a multiple-access time and frequency spectrum-spreading...

Research ArticleA Multiple-Access Time and FrequencySpectrum-Spreading Modulation

Samer S Saab Joe Khalife and Rayana H Jaafar

Department of Electrical and Computer Engineering Lebanese American University Byblos Lebanon

Correspondence should be addressed to Samer S Saab ssaablauedulb

Received 13 June 2018 Revised 30 September 2018 Accepted 8 October 2018 Published 25 October 2018

Academic Editor Andre de Almeida

Copyright copy 2018 Samer S Saab et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

In this paper a novel modulation scheme called Carrier Interleaved Multiple Access (CIMA) is proposed CIMA provides analternative for multiple-access modulation accommodating resistance to noise and channel interferenceThe approach is based onpolar signaling modulated with an FM-like composite sinusoidal functionThe user assigned frequency deviation and modulationindex are strictly related and unique The latter parameters are generated using a nontraditional pseudorandom noise generator(PRNG) This PRNG provides CIMA with low interference capability between cochannels and adjacent channels CIMA can beconsidered for a single-user or multiple-access technique Selected CIMA characteristics are presented In order to numericallyillustrate the effectiveness of the proposedmodulation scheme the performance of CIMA is comparedwith the conventional direct-sequence spread spectrum binary phase-shift keying (DSSS-BPSK) modulation

1 Introduction

Wireless communications connect more devices than peopleand the trend is only increasing in both venues The numberof connected devices per person rose to 184 in 2010 [1] and itis expected that we will have seven trillion devices connectedwirelessly by 2020 [2] Over the past ten years smartphonesand tablet PCs resulted in a significant increase in the numberof devices connected to the internet However other prospec-tive wireless applications such as vehicle-to-vehicle commu-nication applications based on the use of radio frequencyidentification (RFID) wireless electric meters and otherapplications not yet envisaged may evolve Consequently anincrease in investigation activities towards various and novelwireless communication schemes associated with differentapplications is desired Common characteristics for wirelesscommunication systems remain to include spectral efficiencysecurity and interference resistance

Spread spectrum techniques are employed for securecommunications increasing resistance to interference noiseand jamming Different techniques of spread spectruminclude frequency-hopping spread spectrum (FHSS) direct-sequence spread spectrum (DSSS) time-hopping spreadspectrum (THSS) chirp spread spectrum (CSS) and in

some cases combinations of these forms For example inMulticarrier Direct-SequenceCDMA (MC-DS-CDMA) timeand frequency spreading is used [3] also lattice reductiontheory and aidedmultiple user detection is applied to a spreadspectrum system leading to near-far effect suppression [4]A conventional spread spectrum system employs pseudo-noise (PN) code generators while other schemes employnondeterministic spreading codes generated from a randominput data stream such as the self-encoded spread spectrum(SESS) [5]

Ultra-wideband (UWB) is another modulation technique[6] that possesses similar characteristics to spread spectrumIt is based on transmitting short duration pulses and isapplied to short-range wireless communication In orderto improve its performance DSSS techniques have beenintroduced to UWB systems [7] Another technique is thechaotic communicationwhere a noise-like aperiodic chaoticsignal is employed to modulate the information signalDifferent chaos modulation techniques have been proposed(see eg [8 9] and references therein) In Differential ChaosShift Keying (DCSK) index modulation is integrated toimprove the systemrsquos data rate and energy efficiency such aspermutation index DCSK (PI-DCSK) [10] and CommutationCode Index DCSK (CCI-DCSK) [11] Recently Code Index

HindawiWireless Communications and Mobile ComputingVolume 2018 Article ID 8920746 10 pageshttpsdoiorg10115520188920746

2 Wireless Communications and Mobile Computing

Modulation (CIM) has been proposed for spread spectrumsystems [12] In CIM the indices of spreading codes are usedin conjunction with symbol constellation for bits mappingThe latter scheme aims to achieve high data rate commu-nication without sacrificing system complexity and energyrequirement In noncoherent multicarrier spread spectrumsystems the reference signal is sent once for multiple parallelbits yielding significant energy savings and a higher spec-tral efficiency as compared to other DSCK systems Othermethods employing efficient coding techniques aimed atreducing energy costs ie memory and processing costin standard spread spectrum (SS) communication systems[13] Continuous phase modulation combined with DSSS isproposed in [14] and further investigated in [15ndash18] Recentlyindexmodulation has been applied to a coherent chaos-basedscheme where the initial conditions of the chaotic sequenceare used as a new dimension to map information and carryextra bits [19] All the proposed modulation methods abovecome with a number of unique features

Siding away from spread spectrum techniques the rela-tively new spatial-shift keying (SSK) which is widely imple-mented formultiple-input multiple-output (MIMO) systemsis considered as a strong candidate for next generationwireless communication systems [20] The same applies fororthogonal frequency division multiplexing (OFDM) whichis believed to be the best in multicarrier modulation and isalso extensively used in broadband and MIMO systems [21]Howevermulticarrier OFDM and even single-carrier OFDMhave some drawbacks [21] For example due to leakage of theFFT OFDM is more sensitive to carrier frequency offset anddrift than single-carrier systems the need of high peak-to-average-power ratio [22] and sensitivity due channel spatialcorrelation In [23] a frequency index modulation scheme isproposed to reduce peak-to-average-power ratio of OFDMsystems without sacrificing data rate

The commonly pseudorandom sequences used in com-munication systems are maximal length sequences [24]Mersenne Twister code Walsh sequences and Gold codes[25] Kasami codes [26] and Barker codes [27] In orderto improve the spectral efficiency in MIMO systems space-time block codes [28 29] and space-time trellis codes areemployed However none of the communication systemsemploys the nontraditional pseudorandom noise generator(PRNG) proposed in [30]The latter is based on a linear com-bination of continuous-time composite sinusoidal signalsThe desired signalsrsquo key parameters are easily constructed bychoosing a set of prime numbers with bounds dependingon the typical requirements of the PRNG [30] The keycharacteristics of the PRNG are as follows The period of thesignal can be made arbitrarily large at least 98 of the signaltotal average power is contained in the desired frequencybandwidth a desired bandwidth can be arbitrarily selectedand the cross-correlation between any pair of generatedsignals can be made arbitrarily small This answers concernson interchannel interference raised by many researches onspread spectrum techniques such as in FHSS [31]

In this paper a newmodulation scheme named CIMA isproposed In DSSS there is a fast phase shift of 180∘ througha predefined sequence known to both the receiver and the

transmitter In FHSS there is a fast hopping of the signal intodifferent frequencies The set of frequencies is also knownto both the receiver and the transmitter In CIMA insteadof having a discrete phase shift or frequency shift like DSSSor FHSS we have both phase and frequency change in theform of a predefined composite sinusoidal function knownto both the receiver and the transmitter CIMA modulatoris formed by multiplying a bipolar digital message signalwith cos(2120587119891119888119905+120573119898sin(2120587119891119898119905)) where each message signal isassociated with a unique signature pair (120573119898 119891119898) The choiceof 120573119898 and 119891119898 is the key in rejecting cochannel interferencewhich is an essential cause of the signalrsquos quality degradationand capacity constraint in wireless mobile telephony andother applications The proposed PRNG in [30] is employedfor generating different pairs (120573119898 119891119898) Each pair is strictlycorrelated and all different pairs are made weakly correlatedbut equally constrained to a bandwidth measure

This proposed method can be used as a single-user or amultiple-access technique Due to the composite sinusoidalfunction employed at the modulator the sinc functionscorresponding to the polar signaling are spread around thecarrier within the same channel with frequency separation of119899119891119898 119899 = 0 plusmn1 plusmn2 plusmn120573119898 + 1 In multiple-access applica-tion each user is assigned different (120573119898 119891119898) Consequentlyall the sinc functions associated with different users are sepa-rated by different values of 119891119898 which are all situated aroundthe carrier within the same channel and the instantaneousfrequency of a CIMA signal is given by 119891119894119899119904119905(119905) = 119891119888 +119891119898120573119898cos(2120587119891119898119905)) This type of spectral interleaving aroundthe carrier awards ldquoCarrier Interleaved Multiple Accessrdquoterminology CIMA aims at rejecting adjacent and cochannelinterference

The characteristics of the proposed modulation schemeare analytically presented including bandwidth analysis biterror rate (BER) due to channel noise and cochannel andadjacent channel interference Numerical simulations exam-ine the performance of the proposed scheme contrastedwith DSSS-BPSK while considering a more complex channelmodel

The rest of this paper is organized as follows Section 2describes the proposed CIMA system and the employedPRNG and it presents relevant parameters and new charac-teristics of the PRNG Section 3 contains analytical analysisdescribing CIMA characteristics Section 4 includes a com-parative study with DSSS-BPSK scheme based on numericalsimulations and finally Section 5 contains conclusions andfuture work

2 Proposed System Model

In this sectionwe present the basics of CIMAmodulation anddemodulation and the employed PRNG algorithm and estab-lish some preliminary new results relevant to the employedPRNG

21 System Transmitter and Receiver At the transmitter sidethe 119895th message signal 119898119895(119905) is assumed to be in the formof polar digital signaling with a bit rate 119877 where 119877 = 1119879119887

Wireless Communications and Mobile Computing 3

ReceivedSignal

Integrateamp dump

resholdDevice

PMfc

Oscillatorf=fj PRNG

jfj

jDP

Figure 1 Proposed CIMA receiver

and 119879119887 is the time it takes to send 1 bit of data The proposedmodulator has the following form

119910119895 (119905) = 119860119898119895 (119905) cos (2120587119891119888119905 + 120573119895 sin (2120587119891119895119905)) 1 le 119895 le 119871 (1)

where 119871 is the number of multiple users 119891119888 is the carrierfrequency and 120573119895 and 119891119895 are two parameters which arechosen according to the PRNG algorithm [30] and 119860 is anynonzero real number included to specify the power level

It is important to note that (1) is somehow similar to bothDSSS and FHSS Unlike FHSS where the transmitted signalrapidly switches its carrier among many frequency channelswithin a bandwidth 119861119910 CIMA (1) spreads its signal within119861119910 continuously according to the PRNG presented in [30]CIMAmakes the resulting wideband signal appear as a noisesignal It is that the specific spreading associated with PRNGsignal gives much more freedom than the conventionalspread spectrum techniques

An analog platform for generating the composite sinu-soidal signal cos(2120587119891119888119905+120573119895sin(2120587119891119895119905)) is shown in the dashedbox of Figure 1 The constant 119863119875 is the phase sensitivity ofthe phase modulator (PM) Figure 1 presents one platformfor a CIMA receiver The transmitter consists of a multiplierthat multiplies the polar data signal 119898119895(119905) with the samecomposite sinusoidal signal used in the receiver where it isassumed that the parameters 120573119895 and 119891119895 are known to both thereceiver and the transmitter

Implementation remarks on generating the PRNGsignals[30] Depending on the specific application the user shouldselect the appropriate platform For example if numericalsimulations (eg Monte Carlo simulations) are intendedthen a PC-based platform can be used in a non-real-time fashion However for real-time application the choiceof platform becomes essential For example if the PRNGis intended to be used in an analog platform then thePRNG signal can be generated by using a voltage-controlledoscillator However for real-time digital applications a DSPplatform with moderate memory size can be consideredHowever in case of applications where 119871 is large then theFPGA platform can be advantageous over the DSP platformfor its superiority in handling parallel processing executionThe limitation depends on the size of 119871 119891119888 119861 the processorspeed and processor architecture The complexity of theproposed algorithm becomes 119874(119899) That is we have a linear

algorithm with a performance ctimesn where c is the cost of onerun and 119899 is the size of the input

22 PRNG Algorithm This section presents a special case ofthe PRNG algorithm proposed in [30] that is employed byCIMA It also establishes results that are essential for studyingsome of the characteristics of the proposed modulationscheme

The 119895119905ℎ PRNG signal as presented in [27] is given by

119909119895 (119905) = 119860119895119873sum119894=1

cos (2120587119891119888119905 + 120573119894119895 sin (2120587119891119894119895119905)) 1 le 119895 le 119871

(2)

where 119871 is the number of feasible generated signals and 119873 isthe number of composite sinusoidal signals It is importantto note that as119873 is increased the period of the PRNG signalbecomes larger and its spectrum becomes flatter within itsbandpass centered at 119891119888 A larger value of 119873 is intended forband jamming application Consequently in this paper weconsider a special case of (2) with 119873 = 1 and set 119860119895 equiv 119860for all j Therefore we omit the index 119894 from the equationto obtain the unmodulated CIMA signal presented in thefollowing form

119909119895 (119905) = 119860 cos (2120587119891119888119905 + 120573119895 sin (2120587119891119895119905)) (3)

The power spectral density (PSD) of 119909(119905) is given by [28]

119875119909119895 (119891) = 11986024infinsum119899=minusinfin

1198692119899 (120573119895)sdot [120575 (119891 minus 119891119888 minus 119899119891119895) + 120575 (119891 + 119891119888 + 119899119891119895)]

(4)

where 119869119899(120573119895) represents the Bessel function of the first kindof order 119899 and argument 120573119895 The carrier frequency is 119891119888 andthe single-sided bandwidth of the unmodulated signal 119909119895(119905)is 119861 = 2(120573119895 + 1)119891119895 120573119895 gt 1 where at least 98 of the totalaverage power of each signal is contained in the bandwidth 119861Theparameters (theweak correlation among the pairs (119891119895 120573119895)is illustrated in Corollary 1 and Theorem 1 of [30]) of theproposed PRNG are constructed as follows [30]

119891119895 = 119901119895119897 = 1198612 (120573119895 + 1) 1 le 119895 le 119871 (5)

Or 120573119895 = 1198971198612119901119895 minus 1 where 119897 is a positive real number thatdepends on 119871 and 119901119895 is any prime number such that

(1) 119901119895 = 119897 for all 119895(2) 119901119895 = 119861 for all 119895(3) 119901min equiv min(119901119895) ge 119877119897 gt 119890 1 le 119895 le 119871(4) 119901max equiv max(119901119895) le 1198611198972(120573min + 1) 1 le 119895 le 119871

In order to guarantee that 119901max gt 119901min then B should besignificantly larger than 2(120573min + 1)119877 which leads to 119891119895 gt119877 1 le 119895 le 119871


Depending on the upper and lower bound of 119901119895 the pro-posed algorithm can generate L continuous-time cochannelsignals 119909119895(119905) 1 le 119895 le 119871 Since 119891119895 = 119901119895119897 then settingmin119895(119901119895) = 119897119877 guarantees min119895(119891119895) gt 119877 When 120573min isnotably larger than one then the upper bound of 119901119895 guaran-tees that at least 98 of the total average power of each signalis contained in the bandwidth 119861 Since the bandwidth 119861 ismuch larger than 119877 we refer to 119861 as the spread bandwidth

In what follows we introduce two CIMA-relevant param-eters 120574 and 120572 that are directly related to the spread bandwidthB and the number of signals 119871 We express 119861 in terms of thebit rate 119877 in particular 119861 equiv 120572119877 where 120572 gt 2(120573min + 1) andwe express 119871 in function of 120572 and 120574 119871 equiv 120574120572 where 120574 gt 0 Infact 120572 is considered as the spreading factor and 120574 for 120572 ≫ 1the spectral efficiency The value of 120574 is elaborated in (11)

In the next section we show that the null-to-null band-width of 119910119895(119905) asymp (120572 + 2)119877 For example if 120572 = 100 and120574 = 13 then 130 CIMA signals can share a common channelwith bandwidth equal to 102R

Remark 1 In multiple-access applications of the proposedmodulation scheme the desired number of cochannel sig-nals 119871 is specified Proposition A2 (see Appendix) indicatesthat 119871 increases if and only if 119897 increases However sincehow to obtain meaningful analytical formulation for 119897 infunction of the relevant parameters is not clear 119897 is obtainednumerically (see Appendix)

Remark 2 The spacing between two consecutive frequenciesis given by

Δ119891119895 equiv 119891119895 minus 119891119895minus1 = 119901119895 minus 119901119895minus1119897 ge 2119897 (6)

Therefore as 119871 increases 119897 increases and Δ119891119895 decreasesBased on Monte Carlo simulations while considering 119891119895being an ordered set of increasing values the followingapproximations are obtained

min2le119895le119871

(10038161003816100381610038161003816119891119895 minus 119891119895minus110038161003816100381610038161003816) = 2119897 asymp 01119877120574min3le119895le119871

(10038161003816100381610038161003816119891119895 minus 119891119895minus210038161003816100381610038161003816) asymp 03119877120574 (7)

In addition min119898+1le119895le119871(|119891119895 minus119891119895minus119898|) significantly increases as119898 increases

Lemma 3 For fixed values of 120574 and 120572 where 120572 gt 2(120573min + 1)and 120574 gt 0 the product 119877 times 119897 is equal to a positive constant

The proof of Lemma 3 is provided in Appendix alongwith other novel and relevant results Lemma 3 helps inestablishing basic characteristics pertaining to CIMA

3 CIMA Characteristics

In this section we analytically present the PSD and band-width of a CIMA signal spectral efficiency and the bit errorrate (BER) due to channel noise In addition we study thecochannel interference rejection capability of the proposedscheme

31 PSD Bandwidth and Spectral Efficiency The PSD of aCIMA signal is first derived Consider

119909 (119905) = 119860 cos (2120587119891119888119905 + 120573119898 sin (2120587119891119898119905)) (8)

and consider a polar nonreturn-to-zero (NRZ) signaldenoted by 119898(119905) to be the baseband polar signal representedby119898(119905) = sum119899=infin119899=minusinfin 119886119899119911(119905 minus 119899119879119887) where 119911(119905) = 119903119890119888119905(119905119879119887)

It is assumed that the values of 119886119899 are equally likelyto occur the data are independent and for simplicity thepossible levels for 119886119899rsquos are plusmn1 The modulated signal is 119910(119905) =119898(119905)119909(119905) It can be shown that the PSD of 119911(119905) is given byP119911(119891) = 119879119887sinc2(119879119887119891) and the PSD of 119910(119905) is given by

P119910 (119891) = 11986021198791198872infinsum119899=minusinfin

1198692119899 (120573119898)sdot [sinc2 (119879119887 (119891 minus 119891119888 minus 119899119891119898))+ sinc2 (119879119887 (119891 + 119891119888 + 119899119891119898))]

(9)

Therefore the PSD of the signal consists of shifted versions ofsinc2(sdot) functions weighted by the Bessel functions 1198692119899(120573119898)Consequently the single-sided ldquonull-to-nullrdquo bandwidth of119898(119905) 119861119910 is

119861119910 cong 119861 + 2119877 = (120572 + 2) 119877 (10)

When 120572 ≫ 1 then 119861119910 cong 119861 = 120572119877 Therefore a channel withbandwidth = 119861119910 can accommodate 119871 = 120574120572 different signalsNote that the above equation assumes that the data used isnot prefiltered and has the polar NRZ form If the messagesignal is prefiltered for example by using aGaussian filter thebandwidth occupied by the signal will become smaller andthe performance due to adjacent channel interference (ACI)will be improved

The spectral efficiency is defined as 120578119871 equiv 119871119877119861119910 whichleads to

120578119871 = 119871119877119861119910 = 120574120572120572 + 2 cong 1205741003816100381610038161003816120572≫1 (11)

32 Bit Error Rate due to Channel Noise The BER is derivedfor the proposed scheme due to white Gaussian channelnoise Derivations assume that the receiver is based oncoherent detection incorporating a multiplier and a matchedfilter as illustrated in Figure 1 In addition it is assumed thatthe CIMA signal 119910(119905) plus white Gaussian noise 119899(119905) (over theequivalent bandpass) is present at the input of the matchedfilter The PSD of 119899(119905) over the equivalent bandpass is11987302

Since the CIMA scheme is based on coherent receptionthen it can be shown that the probability of error (or BER) formatched-filter reception with an optimum threshold is givenby 119875119890 = 119876(radic11986411988921198730) where 119876(119911) = (1radic2120587) intinfin

119911119890minus12058522119889120585

and 119864119889 is the difference signal energy at the receiver inputSince for all practical purposes 119891119888 ≫ 1119879119887 then 119864119889 cong 21198602119879119887The average energy per bit becomes 119864119887 cong 11986021198791198872 Thereforethe BER is 119875119890 cong 119876(radic11986021198791198871198730) = 119876(radic21198641198871198730) which issimilar to the BER corresponding to BPSK


33 Cochannel Interference (CCI) In what follows thecochannel interference of the proposed CIMA system interms of its capability of partially rejecting other CIMAcochannel signals is analyzed both in the time domain andthen in the frequency domain

Assume that the number of cochannel signals 119871 = 120583119872where119872 is the number of cells in a cluster and 120583 is a positiveinteger Inwhat follows the phase shift is disregarded and thematched filter is tuned to receive

119910119896 (119905) = 119860119898119896 (119905) cos (2120587119891119888119905 + 120573119896sin (2120587119891119896119905)) (12)

Time Domain Analysis The output of the matched filter atsampling instant 1199050 is given by

V119896 (1199050) = int119879119887

[[[119871sum119895=1

120582119895119910119895 (119905)]]]119909119896 (119905) 119889119905 (13)

where it is assumed that the spatial attenuation factor 120582119895 is0 lt 120582119895 ≪ 1 for the signals associated with theM minus 1 adjacentcells and 120582119896 = 1 for the 120583 signals belonging to the home cellSince 119891119888 ≫ 1119879119887 then

V119896 (119905) cong 11986022 119898119896 (119905) + 11986022 int119879119887

119871sum119895=1119895 =119896

120582119895119898119895 (119905)

sdot cos (120573119896 sin (2120587119891119896119905) minus 120573119895 sin (2120587119891119895119905)) 119889119905(14)

At the end of every bit interval 119879119887 the samples V119896(119899119879119887) arefed into a threshold device with threshold 0 to produce thebinary waveform 119896(119905) Consequently the magnitude of theterm on the right hand side should dominate the second termfor good performance

Since 119891119894 = 119891119896 and 120573119894 = 120573119896 for 119894 = 119896 and 119891119894 gt 1119879119887and 120573119894 gt 1 for all 119894 then the argument correspondingto cos(sdot) terms can reflect diverse large angles and theircos(sdot) take on positive and negative values within 119879119887 Theintegral of each cos(sdot) term within 119879119887 becomes≪1 with eitherpositive or negative values The summation of small positiveand negative values would become significantly smaller thanthe summation of their magnitudes The summation ofthese terms can be thought of as a random walk processConsequently as L increases the performance is expected todegrade

Frequency Domain AnalysisThe Fourier transform of 119910119896(119905) isgiven by


119869119899 (120573119896)times [sinc (119879119887 (119891 minus 119891119888 minus 119899119891119896))+ sinc (119879119887 (119891 + 119891119888 + 119899119891119896))]

(15)

As a part of matched-filter reception the multiplication119910119895119910119896 1 le 119895 le 119871 in (13) implies the convolution oftheir spectra in the frequency domain In order to illustratethe phenomena of rejecting CCI signals we will examine

common spectral bands particularly the overlapping of themajor part of the sinc functions resulting frommatched-filterreception (13) within the bandwidth119861with cochannel signalsIt is worth noting that 119861 = 2(120573119896 + 1)119891119896 = 2(120573119894 + 1)119891119894 forall119896 119894and those spectral components outside 119861 are considerednegligible There are two scenarios that should be examinedin particular whenever we have

(a) 119899119891119895 = 119898119891119896 andor(b) |119899119891119895 minus 119898119891119896| is relatively small with respect to 119877

for j = k and for |119899| = 0 1 2 120573119895+1 |119898| = 0 1 2 120573119896+1Scenario (a)The associated setting implies that at least one ofthe ldquosincrdquo functions in (15) would entirely overlap resultingin CCI That is if 119899119891119895 = 119898119891119896 997904rArr 119899 = 119898(119901119896119901119895) Since 119901119896119901119895is irreducible 997904rArr 119898 = plusmn119894119901119895 where 119894 is a nonnegative integer119901119895 is a prime number and 119894119901119895 le 120573119896 We have

119894119890 lt |119898| = 119894119877 times 119897 lt 119894119901119895 le 120573119896 lt 1198612119877 minus 1 (16)

Since 119877times 119897 is constant (Lemma 3) and 119894119890 lt 119894119877119897 lt 1198612119877minus 1 forall values of 119877 then 119894 can only be equal to zero

Therefore the only common spectral component insideB can be the one corresponding to the discrete carrier whichcould be made smaller for larger values of 120573119896 (since theenvelope of 119869119899(120573119896) decreases) or around the zeros of 119869119899(120573119896)Scenario (b) This setting implies that at least one of theldquosincrdquo functions (15) would partly overlap leading also toCCISimilar to the discussion in the above scenario we consider|119891119895 plusmn 119894119901119895119891119896| to be relatively small with respect to R where 119894is a nonnegative integer 119901119895 is a prime number and 119894119901119895 le 120573119896We consider the worst case scenario where min119895|119891119895 minus 119894119901119895119891119896|since min119895|119891119895 minus 119894119901119895119891119896| le |119891119895 minus 119894119901119895119891119896| le |119891119895 plusmn 119894119901119895119891119896|

From (7) in Remark 2 min119895|119891119895 minus 119894119901119895119891119896| decreases as 120574increases (or spectral efficiency increases) leading to moreoverlapping spectral bands or worse BER due to SIR In addi-tion for a fixed spreading factor 120572 120574 increases as the numberof users 119871 increases which could worsen the performance

However for a relatively small value of 120574 the significantoverlapping band would be at the carrier (Scenario (a)) anda few others may partly overlap depending on the value of 120574

The latter analysis indicates that the proposed scheme iscapable of significantly rejecting CCI signals

4 Numerical Simulations

This section examines the performance of the proposedscheme using numerical simulations The performance ofCIMA is compared with the performance of DSSS-BPSKsince both schemes allow multiple access and require coher-ent detectionThe comparison is based on consistent numeri-cal implementation as far as selecting the relevant parametersIt is important to note that baseband implementation doesnot exactly match the expected baseband performance whenemploying the proposed scheme The reason behind thismismatch is illustrated with the following simple example If119891119888 = 0 then the frequency separation of the signal doubles


eg the period of 119909(119905) = 119860 cos(2120587119891119888119905+120573119898sin(2120587119891119898119905)) is 1119891119898however the period of119909(119905) = 119860 cos(120573119898sin(2120587119891119898119905)) is 1(2119891119898)since cos(sin(plusmn120572)) = cos(sin(120572))

Consequently the passband approach is implemented forboth schemes The carrier frequency [Hz] in all scenarios isset at 119891119888 = 8120572119877 and the sampling frequency [Hz] at 119891119904 =8(119891119888 + 120572119877) where 120572 and 119877 are the spreading factor and thebit rate for both CIMA and DSSS-BPSK For consistency weselect the chip period employed in DSSS-BPSK to be equalto 1(120572119877) TheMersenne Twister PRNG which is used as thedefault stream atMATLAB startup and several other softwaresystems is adopted for generating the codes associated withDSSS-BPSK Although it is the most widely used PRNG[32] the codes generated by Mersenne Twister have finitecorrelation values for other than zero delay MATLAB wasemployed to carry out all the simulations

In what follows we first examine the PSD and thebandwidth of three CIMA signals to further illustrate thefrequency interleaving CIMA employs Next we computethe BER due to channel noise with and without multipathchannel consideration and cochannel interference (CCI) forCIMA and DSSS-BPSK Several plots have been presentedto encompass all aspects of CIMA performance by vary-ing the spreading factor spectral efficiency and signal-to-interference ratio (SIR) of CCI signals All simulations aredone on passband signals with a bit rate of R = 20 bitss andwith 119891119888 and 119891119904 as defined above

41 CIMA PSD and Bandwidth This part examines thesingle-sided spectrum and bandwidth of three CIMA signalsThe purpose of this study is not meant to evaluate theperformance of the proposed algorithm but only to illustratethe relevant analytical work including (10)

The employed spreading factor is 120572 = 100 and thespectral efficiency 120574 = 03 bitssecHz Following from (10)in Section 3 the null-to-null bandwidth 119861119910 cong (120572 + 2)119877 =2040 Hz asymp 119861 = 120572119877 = 2000Hz 120573119895 and 119891119895 are chosen suchthat 2(120573119895 + 1)119891119895 = 119861 = 2000 Hz for j = 1 2 or 3 ExaminingFigure 2 we notice that no significant power occurs beyond1020 Hz which confirms (10) In addition as discussed inSection 33 (frequency domain analysis) the only completelyoverlapping ldquosincrdquo function is at the carrier (Scenario (a))and few others partly overlap The spectrum holes are due tothe employed relatively large spreading factor for only threeusers

42 AWGNandMultipath Fading Channel Theperformanceof CIMA and DSSS-BPSK in the presence of an additivewhite Gaussian noise (AWGN) channel is examined in thispart of the simulations Simulations for one and seven usersunder AWGN and multipath fading channel are carriedout A spreading factor of 120572 = 60 is considered for bothmodulation schemes The BER versus 1198641198871198730 in the AWGNwith no multipath channel for both schemes is shown inFigure 3 where 1198641198871198730 ranges from minus1 to 9 dB in incrementsof 1 dB It is important to note that single-user CIMA andDSSS-BSPK perform similarly to BPSK For seven users theproposed method outperforms DSSS-BPSK under consider-ation Based on numerical simulations the DSSS-BPSK BER

User 1User 2User 3

200 400 600 800 1000 12000Frequency (Hz)

10minus3

10minus2

10minus1

100

101

102

Pow

erF

requ

ency

(dB

Hz)

Figure 2 Power spectral density of 3 CIMA signals with corre-sponding PRNG parameter pairs 1205731 = 124783 1198911 = 741935 Hz 1205732= 40820 1198912 = 1967742 Hz 1205733 = 21959 1198913 = 3129032 Hz

using Mersenne Twister PRNG in presence of AWGN (eg120572 = 60 and 119871 = 7) can be closely approximated by theanalytical model of DSSS-BPSK which is given by

BER = 119876[ 1radic(119871 minus 1) 120572 + 11987302119864119887 ] (17)

However the performance ofDSSS-BPSK should be generallyaffected by the nonzero correlation among the randomspreading codes generated by the Mersenne Twister PRNG

In order to further demonstrate the potential of theproposed scheme a simulation in a multipath fading channelis depicted in Figure 4 Four taps with relative path gainsof 0 dB -3 dB -6 dB and -9 dB and uniformly distributedrandom path delays between 119879119888119901 and 3119879119888119901 are consideredfor the multipath fading channel where 119879119888119901 = 1120572119877 is theDSSS-BPSK chip period The results in Figure 4 show thatthe performance of CIMA and DSSS degrades in a multipathchannel with CIMA still performing similarly to DSSS insingle-user application and better with seven users

43 Cochannel Interference Since both schemes allow mul-tiple access it is important to assess their performance infunction of the spreading factor for a specific number of usersWe examine the BER in function of the spreading factor fora fixed number of users This implies that as the spreadingfactor increases the spreading bandwidth increases andsubsequently the spectral efficiency decreases Figure 5 showsthe BER for different spreading factors The number of usersis set to 10 for both CIMA and DSSS The spreading factoris varied from 10 to 60 It is important to note that theproduct 120574120572 = 119871 was held constant in the case of CIMAwhere L is the number of users sharing the same channelFigure 5 shows the BER for different spreading factors As


100

10minus1

10minus2

10minus3

10minus4

10minus5

BER

minus1 0 1 2 3 4 5 6 7 8 9

＜0 (dB)

DSSS One UserDSSS Seven UsersCIMA One UserCIMA Seven Users

Figure 3 BER versus1198641198871198730 of CIMAandDSSS-BPSK in anAWGNchannel for 1 and 7 users and 120572 = 60

100

10minus1

10minus2

10minus3

10minus4

BER

minus1 0 1 2 3 4 5 6 7 8 9

＜0 (dB)


Figure 4 BER versus1198641198871198730 ofCIMAandDSSS-BPSK in anAWGNwith a four-tap multipath channel for 1 and 7 users and 120572 = 60

expected the performance of both schemes improves as thespreading factor increases since the spreading bandwidth isalso increasing

44 Spectral Efficiency We compare the performance ofCIMA with DSSS-BPSK in terms of the spectral efficiencyContrary to the previous scenario we look at how the BERis affected by the number of users when the spreading factoris fixed Figure 6 presents the BER while varying the valuesof 120574 where 120574 = 119871120572 120572 = 100 and L is the number ofusers ranging from 30 to 130 The power of each cochannelinterferer is 50 of the targeted signal power The resultingBER in Figure 6 shows that performance of both CIMAand DSSS-BPSK degrades as the spectral efficiency increaseswhich is expected since more users are accessing the channelIt follows directly from Figure 6 that CIMA performs betterthan DSSS for all spectral efficiencies It is important tonote that the BER pertaining to CIMA at a 130 spectralefficiency is about three times smaller than the corresponding

10 15 20 25 30 35 40 45 50 55 60Spreading Factor

DSSSCIMA

100

10minus1

10minus2

10minus3

10minus4

BER

Figure 5 BER versus the spreading factor 120572 for CIMA and DSSS-BPSK for 10 users

02 04 06 08 1 12 14 16

Gamma

DSSSCIMA

100

10minus1

10minus2

10minus3

10minus4

BER

Figure 6 BER versus the spectral efficiency 120574 for CIMA and DSSS-BPSK for spreading factor 120572 = 100 and the number of users variedfrom 30 to 130

BER associated with DSSS-BPSK which further affirms thepotential of the proposed scheme

45 Signal-to-Interference Ratio The performance of bothschemes for different signal-to-interference ratios (SIRs) isalso evaluated at a 100 spectral efficiency The transmittedsignal power to the total interfering signalsrsquo power ratio isvaried from -10 dB to 0 dB In order to achieve such SIRvariations we are artificially changing the transmitted powerof users to modify the power ratio between the user ofinterest and other users The total interfering signal poweris considered to be the sum of the powers of individualinterferers A spreading factor of 10 and a number of 10users are considered for this part of the simulation TheBER curves are shown in Figure 7 It is also evident thatCIMA performs better than DSSS-BPSK for all SIRs with anacceptable performance at -10 dB and a BER almost 35 timessmaller than DSSS-BPSK at 0 dB


minus10 minus9 minus8 minus7 minus6 minus5 minus4 minus3 minus2 minus1 0

SIR (dB)

DSSSCIMA BPSK

100

10minus1

10minus2

10minus3

10minus4

10minus5

BER

Figure 7 BER versus SIR for CIMA and DSSS-BPSK for 10 usersand spreading factor 120572 = 10

5 Conclusion

In this paper a novel multiple-access modulation scheme wasproposed that employs a nontraditional PRNG The systemprovided a capability of significantly rejecting cochannel andadjacent channel interference Based on numerical simula-tions CIMA performance in the presence of channel noisewas shown to be similar to DSSS-BPSK with orthogonalspreading codes In addition CIMA outperforms DSSS-BPSKusingMersenneTwister PRNG in the case ofmultipathdelay with multiple users CCI spectral efficiency and SIRThis work unlocked the door for consideration of othermodulation schemes in employing the nontraditional PRNGproposed in [30] Future works may include the use of aGaussian filter along with an equalizer integrated with CIMAto reduce the effects of intersymbol interference caused by theGaussian filter on the modulating data Using the appropriateequalizer can further improve the performance of CIMA inthe presence of noise and cochannel interference

Appendix

In the following we present three propositions that help inestablishing further characteristics pertaining to CIMA

Proposition A1 The number of prime numbers generated bythe proposed algorithm is given by

119871 cong int119901max

119901min

119889120590ln (120590) (A1)

Proof The proof can be readily deduced from fact that thenumber of prime numbers below a given number 119899 is wellapproximated by the offset logarithmic integral given by

Li (119899) = int1198992

119889120590ln (120590) (A2)

Proposition A2 119897 increases if and only if 119871 increases

Proof Necessary condition This can be verified by consider-ing the following

119889119889119897119871 cong 119889119889119897 int119901max

119901min

119889120590ln (120590)

= 119889119901maxln (119901max) minus 119889119901min119889119897 1

ln (119901min)cong 119861

2 (120573min + 1)1

ln (1198971198872 (120573min + 1)) minus 119877 1ln (119897119877)

(A3)

Note (119889119889119911)(119911ln(119897119911)) = (ln(119897119911) minus 1)(ln(119897119911))2 gt 0 119897119911 gt 119890since 119901max = 1198611198972(120573min + 1) gt 119901min ge 119877119897 gt 119890 997904rArr 119889119871119889119897 gt0Consequently as l increases L increasesSufficient condition Let119892(sdot) be the function such that 119871 =119892(119897) Since 119871 is a continuous (and differentiable) function and119892(sdot) is a strictly increasing function over the specified domain

then 119892minus1(sdot) exists where 119897 = 119892minus1 (L) and 119892minus1(sdot) is continuousand strictly increasing hence as 119871 increases l increases

Proof of Lemma 3 The proof is conducted using a contradic-tion argument Based on Proposition A1 119871 can be presentedas

119871 = 119892 (1199111) = int11988811991111199111

119889120590ln (120590) (A4)

where 1199111 equiv 119877 times 119897 gt 119890 and 119888 equiv 1205722(120573min + 1) gt 1119871 = 120574120572 is fixed assume there exists 1199112 = 1199111 where 1199112 gt 119890such that

119871 = int11988811991121199112

119889120590ln (120590) 997904rArr 119889119871119889119888 = 1199112

ln (1198881199112) (A5)

However since 119888 gt 1 and 119888119911 gt 119890 119911ln(119888119911) is a strictlyincreasing function Therefore for 1199111 = 1199112 it leads to 119871 = 119871which leads to a contradiction Consequently the product119877 times 119897 is constantCorollary A3 Assume 119891119888 ≫ 119877 then 120573119895 and BER areindependent of119877 for fixed values of 120574 and 120572where 120572 gt 2(120573min+1) and 120574 gt 0Proof From Lemma 3 the product 119877119897 is constant andindependent of 119877 for fixed values of 120574 and 120572 Consequentlythe lower and upper bound of the prime numbers 119901119895 areindependent of R hence 119901119895 is a set of values independentof 119877 Since 120573119895 = 1198971198612119901119895 minus 1 = 1205721198971198772119901119895 minus 1 forall119895 997904rArr 120573119895 is aset of values independent of 119877 Consider 119891119895 = 1198612(120573119895 + 1) =(1205722(120573119895 + 1))119877

Therefore the output of the corresponding matched filer(14) yields

V119896 (119905) cong 11986022 119898119896 (119905) + 11986022 int1

119871sum119895=1119895 =119896

120582119895119898119895 (119905)

sdot cos(120573119896 sin( 120587120572119905120573119896 + 1) minus 120573119895 sin( 120587120572119905120573119895 + 1))119889119905(A6)


Since the output of the matched filter is independent of R and119891119888 so is the output of the receiver and hence the BER

A Proposed Approach for Generating 119891119894 and 120573119894The inputs of a code that generates different pairs (120573119894 119891119894) canbe the spreading factor 120572 the spectral efficiency 120574 and thebit rate R (and 120573119898119894119899 is set to a constant eg 120573119898119894119899 = 12)Consequently the spread bandwidth becomes 119861 = 120572119877 Thebounds for 119901119895 become 119877119897 le 119901119895 le 1198611198972(120573min + 1) 1 le 119895 le 119871

In order to find a sufficiently large value of l correspond-ing to the desired value of 119871 = 120572120574 (desired number of users)it is recommended to start at 3R (in order to guarantee that119877119897 gt 119890) and keep on increasing l (eg while loop) until Lprime numbers are generated

Set 119891119895 equiv 119901119895119897 1 le 119895 le 119871 and 120573119895 equiv 1198612119891119895 minus 1 1 le 119895 le 119871Data Availability

Thedata can be easily generated by using the model providedin the manuscript

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

The authors would like to thank Mr Michel Nacouzi forconducting helpful numerical simulations relevant to CIMAwhich are not shown in this manuscript The authors wouldalso like to thank the anonymous reviewers for their helpfulcomments

References

[1] D Evans The Internet of Things How the Next Evolution ofthe Internet is Changing Everything Cisco Internet BusinessSolutions Group April 2011

[2] K David D Dixit and N Jefferies ldquo2020 Visionrdquo IEEEVehicular Technology Magazine vol 5 no 3 pp 22ndash29 2010

[3] S Kondo and B Milstein ldquoPerformance of multicarrier DSCDMA systemsrdquo IEEE Transactions on Communications vol44 no 2 pp 238ndash246

[4] B Yu Y Bao H Wei X Huang and Y Shu ldquoCollaborativecovert communication design based on lattice reduction aidedmultiple user detection methodrdquoWireless Communications andMobile Computing vol 2017 Article ID 8949430 8 pages 2017

[5] L Nguyen ldquoSelf-encoded spread spectrum communicationsrdquoin Proceedings of the Conference on Military Communications(MILCOMrsquo99) pp 182ndash186 Atlantic City NJ USA

[6] K Siwiak ldquoUltra-wide band radio Introducing a new technol-ogyrdquo in Proceedings of the IEEE VTS 53rd Vehicular TechnologyConference (VTS SPRING 2001) pp 1088ndash1093 Greece May2001

[7] Y-R Tsai and X-S Li ldquoKasami code-shift-keying modulationfor ultra-wideband communication systemsrdquo IEEE Transac-tions on Communications vol 55 no 6 pp 1242ndash1252 2007

[8] G Kaddoum F-D Richardson and F Gagnon ldquoDesign andanalysis of a multi-carrier differential chaos shift keying com-munication systemrdquo IEEE Transactions on Communicationsvol 61 no 8 pp 3281ndash3291 2013

[9] M K Patel S M Berber and K Sowerby ldquoAntijammingperformance of adaptive chaos based CDMA system withMRC in imperfect channel estimation environmentrdquo WirelessCommunications and Mobile Computing vol 2017 Article ID2716949 5 pages 2017

[10] M Herceg G Kaddoum D Vranjes and E Soujeri ldquoPermu-tation index DCSK modulation technique for secure multiuserhigh-data-rate communication systemsrdquo IEEE Transactions onVehicular Technology vol 67 no 4 pp 2997ndash3007 2018

[11] M Herceg D Vranjes G Kaddoum and E Soujeri ldquoCom-mutation Code Index DCSK Modulation Technique for High-Data-Rate Communication Systemsrdquo IEEE Transactions onCircuits and Systems II Express Briefs 2018

[12] G Kaddoum Y Nijsure and H Tran ldquoGeneralized codeindexmodulation technique for high-data-rate communicationsystemsrdquo IEEETransactions onVehicular Technology vol 65 no9 pp 7000ndash7009 2016

[13] A Cassola T Jin G Noubir and B Thapa ldquoEfficient spreadspectrum communication without preshared secretsrdquo IEEETransactions on Mobile Computing vol 12 no 8 pp 1669ndash16802013

[14] W D Lane and A M Bush ldquoSpread-spectrum multi-h modu-lationrdquo IEEE Journal on Selected Areas in Communications vol8 no 5 pp 728ndash742 1990

[15] F Giannetti M Luise and R Reggiannini ldquoContinuous-PhaseModulations for CDMA Radio Communications ModemArchitecture and Performancerdquo European Transactions onTelecommunications vol 7 no 3 pp 225ndash233 1996

[16] R T Hsu and J S Lehnert ldquoThe performance of continuous-phase-coded DSSSMA communicationsrdquo IEEE Transactionson Communications vol 46 no 4 pp 533ndash543 1998

[17] F Yang S H Leung C Y Ngan and G Bi ldquoThe perfor-mance and design criterion of phase spreading sequencesfor DSSSMA communications with full response CPM overRayleigh fading channelsrdquo in Proceedings of the IEEE GlobalTelecommun Conference - GLOBECOMrsquo99 vol 1B pp 914ndash918December 1999

[18] A T McDowell J S Lehnert and Y K Jeong ldquoDual-phasecontinuous phase modulation for spread-spectrum multiple-access communicationrdquo IEEETransactions onCommunicationsvol 52 no 5 pp 823ndash833 2004

[19] E Soujeri G Kaddoum and M Herceg ldquoDesign of an initialcondition-index chaos shift keying modulationrdquo IEEE Electron-ics Letters vol 54 no 7 pp 447ndash449 2018

[20] P Som and A Chockalingam ldquoPerformance analysis of space-shift keying in decode-And-forward Multihop MIMO net-worksrdquo IEEE Transactions on Vehicular Technology vol 64 no1 pp 132ndash146 2015

[21] X Li S Hong V D Chakravarthy M Temple and Z WuldquoIntercarrier interference immune single carrier OFDM viamagnitude-keyed modulation for high speed aerial vehiclecommunicationrdquo IEEE Transactions on Communications vol61 no 2 pp 658ndash668 2013

[22] S Vaughan-Nichols ldquoOFDM back to the wireless futurerdquo TheComputer Journal vol 35 no 12 pp 19ndash21 2002

[23] E Soujeri G Kaddoum M Au and M Herceg ldquoFrequencyIndex Modulation for Low Complexity Low Energy Commu-nication Networksrdquo IEEE Access vol 5 pp 23276ndash23287 2017


[24] R L PetersonR E Ziemer andEDavid Introduction to SpreadSpectrumCommunications Prentice Hall Englewood Cliffs NJUSA 1995

[25] R Gold and R Dixon ldquoMethod andApparatus for DespreadingSpread Spectrum Signalsrdquo Patent Number vol 5 pp 761-2391998

[26] T Kasami ldquoWeight distribution formula for some class ofcyclic codesrdquo Defense Technical Information Center R-285(AD632574) Coordinated Science Lab Univ Urbana Ill USA1966

[27] R H Barker and R H ldquoGroup Synchronizing of BinaryDigital Sequencesrdquo in Communication Theory pp 273ndash287Butterworth London 1953

[28] V Tarokh H Jafarkhani and A R Calderbank ldquoSpace-timeblock codes from orthogonal designsrdquo IEEE Transactions onInformation Theory vol 45 no 5 pp 1456ndash1467 1999

[29] V Tarokh N Seshadri and A R Calderbank ldquoSpace-timecodes for high data rate wireless communication performancecriterion and code constructionrdquo IEEE Transactions on Infor-mation Theory vol 44 no 2 pp 744ndash765 1998

[30] S S Saab J G Hobeika and I E Ouaiss ldquoA novel pseudo-random noise and band jammer generator using a compositesinusoidal functionrdquo IEEE Transactions on Signal Processingvol 58 no 2 pp 535ndash543 2010

[31] J Gu W S Jeon and J M Kim ldquoProactive frequency-hoppingdynamic spectrum access against asynchronous interchannelspectrum sensingrdquo IEEE Transactions on Vehicular Technologyvol 62 no 8 pp 3614ndash3626 2013

[32] S Marsland Machine Learning An Algorithmic PerspectiveCRC Press 2011

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Modulation (CIM) has been proposed for spread spectrumsystems [12] In CIM the indices of spreading codes are usedin conjunction with symbol constellation for bits mappingThe latter scheme aims to achieve high data rate commu-nication without sacrificing system complexity and energyrequirement In noncoherent multicarrier spread spectrumsystems the reference signal is sent once for multiple parallelbits yielding significant energy savings and a higher spec-tral efficiency as compared to other DSCK systems Othermethods employing efficient coding techniques aimed atreducing energy costs ie memory and processing costin standard spread spectrum (SS) communication systems[13] Continuous phase modulation combined with DSSS isproposed in [14] and further investigated in [15ndash18] Recentlyindexmodulation has been applied to a coherent chaos-basedscheme where the initial conditions of the chaotic sequenceare used as a new dimension to map information and carryextra bits [19] All the proposed modulation methods abovecome with a number of unique features

Siding away from spread spectrum techniques the rela-tively new spatial-shift keying (SSK) which is widely imple-mented formultiple-input multiple-output (MIMO) systemsis considered as a strong candidate for next generationwireless communication systems [20] The same applies fororthogonal frequency division multiplexing (OFDM) whichis believed to be the best in multicarrier modulation and isalso extensively used in broadband and MIMO systems [21]Howevermulticarrier OFDM and even single-carrier OFDMhave some drawbacks [21] For example due to leakage of theFFT OFDM is more sensitive to carrier frequency offset anddrift than single-carrier systems the need of high peak-to-average-power ratio [22] and sensitivity due channel spatialcorrelation In [23] a frequency index modulation scheme isproposed to reduce peak-to-average-power ratio of OFDMsystems without sacrificing data rate

The commonly pseudorandom sequences used in com-munication systems are maximal length sequences [24]Mersenne Twister code Walsh sequences and Gold codes[25] Kasami codes [26] and Barker codes [27] In orderto improve the spectral efficiency in MIMO systems space-time block codes [28 29] and space-time trellis codes areemployed However none of the communication systemsemploys the nontraditional pseudorandom noise generator(PRNG) proposed in [30]The latter is based on a linear com-bination of continuous-time composite sinusoidal signalsThe desired signalsrsquo key parameters are easily constructed bychoosing a set of prime numbers with bounds dependingon the typical requirements of the PRNG [30] The keycharacteristics of the PRNG are as follows The period of thesignal can be made arbitrarily large at least 98 of the signaltotal average power is contained in the desired frequencybandwidth a desired bandwidth can be arbitrarily selectedand the cross-correlation between any pair of generatedsignals can be made arbitrarily small This answers concernson interchannel interference raised by many researches onspread spectrum techniques such as in FHSS [31]

In this paper a newmodulation scheme named CIMA isproposed In DSSS there is a fast phase shift of 180∘ througha predefined sequence known to both the receiver and the

transmitter In FHSS there is a fast hopping of the signal intodifferent frequencies The set of frequencies is also knownto both the receiver and the transmitter In CIMA insteadof having a discrete phase shift or frequency shift like DSSSor FHSS we have both phase and frequency change in theform of a predefined composite sinusoidal function knownto both the receiver and the transmitter CIMA modulatoris formed by multiplying a bipolar digital message signalwith cos(2120587119891119888119905+120573119898sin(2120587119891119898119905)) where each message signal isassociated with a unique signature pair (120573119898 119891119898) The choiceof 120573119898 and 119891119898 is the key in rejecting cochannel interferencewhich is an essential cause of the signalrsquos quality degradationand capacity constraint in wireless mobile telephony andother applications The proposed PRNG in [30] is employedfor generating different pairs (120573119898 119891119898) Each pair is strictlycorrelated and all different pairs are made weakly correlatedbut equally constrained to a bandwidth measure

This proposed method can be used as a single-user or amultiple-access technique Due to the composite sinusoidalfunction employed at the modulator the sinc functionscorresponding to the polar signaling are spread around thecarrier within the same channel with frequency separation of119899119891119898 119899 = 0 plusmn1 plusmn2 plusmn120573119898 + 1 In multiple-access applica-tion each user is assigned different (120573119898 119891119898) Consequentlyall the sinc functions associated with different users are sepa-rated by different values of 119891119898 which are all situated aroundthe carrier within the same channel and the instantaneousfrequency of a CIMA signal is given by 119891119894119899119904119905(119905) = 119891119888 +119891119898120573119898cos(2120587119891119898119905)) This type of spectral interleaving aroundthe carrier awards ldquoCarrier Interleaved Multiple Accessrdquoterminology CIMA aims at rejecting adjacent and cochannelinterference

The characteristics of the proposed modulation schemeare analytically presented including bandwidth analysis biterror rate (BER) due to channel noise and cochannel andadjacent channel interference Numerical simulations exam-ine the performance of the proposed scheme contrastedwith DSSS-BPSK while considering a more complex channelmodel

The rest of this paper is organized as follows Section 2describes the proposed CIMA system and the employedPRNG and it presents relevant parameters and new charac-teristics of the PRNG Section 3 contains analytical analysisdescribing CIMA characteristics Section 4 includes a com-parative study with DSSS-BPSK scheme based on numericalsimulations and finally Section 5 contains conclusions andfuture work

2 Proposed System Model

In this sectionwe present the basics of CIMAmodulation anddemodulation and the employed PRNG algorithm and estab-lish some preliminary new results relevant to the employedPRNG

21 System Transmitter and Receiver At the transmitter sidethe 119895th message signal 119898119895(119905) is assumed to be in the formof polar digital signaling with a bit rate 119877 where 119877 = 1119879119887


ReceivedSignal

Integrateamp dump

resholdDevice

PMfc

Oscillatorf=fj PRNG

jfj

jDP



119910119895 (119905) = 119860119898119895 (119905) cos (2120587119891119888119905 + 120573119895 sin (2120587119891119895119905)) 1 le 119895 le 119871 (1)








119909119895 (119905) = 119860119895119873sum119894=1

cos (2120587119891119888119905 + 120573119894119895 sin (2120587119891119894119895119905)) 1 le 119895 le 119871

(2)


119909119895 (119905) = 119860 cos (2120587119891119888119905 + 120573119895 sin (2120587119891119895119905)) (3)



1198692119899 (120573119895)sdot [120575 (119891 minus 119891119888 minus 119899119891119895) + 120575 (119891 + 119891119888 + 119899119891119895)]

(4)


119891119895 = 119901119895119897 = 1198612 (120573119895 + 1) 1 le 119895 le 119871 (5)












min2le119895le119871









119909 (119905) = 119860 cos (2120587119891119888119905 + 120573119898 sin (2120587119891119898119905)) (8)





(9)


119861119910 cong 119861 + 2119877 = (120572 + 2) 119877 (10)



120578119871 = 119871119877119861119910 = 120574120572120572 + 2 cong 1205741003816100381610038161003816120572≫1 (11)



119911119890minus12058522119889120585





119910119896 (119905) = 119860119898119896 (119905) cos (2120587119891119888119905 + 120573119896sin (2120587119891119896119905)) (12)


V119896 (1199050) = int119879119887

[[[119871sum119895=1

120582119895119910119895 (119905)]]]119909119896 (119905) 119889119905 (13)


V119896 (119905) cong 11986022 119898119896 (119905) + 11986022 int119879119887

119871sum119895=1119895 =119896

120582119895119898119895 (119905)







(15)




















User 1User 2User 3

200 400 600 800 1000 12000Frequency (Hz)

10minus3

10minus2

10minus1

100

101

102

Pow

erF

requ

ency

(dB

Hz)



BER = 119876[ 1radic(119871 minus 1) 120572 + 11987302119864119887 ] (17)





100

10minus1

10minus2

10minus3

10minus4

10minus5

BER

minus1 0 1 2 3 4 5 6 7 8 9

＜0 (dB)



100

10minus1

10minus2

10minus3

10minus4

BER

minus1 0 1 2 3 4 5 6 7 8 9

＜0 (dB)






DSSSCIMA

100

10minus1

10minus2

10minus3

10minus4

BER


02 04 06 08 1 12 14 16

Gamma

DSSSCIMA

100

10minus1

10minus2

10minus3

10minus4

BER






SIR (dB)

DSSSCIMA BPSK

100

10minus1

10minus2

10minus3

10minus4

10minus5

BER


5 Conclusion


Appendix




119901min

119889120590ln (120590) (A1)


Li (119899) = int1198992

119889120590ln (120590) (A2)



119889119889119897119871 cong 119889119889119897 int119901max

119901min

119889120590ln (120590)


ln (119901min)cong 119861

2 (120573min + 1)1

ln (1198971198872 (120573min + 1)) minus 119877 1ln (119897119877)

(A3)




119871 = 119892 (1199111) = int11988811991111199111

119889120590ln (120590) (A4)


119871 = int11988811991121199112

119889120590ln (120590) 997904rArr 119889119871119889119888 = 1199112

ln (1198881199112) (A5)



V119896 (119905) cong 11986022 119898119896 (119905) + 11986022 int1

119871sum119895=1119895 =119896

120582119895119898119895 (119905)










Acknowledgments


References




































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



ReceivedSignal

Integrateamp dump

resholdDevice

PMfc

Oscillatorf=fj PRNG

jfj

jDP



119910119895 (119905) = 119860119898119895 (119905) cos (2120587119891119888119905 + 120573119895 sin (2120587119891119895119905)) 1 le 119895 le 119871 (1)








119909119895 (119905) = 119860119895119873sum119894=1

cos (2120587119891119888119905 + 120573119894119895 sin (2120587119891119894119895119905)) 1 le 119895 le 119871

(2)


119909119895 (119905) = 119860 cos (2120587119891119888119905 + 120573119895 sin (2120587119891119895119905)) (3)



1198692119899 (120573119895)sdot [120575 (119891 minus 119891119888 minus 119899119891119895) + 120575 (119891 + 119891119888 + 119899119891119895)]

(4)


119891119895 = 119901119895119897 = 1198612 (120573119895 + 1) 1 le 119895 le 119871 (5)












min2le119895le119871









119909 (119905) = 119860 cos (2120587119891119888119905 + 120573119898 sin (2120587119891119898119905)) (8)





(9)


119861119910 cong 119861 + 2119877 = (120572 + 2) 119877 (10)



120578119871 = 119871119877119861119910 = 120574120572120572 + 2 cong 1205741003816100381610038161003816120572≫1 (11)



119911119890minus12058522119889120585





119910119896 (119905) = 119860119898119896 (119905) cos (2120587119891119888119905 + 120573119896sin (2120587119891119896119905)) (12)


V119896 (1199050) = int119879119887

[[[119871sum119895=1

120582119895119910119895 (119905)]]]119909119896 (119905) 119889119905 (13)


V119896 (119905) cong 11986022 119898119896 (119905) + 11986022 int119879119887

119871sum119895=1119895 =119896

120582119895119898119895 (119905)







(15)




















User 1User 2User 3

200 400 600 800 1000 12000Frequency (Hz)

10minus3

10minus2

10minus1

100

101

102

Pow

erF

requ

ency

(dB

Hz)



BER = 119876[ 1radic(119871 minus 1) 120572 + 11987302119864119887 ] (17)





100

10minus1

10minus2

10minus3

10minus4

10minus5

BER

minus1 0 1 2 3 4 5 6 7 8 9

＜0 (dB)



100

10minus1

10minus2

10minus3

10minus4

BER

minus1 0 1 2 3 4 5 6 7 8 9

＜0 (dB)






DSSSCIMA

100

10minus1

10minus2

10minus3

10minus4

BER


02 04 06 08 1 12 14 16

Gamma

DSSSCIMA

100

10minus1

10minus2

10minus3

10minus4

BER






SIR (dB)

DSSSCIMA BPSK

100

10minus1

10minus2

10minus3

10minus4

10minus5

BER


5 Conclusion


Appendix




119901min

119889120590ln (120590) (A1)


Li (119899) = int1198992

119889120590ln (120590) (A2)



119889119889119897119871 cong 119889119889119897 int119901max

119901min

119889120590ln (120590)


ln (119901min)cong 119861

2 (120573min + 1)1

ln (1198971198872 (120573min + 1)) minus 119877 1ln (119897119877)

(A3)




119871 = 119892 (1199111) = int11988811991111199111

119889120590ln (120590) (A4)


119871 = int11988811991121199112

119889120590ln (120590) 997904rArr 119889119871119889119888 = 1199112

ln (1198881199112) (A5)



V119896 (119905) cong 11986022 119898119896 (119905) + 11986022 int1

119871sum119895=1119895 =119896

120582119895119898119895 (119905)










Acknowledgments


References




































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia










min2le119895le119871









119909 (119905) = 119860 cos (2120587119891119888119905 + 120573119898 sin (2120587119891119898119905)) (8)





(9)


119861119910 cong 119861 + 2119877 = (120572 + 2) 119877 (10)



120578119871 = 119871119877119861119910 = 120574120572120572 + 2 cong 1205741003816100381610038161003816120572≫1 (11)



119911119890minus12058522119889120585





119910119896 (119905) = 119860119898119896 (119905) cos (2120587119891119888119905 + 120573119896sin (2120587119891119896119905)) (12)


V119896 (1199050) = int119879119887

[[[119871sum119895=1

120582119895119910119895 (119905)]]]119909119896 (119905) 119889119905 (13)


V119896 (119905) cong 11986022 119898119896 (119905) + 11986022 int119879119887

119871sum119895=1119895 =119896

120582119895119898119895 (119905)







(15)




















User 1User 2User 3

200 400 600 800 1000 12000Frequency (Hz)

10minus3

10minus2

10minus1

100

101

102

Pow

erF

requ

ency

(dB

Hz)



BER = 119876[ 1radic(119871 minus 1) 120572 + 11987302119864119887 ] (17)





100

10minus1

10minus2

10minus3

10minus4

10minus5

BER

minus1 0 1 2 3 4 5 6 7 8 9

＜0 (dB)



100

10minus1

10minus2

10minus3

10minus4

BER

minus1 0 1 2 3 4 5 6 7 8 9

＜0 (dB)






DSSSCIMA

100

10minus1

10minus2

10minus3

10minus4

BER


02 04 06 08 1 12 14 16

Gamma

DSSSCIMA

100

10minus1

10minus2

10minus3

10minus4

BER






SIR (dB)

DSSSCIMA BPSK

100

10minus1

10minus2

10minus3

10minus4

10minus5

BER


5 Conclusion


Appendix




119901min

119889120590ln (120590) (A1)


Li (119899) = int1198992

119889120590ln (120590) (A2)



119889119889119897119871 cong 119889119889119897 int119901max

119901min

119889120590ln (120590)


ln (119901min)cong 119861

2 (120573min + 1)1

ln (1198971198872 (120573min + 1)) minus 119877 1ln (119897119877)

(A3)




119871 = 119892 (1199111) = int11988811991111199111

119889120590ln (120590) (A4)


119871 = int11988811991121199112

119889120590ln (120590) 997904rArr 119889119871119889119888 = 1199112

ln (1198881199112) (A5)



V119896 (119905) cong 11986022 119898119896 (119905) + 11986022 int1

119871sum119895=1119895 =119896

120582119895119898119895 (119905)










Acknowledgments


References




































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia





119910119896 (119905) = 119860119898119896 (119905) cos (2120587119891119888119905 + 120573119896sin (2120587119891119896119905)) (12)


V119896 (1199050) = int119879119887

[[[119871sum119895=1

120582119895119910119895 (119905)]]]119909119896 (119905) 119889119905 (13)


V119896 (119905) cong 11986022 119898119896 (119905) + 11986022 int119879119887

119871sum119895=1119895 =119896

120582119895119898119895 (119905)







(15)




















User 1User 2User 3

200 400 600 800 1000 12000Frequency (Hz)

10minus3

10minus2

10minus1

100

101

102

Pow

erF

requ

ency

(dB

Hz)



BER = 119876[ 1radic(119871 minus 1) 120572 + 11987302119864119887 ] (17)





100

10minus1

10minus2

10minus3

10minus4

10minus5

BER

minus1 0 1 2 3 4 5 6 7 8 9

＜0 (dB)



100

10minus1

10minus2

10minus3

10minus4

BER

minus1 0 1 2 3 4 5 6 7 8 9

＜0 (dB)






DSSSCIMA

100

10minus1

10minus2

10minus3

10minus4

BER


02 04 06 08 1 12 14 16

Gamma

DSSSCIMA

100

10minus1

10minus2

10minus3

10minus4

BER






SIR (dB)

DSSSCIMA BPSK

100

10minus1

10minus2

10minus3

10minus4

10minus5

BER


5 Conclusion


Appendix




119901min

119889120590ln (120590) (A1)


Li (119899) = int1198992

119889120590ln (120590) (A2)



119889119889119897119871 cong 119889119889119897 int119901max

119901min

119889120590ln (120590)


ln (119901min)cong 119861

2 (120573min + 1)1

ln (1198971198872 (120573min + 1)) minus 119877 1ln (119897119877)

(A3)




119871 = 119892 (1199111) = int11988811991111199111

119889120590ln (120590) (A4)


119871 = int11988811991121199112

119889120590ln (120590) 997904rArr 119889119871119889119888 = 1199112

ln (1198881199112) (A5)



V119896 (119905) cong 11986022 119898119896 (119905) + 11986022 int1

119871sum119895=1119895 =119896

120582119895119898119895 (119905)










Acknowledgments


References




































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia









User 1User 2User 3

200 400 600 800 1000 12000Frequency (Hz)

10minus3

10minus2

10minus1

100

101

102

Pow

erF

requ

ency

(dB

Hz)



BER = 119876[ 1radic(119871 minus 1) 120572 + 11987302119864119887 ] (17)





100

10minus1

10minus2

10minus3

10minus4

10minus5

BER

minus1 0 1 2 3 4 5 6 7 8 9

＜0 (dB)



100

10minus1

10minus2

10minus3

10minus4

BER

minus1 0 1 2 3 4 5 6 7 8 9

＜0 (dB)






DSSSCIMA

100

10minus1

10minus2

10minus3

10minus4

BER


02 04 06 08 1 12 14 16

Gamma

DSSSCIMA

100

10minus1

10minus2

10minus3

10minus4

BER






SIR (dB)

DSSSCIMA BPSK

100

10minus1

10minus2

10minus3

10minus4

10minus5

BER


5 Conclusion


Appendix




119901min

119889120590ln (120590) (A1)


Li (119899) = int1198992

119889120590ln (120590) (A2)



119889119889119897119871 cong 119889119889119897 int119901max

119901min

119889120590ln (120590)


ln (119901min)cong 119861

2 (120573min + 1)1

ln (1198971198872 (120573min + 1)) minus 119877 1ln (119897119877)

(A3)




119871 = 119892 (1199111) = int11988811991111199111

119889120590ln (120590) (A4)


119871 = int11988811991121199112

119889120590ln (120590) 997904rArr 119889119871119889119888 = 1199112

ln (1198881199112) (A5)



V119896 (119905) cong 11986022 119898119896 (119905) + 11986022 int1

119871sum119895=1119895 =119896

120582119895119898119895 (119905)










Acknowledgments


References




































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



100

10minus1

10minus2

10minus3

10minus4

10minus5

BER

minus1 0 1 2 3 4 5 6 7 8 9

＜0 (dB)



100

10minus1

10minus2

10minus3

10minus4

BER

minus1 0 1 2 3 4 5 6 7 8 9

＜0 (dB)






DSSSCIMA

100

10minus1

10minus2

10minus3

10minus4

BER


02 04 06 08 1 12 14 16

Gamma

DSSSCIMA

100

10minus1

10minus2

10minus3

10minus4

BER






SIR (dB)

DSSSCIMA BPSK

100

10minus1

10minus2

10minus3

10minus4

10minus5

BER


5 Conclusion


Appendix




119901min

119889120590ln (120590) (A1)


Li (119899) = int1198992

119889120590ln (120590) (A2)



119889119889119897119871 cong 119889119889119897 int119901max

119901min

119889120590ln (120590)


ln (119901min)cong 119861

2 (120573min + 1)1

ln (1198971198872 (120573min + 1)) minus 119877 1ln (119897119877)

(A3)




119871 = 119892 (1199111) = int11988811991111199111

119889120590ln (120590) (A4)


119871 = int11988811991121199112

119889120590ln (120590) 997904rArr 119889119871119889119888 = 1199112

ln (1198881199112) (A5)



V119896 (119905) cong 11986022 119898119896 (119905) + 11986022 int1

119871sum119895=1119895 =119896

120582119895119898119895 (119905)










Acknowledgments


References




































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




SIR (dB)

DSSSCIMA BPSK

100

10minus1

10minus2

10minus3

10minus4

10minus5

BER


5 Conclusion


Appendix




119901min

119889120590ln (120590) (A1)


Li (119899) = int1198992

119889120590ln (120590) (A2)



119889119889119897119871 cong 119889119889119897 int119901max

119901min

119889120590ln (120590)


ln (119901min)cong 119861

2 (120573min + 1)1

ln (1198971198872 (120573min + 1)) minus 119877 1ln (119897119877)

(A3)




119871 = 119892 (1199111) = int11988811991111199111

119889120590ln (120590) (A4)


119871 = int11988811991121199112

119889120590ln (120590) 997904rArr 119889119871119889119888 = 1199112

ln (1198881199112) (A5)



V119896 (119905) cong 11986022 119898119896 (119905) + 11986022 int1

119871sum119895=1119895 =119896

120582119895119898119895 (119905)










Acknowledgments


References




































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia










Acknowledgments


References




































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia














RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


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