symbol periods to form a sub-path waveform whose waveform will fall withi the modulatio segmet ( (M r g )KT) i the symbol period, so the sub-path will be aliased with the mai path waveform. 2. Whe (M r g )KT τ mt < NT (M r g )KT, the mai path delays m symbol periods to form a sub-path waveform, ad the waveform will fall outside the symbol modulatio period ( (M r g )KT) i the symbol period, so multipath does ot affect the mai path waveform. I order for this coditio to be true, it is also ecessary to satisfy 2(M r g )K < N.

7 Sesors 29, 9, of 7 Therefore, i order to satisfy this coditio, after the carrier frequecy of the trasmitted sigal is fixed, it is ecessary to select the parameters K ad N of the MPPSK pulse modulatio sigal accordig to the delay to satisfy the separatio of the mai paths ad sub-paths Normalized Symbol Joit Decisio The premise of symbol joit decisio is to estimate the multipath delay ad the the separatio of multipath. The key is to make the symbol iformatio cotaied i the sub-path participate i the decisio, that is, the samplig itegral decisio value of the curret symbol ad the samplig itegral decisio value icludig the curret symbol i the multipath are used as the decisio basis [7]. The symbol joit decisio also itroduces the oise of the sub-path whe usig the sub-path symbol iformatio to participate i the decisio, which causes the bit error rate ot to reach the miimum level. Therefore, this paper proposes a ormalized symbol joit decisio method. After the sigal is trasmitted through multipath chael, the receivig expressio is give by Equatio (3). After obtaiig the relative delay of each path, the delay value of the i-th path is elimiated ad the waveform with o delay for each path is obtaied. The, each path sigal is ormalized ad added to the mai path, ad the oise itroduced by the sub-path is reduced while usig the symbol iformatio icluded i the sub-path, thereby improvig the sigal-to-oise ratio ad reducig the bit error rate. The added sigal is give by a r(t) = i a a i g(t) (6) i= where a is the path gai of the mai path ad a i a is the value obtaied by ormalizig the path gai of the i-th path with the mai path gai. It is assumed that whe the sigal is trasmitted, the eergy of each symbol is E s, ad the amplitude gai of the i-th path is a i, so the amplitude of the equivalet basebad sigal o the i-th path is a i Es, ad the symbol eergy is a i 2 E s. Assumig that the oise power spectral desity is N, the sigal-to-oise ratio o the i-th path is give by γ i = a i 2 E s N (7) whe the received sigals are combied, the weightig coefficiet of each path is x i, the the amplitude of the equivalet basebad sigal of the i-th path after weightig is x i a i Es, ad the amplitude of the combied sigal is give by A = x i a i Es (8) i= The sigal-to-oise ratio of the combied sigal is give by ( x i a i Es ) 2 i= γ(x, x 2,, x ) = x 2 i N i= = E ( x i a i ) 2 s i= N x 2 i i= (9). Whe the receiver adopts the symbol joit decisio scheme, the weightig coefficiet of each path is, that is, x i = (i =, 2,, ). The sigal-to-oise ratio of the combied sigal is give by

8 Sesors 29, 9, of 7 γ S (x, x 2,, x ) = E s N ( a i ) 2 i= () 2 i= 2. Whe the receiver adopts the ormalized symbol joit decisio scheme, the weightig coefficiets of the i-th path is a i a, that is, x i = a i a. The sigal-to-oise ratio of the combied sigal is give by γ N (x, x 2,, x ) = E s N ( i= a 2 i a ) 2 () ( a i a ) 2 i= The calculatio shows that γ N (x, x 2,, x ) is larger tha γ S (x, x 2,, x ), that is, the ormalized symbol joit decisio scheme improves the sigal-to-oise ratio ad reduces the bit error rate compared with the symbol joit decisio scheme. The proof is show i Appedix A. 4. Simulatio ad Numerical Results I this sectio, time delay ad joit decisio are simulated for sigals with modulatio parameters K = 5, N = 6 ad f c = 455 KHZ. Table gives the estimated delays for usig the LMSTDE scheme with a delay of ms. Table 2 gives a estimate of the multipath delay by usig a autocorrelatio scheme. The compariso results of badwidth betwee modulatio parameter schemes ad spread spectrum schemes are give i Table 3. I additio, the ormalized symbol decisio method is compared with the the curret maistream method by takig the sigal-to-oise ratio ad the sub-path gai as variables. 4.. Time Delay Estimatio Accordig to the requiremets of modulatio parameter settig, the modulatio parameters selected i this paper are K = 5, N = 6, f c = 455 KHZ ad τ = ms, ad there are oly two paths of mai path ad sub-path. The delay rage is calculated to get m value (m = 7), ad the τ mt coforms to the secod case of parameter settig i Sectio 3, that is, the delay waveform of the previous seveth symbol is icluded i the curret symbol period, ad the delay waveform of the curret symbol is icluded i the seveth symbol period later. Whe the mai path ad the sub-path ca be separated, the sigal waveform of the received sigal i two symbol periods after demodulatio is show i Figure 7. 4 Mai path sigal 2 Multipath sigal Ts/3 2Ts/3 Ts 4Ts/3 5Ts/3 2Ts Time Figure 7. Waveform of two symbol periods after the received sigal is demodulated.

9 Sesors 29, 9, of 7 It ca be see from Figure 7 that whe the MPPSK modulated sigal passes through the multipath chael, two peaks appear i oe symbol period, oe of which is the decisio peak of the curret symbol, ad the other is the multipath peak of the previous seveth symbol delay to the curret symbol period. Whe the sigal-to-oise ratio takes differet values, the sigal modulatio parameter multipath gai is modified, ad the multipath delay is estimated usig the LMSTDE method. The delay value of the sub-path relative to the mai path is give i Table. Table. LMSTDE Delay Estimatio with Multipath Gai Chage. SNR (db) Parameter K Multipath Gai Delay (s) As ca be see from Table, whe the multipath gai is modified, the accuracy of time delay estimatio usig LMSTDE method is ot sigificatly affected. Therefore, the LMSTDE method ca be used to estimate the time delay of MPPSK multipath sigals. The traditioal multipath separatio techique spreads the sigal through a Pseudo-Noise Sequeces of a specific desig, ad the receiver performs correlatio operatios to separate the multipath. Sice the Pseudo-Noise Sequeces has a sharp autocorrelatio property, the receiver seds the received multipath sigal to a plurality of correlators, ad each path sigal ca be separated. The premise of multipath separatio is multipath delay estimatio. Therefore, after spreadig the MPPSK sigal spectrum, a m-sequece kow to the receiver is iserted i frot of the symbol to be trasmitted. Whe the receiver correlates the received multipath sigal with the kow m-sequece, the multipath delay ca be determied by the time iterval betwee the peaks of the correlatio fuctio graph. With the same parameters as above, the multipath delay is estimated by usig autocorrelatio method uder differet sigal-to-oise ratios, differet multipath gais ad differet m-sequeces. Whe usig the autocorrelatio method, the delay of the sub-path relative to the mai path is show i Table 2.

10 Sesors 29, 9, 938 of 7 Table 2. Autocorrelatio Scheme Delay Estimatio with Multipath Gai Chage. SNR (db) Period of m-sequece Multipath Gai Delay (s) Table 2 shows that sice m-sequece has good autocorrelatio characteristics, the time delay of MPPSK sigal after the spread spectrum ca be estimated by autocorrelatio method, so that multipath separatio ca be achieved i the receiver. To measure the badwidth of the two multipath separatio

11 Sesors 29, 9, 938 of 7 schemes metioed above, oe is to adjust the modulatio parameters to separate the multipath, the other is to separate the multipath by usig the correlatio receptio method after the spread spectrum of the sigal. Whe the spectrum of 4PPSK sigal is spread, four quaterary symbols are correspodig to four differet biary sequeces, ad the the biary sequece is modulated by the m-sequece, ad fially the sigal that eeds to be trasmitted is obtaied by 4PPSK modulatio. The correspodig relatioship is correspodig to, correspodig to, 2 correspodig to, ad 3 correspodig to. The 4 db badwidth of the two separated multipath schemes is show i Table 3. Table 3. 4 db Badwidth of The Two Separated Multipath Schemes. Period of m-sequece Adjust Modulatio Parameter Scheme Spread Spectrum Scheme MHZ 7. MHZ MHZ.83 MHZ MHZ 2.7 MHZ As show i Table 3, although both schemes ca separate multipaths, the spread spectrum scheme has wider badwidth tha the modulatio parameter adjustmet scheme. The scheme of adjustig the modulatio parameters ca separate the multipath ad elimiate the iter-symbol iterferece oly by requirig appropriate modulatio parameters, so the separatio method is relatively simple. I the case of trasmittig the same iformatio, adjustig the modulatio parameter scheme saves spectrum resources ad improves frequecy bad utilizatio Bit Error Rate of Normalized Symbol Joit Decisio Uder the coditio that the sub-path ca be separated from the mai path, the curret decisio of the symbol ca be uderstood as a joit decisio betwee the sampled itegrated value of the ormalized sub-path ad the sampled itegrated value of the mai path. This ca be uderstood as the itroductio of ecodig i the trasmitter. The codig mode is to ecode the iformatio of the curret symbol ito the followig seveth symbol without affectig the iformatio represetatio of the followig seveth symbol, thereby esurig that the curret symbol demodulatio performace is improved without lowerig the symbol rate. The modulatio parameters ad chael coditios are the same as the Time delay estimatio sectio. I the case where the mai path gai is.8 ad the sub path gai is.5, the demodulatio performace of the amplitude itegral decisio, the symbol joit decisio ad the ormalized symbol joit decisio is compared. The compariso result is show i Figure 8. itegral decisio Symbol joit decisio Normalized symbol joit decisio - BER SNR (db) Figure 8. Bit error rate compariso of three decisio schemes.

12 Sesors 29, 9, of 7 As show i Figure 8, the ormalized symbol joit decisio reduces the bit error rate of the demodulator compared to the amplitude itegral decisio ad the symbol joit decisio. I the case of low sigal-to-oise ratio coditios, the ormalized symbol joit decisio is improved compared with the symbol joit decisio i terms of bit error rate. As the sigal-to-oise ratio icreases, the oise sigal gradually decreases. Therefore, the weakeig effect of the ormalized symbol joit decisio o the oise is gradually reduced, ad the performace improvemet of the ormalized symbol joit decisio is gradually reduced relative to the joit decisio of the symbol. Whe the sigal-to-oise ratio is 4 db, the chael gai of the mai path is fixed at.8. The effect of the chage i the sub-path gai o the demodulatio performace of the symbol joit decisio ad the ormalized symbol joit decisio is show i Figure 9. Symbol joit decisio Normalized symbol joit decisio BER Sub-path gai Figure 9. Bit error rate compariso of ormalized symbol joit decisio ad symbol joit decisio after fixed mai path gai. As show i Figure 9, after fixig the mai path gai, the demodulator uses the ormalized symbol joit decisio with a lower bit error rate tha the use of the symbol joit decisio at differet sub-path gais. Whe the sub-path gai is., the ormalized symbol joit decisio has the highest improvemet i demodulatio performace relative to the symbol joit decisio, because the ormalized symbol joit decisio ot oly utilizes the symbol iformatio of the sub-path to participate i the decisio, but also miimizes the itroduced oise. As the gai of the sub-path icreases, the ormalized value of the sub-path gai to the mai path gai becomes closer to, that is, the ormalized symbol joit decisio itroduces more ad more oise whe usig the sub-path symbol iformatio. This leads to a gradual decrease i the advatages of the ormalized symbol joit decisio ad the symbol joit decisio. Fially, whe the mai path gai ad the sub path gai are the same, the demodulatio performace of the two decisio modes is the same. Whe the sigal-to-oise ratio is 4 db, the chael gai of the sub-path is fixed at.. The effect of the chage i the mai path gai o the demodulatio performace of the symbol joit decisio ad the ormalized symbol joit decisio is show i Figure. As show i Figure, the coclusio is the same as whe the mai path gai is fixed. Compared with the sub-path gai, the bit error rate is the smallest whe the mai path gai is maximum. Figure shows that whe the demodulator uses the ormalized symbol joit decisio, the bit error rate is a fuctio of the sigal to oise ratio ad the sub-path gai.

13 Sesors 29, 9, of 7 Symbol joit decisio Normalized symbol joit decisio BER Mai path gai Figure. Bit error rate compariso of ormalized symbol joit decisio ad symbol joit decisio after fixed sub-path gai BER Sub-path gai. 2 SNR(dB) Figure. BER for ormalized symbol joit decisio as a fuctio of SNR ad sub-path gai. Figure 2 idicates that the BER is a fuctio of SNR ad sub-path gai as idepedet variables whe the demodulator uses the symbol joit decisio BER Sub-path gai. 2 SNR(dB) -5.2 Figure 2. BER for symbol joit decisio as a fuctio of SNR ad sub-path gai.

14 Sesors 29, 9, of 7 Comparig Figure with Figure 2, cosiderig the ifluece of sigal-to-oise ratio ad multipath gai, it ca be see that the ormalized symbol joit decisio proposed i this paper is superior to the symbol joit decisio i reducig the bit error rate. 5. Coclusios I this paper, the effectiveess of the least mea square time delay estimatio method for the estimatio of MPPSK-modulated sigal delay i a multipath eviromet is verified by experimets. By aalyzig the waveform characteristics of the MPPSK sigal, the coditios of multipath separatio are give. Usig the obtaied delay estimatio value, the modulatio parameters of the system ca be selected to achieve the separatio of the mai path ad the multipath. Compared with the multipath separatio achieved by the spread spectrum scheme, the multipath separatio method proposed by adjustig the MPPSK modulatio parameters i this paper has a arrower badwidth ad higher spectrum utilizatio. The complexity of the whole system is low, ad the demodulator reduces the itroduced oise while usig the multipath iformatio to participate i the decisio. The demodulatio performace is improved compared with the existig method. The results show that the ormalized symbol joit decisio method ca effectively combat multipath. As the sub-path gai gradually decreases, the advatage of the ormalized symbol joit decisio becomes more ad more obvious. Compared with the previous methods, the method reduces the error rate of the demodulator. Future work will probably study the performace of MPPSK modulatio i fadig, strog iterferece eviromets ad the optimizatio of the demodulator. Author Cotributios: H.W. developed the idea, coducted experimets, wrote the origial draft, ad revised the draft. H.T. supervised the process of this work as well as reviewed ad revised the draft. Fudig: This work was fuded by Natioal Natural Sciece Foudatio of Chia (Grat No. 6675). Coflicts of Iterest: The authors declare o coflict of iterest. Abbreviatios The followig abbreviatios are used i this mauscript: LPWAN IoT UNB MPPSK EBPSK DIF IIR SIF HF GCC LMSTDE Low-Power Wide-Area Network Iteret of Thigs Ultra-Narrowbad M-ary Positio Phase Shift Keyig Exted Biary Phase Shift Keyig Digital Impactig Filter Ifiite Impulse Respose Special Impactig Filter High Frequecy Geeralized cross-correlatio Least Mea Square Time Delay Estimatio Appedix A This proof is based o mathematical iductio. If the receiver has a larger sigal-to-oise ratio usig the ormalized symbol joit decisio scheme tha usig the symbol joit decisio scheme, the compariso result is give by γ N (x, x 2,, x ) > γ S (x, x 2,, x ) (A)

15 Sesors 29, 9, of 7 amog them, γ S (x, x 2,, x ) = E s N ( a i ) 2 i= 2 i= = E ( a i ) 2 s i= N (A2) γ N (x, x 2,, x ) = E s N = E s N ( i= a 2 i a ) 2 ( a i a ) 2 i= ( a 2 i )2 ( a ) 2 i= (a i ) 2 ( a ) 2 i= (A3) = E s N = E s N ( a 2 i )2 i= (a i ) 2 i= (a i ) 2 i= Sice a i is the i-th path gai, a > a 2 > > a > exists. γ N (x, x 2,, x ) > γ S (x, x 2,, x ) E s N i= (a i ) 2 > E s N ( a i ) 2 i= (A4) (A5) Sice E s N is greater tha, the formula to be proved is give by i= (a i ) 2 > ( i= a i ) 2 (A6) whe = 2, (a + a 2 ) 2 > a 2 + a2 2 > 2a a 2 2(a 2 + a2 2 ) > a2 + a a a 2 2(a 2 + a2 2 ) > (a + a 2 ) 2 (A7) (A8) (A9) (A) Whe = m, the iequality is workable. m(a 2 + a a2 m) > (a + a a m ) 2 (A)

16 Sesors 29, 9, of 7 whe = m +, (a + a a m + a m+ ) 2 = (a + a a m ) 2 + 2(a + a a m )a m+ + a 2 m+ m(a 2 + a a2 m) > (a + a a m ) 2 (a + a 2 + +a m ) 2 + 2(a + a a m )a m+ + a 2 m+ < m(a2 + a a2 m) + a 2 m+ + 2a a m a m a m+ m(a 2 + a a2 m) + a 2 m+ + 2a a m a m a m+ < m(a 2 + a a2 m) + a 2 m+ + a2 + a a2 m + ma 2 m+ (A2) (A3) (A4) (A5) m(a 2 + a a2 m) + a 2 m+ +a2 + a a2 m + ma 2 m+ = (m + )(a 2 + a a2 m + a 2 m+ ) (A6) (m + )(a 2 + a a2 m + a 2 m+ ) > (a + a a m + a m+ ) 2 (A7) To sum up, the followig formula is true. i= (a i ) 2 > ( i= a i ) 2 (A8) Hece, γ N (x, x 2,, x ) > γ S (x, x 2,, x ) (A9) Refereces. Goursaud, C.; Mo, Y. Radom uslotted time-frequecy ALOHA: Theory ad applicatio to IoT UNB etworks. I Proceedigs of the 26 23rd Iteratioal Coferece o Telecommuicatios (ICT), Thessaloiki, Greece, 6 8 May 26; pp Mo, Y.; Goursaud, C.; Gorce, J.M. Theoretical aalysis of UNB-based IoT etworks with path loss ad radom spectrum access. I Proceedigs of the 26 IEEE 27th Aual Iteratioal Symposium o Persoal, Idoor, ad Mobile Radio Commuicatios (PIMRC), Valecia, Spai, 4 8 September 26; pp What Is LPWAN? Available olie: (accessed o 7 March 29). 4. Naik, N. LPWAN Techologies for IoT Systems: Choice betwee Ultra Narrow Bad ad Spread Spectrum. I Proceedigs of the 28 IEEE Iteratioal Systems Egieerig Symposium (ISSE), Rome, Italy, 3 October 28; pp Walker,H.R. Ultra Narrow Bad Modulatio Textbook. Available olie: viewdoc/dowload?doi= &rep=rep&type=pdf (accessed o 6 Jauary 29). 6. Wu, L.; Feg, M.; Qi, C.; He, F. Recet Patets o Ultra Narrow Bad Modulatios. Recet Patets Sigal Process 2,, [CrossRef] 7. Zheg, G.; Yag, W. The Orthogoal Very Miimum Chirp Keyig (OVMCK) modulatios with very high badwidth efficiecy. I Proceedigs of the 28 IEEE Ateas ad Propagatio Society Iteratioal Symposium, Sa Diego, CA, USA, 5 July 28; pp Zheg, G.; Feg, J.; Jia, M. Very Miimum Chirp Keyig as a ovel ultra arrow bad commuicatio scheme. I Proceedigs of the Iteratioal Coferece o Iformatio, Commuicatios & Sigal Processig, Sigapore, 3 December 27; pp Qi, C.; Wu, L. PLL demodulatio techique for M-ray Positio Phase Shift Keyig. J. Electro. 29, 26, [CrossRef]. Yig, P. New scheme of MPPSK modem. I Proceedigs of the 24 9th Iteratioal Symposium o Commuicatio Systems, Networks & Digital Sig (CSNDSP), Machester, UK, July 24; pp

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