Securing Physical Layer for FHSS Communication System Using Code andPhase Hopping Techniques in CDMA, System Design and Implementation

T he Frequency-hopping Spread Spectrum (FHSS) systems and techniques are using in military and civilianradar recently and in the communication system for securing the information on wireless communications link channels, for example in the Wi-Fi 8.02.X IEEE using multiple number bandwidth and frequencies in the wireless channel in order to hopping on them for increasing the security level during the broadcast, but nowadays FHSS problem, which is, any Smart Software Defined Radio (S-SDR) can easily detect a wireless signal at the transmitter and the receiver for the hopping sequence in both of these, then duplicate this sequence in order to hack the signal on both transmitter and receiver messages using the order of the sequences that will be recognized for next transmissions. In 2017 Code and Phase Hopping Techniques are both proposed to resolve the most recent problem in security-related, but not with FHSS, therefore in this paper presents a new composed proposed system will progress Phase Shift and Code Hopping in Code Division Multiplexing Access (CDMA) to complement with FHSS; because the wireless Communications systems security in the last years became a nightmare for some individuals, also companies, and even countries, also join them needing for higher bits rate in the wireless channels; because of next-generation communication system 5G-6G and the evolution in social networking, IoT, stream media, IoE, visualizations, and cloud computing. The new ideas can be applicable for a large number of users, also fast implementation without synchronization, as well as without any focus on encryption or keys-exchanges, at completion all results are simulation in MATLAB R2017b, the results have been tested by using 8 users in the same time, also our results showing promises effects on security for both applied systems Phases Shift and Codes Hopping especially the Code Hopping, therefor; our results encouraged us to complete research and compare our system with other.


INTRODUCTION for FHSS, CHSS and PSHSS
FHSSit stands for Frequency hopping Spread Spectrum andrunningby way of the spreading bandwidth frequency of propagatingwireless wave signals, also remain to change jumping at encoded sequence order time sequence intervals. The transmitter chooses the frequencies to be used established on the spreading bandwidth frequencies sequences. Fig. 1demonstrates the block flowchart of FHSS scheme. From Fig.1 in FHSS scheme, the data is at initial step, modulated together with the carrier signal, then second phase, spreading it with spreading wave signal whose frequenciesare continuously changing. The frequency of a spreading wave signal is selected from a programmed selection frequency, and it is pinpointed just to the system clients both at the transmitter and the receiver. Consequently, the communication procedure is hard to interrupt if the used frequency of spreading signal was unknown. The equations of the broadcastwave signal of Frequency Hoppingoccursand providedby way of as Eq. (1) to (3) (Widiyatmoko et al., 2018): where dA( ) is transmitted signal of FHSS scheme, u( ) is user information signal, Fhss( ) is the spreading wave signalfunction, and ( ) is the carrier wave signalfunction. user's information signal u( ) is like binary data signal, while carrier signal ( ) and spreading wave signal Fhss( )are not the same and they are expressed by (Widiyatmoko et al., 2018), (Visan, et al., 2019): where is functionalityfor frequency of wave signal, ℎ( ) is function of hopping frequencyalso, hopping frequency ℎ( ) is a function of ℎ , in which ℎ mentions to function of spreading frequency sequence, as given by both agreement between transmitter and receiver as shown in Eq. (4): Communicating system and network raise day after day and become more fast also the security(Mohammed et al., 2006), (Mohammed, 2007)therefor; FHSS is a secure techniques, day after day become more useful in different uses in both civilian and military use, like Wi-Fi8.02X(IEEE Standard, 1997)(Vermeer, 1997)(Chayatand Breeze, 1996)and even in radar, but these days, FHSS be so vulnerable in security (Mototolea, et al., 2020)a new Smart Software Defines Radio (S-SDR), If we using it correctly ways, and If we have a smart receiver for al so (or most) for all bandwidth channels in a frequency hopping spread spectrum scheme; then we can see and recording then hear like unencrypted traffic. In SDR collection procedure, the transmitter must transmit long enough for all channels that will hopping in it, then we can collect all the frequencies to program into our receivers which is will be of course another smart SDR. there for, from above the FHSS become predictable system for its sequence order time in all next transmissions and traffic data link messaging (Mototolea, et al., 2020) (White, et al., 2019).
In the year 2017 a paper provide new novel technique on title "Phase Shift Hopping and Code Hopping in complex CDMA or JCDMA" (Mohammed, 2007)it was proposed to adding or enhancing the security progressively more by actual simple algorithm without adding any hardware stages in the old CDMA system, in further words, the Phase Shift Hopping (PSH) and Code Hopping (CH) together work just excellentwithout slightlylargemodification in the old scheme or in bits rate and bit error rate, in other words good SNR/BER. Moreover, in this paper, we will need this new novel system(Mohammed, 2017)(CH and PSH compacted JCDMA) to adding with FHSS, what is more for this; since today data communications systems and networks having new task in their privacy traffic and cybersecurity consequently, similarly needing a new securing systems with ultra-high bits rate, with growing in number of users and beside narrow or limited bandwidth for authorization license frequencies aimed at hopping in FHSS; which are further and further become major needing in ours current modern life(Mohammed, 2017), and for that it can be proposed systems that using a limitation authorization licenses frequencies or bandwidths (This is will reached in several technique like by communicated a lot users with similar frequencies and/or in same time), one of methods is TDMA ( Fig. 1, where in the finalephase, the system will work as analog system not in digital procedure , and it can be transmitter as analog wireless wavesingle with boundless bits rates like any analog transmitter system, for example Frequency Modulation sineand cosine waves or can be work with Orthogonal Frequency DivisionMultiplexing (OFDM)schemein other words as communicating analog signal to transfer digital data. Also we will try in this paper, introduce a novel new physical layer for FHSS to transmit digital data, to ensure its security when data transmission and receiver, also our new scheme probable to be smart from or through the change procedure of transmitter regularly or randomly, without any growing the number of stages or make more processing, this will guarantee the speed of the system not be reduced, this proposed system well be include mathematically proving for all equations.
To prove the orthogonality for any matrix (Seberry, 1983),(Mohammed, 2012), it is must had to multiply this matrix by its transposeconjugate and checkered whether the product is real numbers or a multiple scalar on the identity matrix or if we have matrix A was square matrix and its diminution mxm(Mohammed, 2012) then [M]mxm is orthogonal matrix if: Anywhere"k"here is a constant number plushere any matrix "in this case square matrix", for example the most well-known orthogonal matrices besides the real and complex numbers for its elements, are Walsh Hadamard Matrix (WHm) and the Fast Fourier transform matrix (FFTm) multiplication matrix for "mxm" , Based on Eq. (1) Journal of Engineering Volume 26 July 2020 Number 7

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Where "m"goes on here to be the dimension of the square matrix that in this condition. Therefor the here issue will be, if the orthogonal matrix makes slight to extreme shift rotating in phase for all numbers or elements belong to the matrix as the same if the matrix will be orthogonal or not? Thus, this will proof our new tow properties in last research works (Mohammed, 2017), (Mohammed, 2012) able to applied here intended for our novel proposal scheme, then the property will be as following from paper (Mohammed, 2017): To see proof the theorem above, can see (Mohammed, 2017),(Mohammed, 2012), the key to it, it is we must persuade the orthogonal matrix's parts elements to Euler's equation formula for all elements in the matrix: The Proof: We have that matrix [Xm] orthogonal square matrix and can representing as: Where x 1,1 = r 1,1 1,1 ….x m,m = r m,m , and so on then switching all elements to Euler's equation formula: Then any act on shifting for all elements to [X]mxmby the consistent angle "θ" will be: Theorem 1: If X is any orthogonal not square matrices with real and complex elements, with dimension mxn , and all elements of X: X→ ℤ are, then any rotating shifting all elements by the same any angle will be not square orthogonal matrix too, with scalar number, where ℤ: including the vectors numbers it are all the set for complex numbers. afterward: But then again, the inverse forX shitting by constant θ for all elements belong [X] will be: And Where: xmxm is X elements, rm,mis the distance from origin or the radius of the unity circle, K is a constant and [I]mxm is identical matrix.
At hand, for the last equations evidencewhich is"if any shifting in phases for all elements to any orthogonal matrix is even so or will be orthogonal matrix too, but with adding together a constant as multiply number equal ( ± )" then the next section will contest the proposed system for using FHSS Phase Hopping with CDMA and complex CDMA the "JCDMA" for sample (but it can be used in OFDM and any digital communication similar to M-QAM), it will be adding together this feature assynthesis for fine-tuning radio station!!.
Followingour derivatizing equations over, now and immediatelywe will must be discoveryinformal and innovative procedure for produce orthogonal matrices in different dimensions for using in Code Hopping Spared Spectrums with FHSS (CHSS) since the oldenmethodsare very complex and problematic to calculate in real time processing even in current computers, swell that and since orthogonal matrices can be used in several different applications, for example similar to image processing and wireless 3G communications (in CDMA or OFDM or together). Therefor; in this paper, we represent how ournovel method generate and findingvarious orthogonal matrices throughapplying tensor products amongseveral orthogonal matrices, tow or more,in bothformation, real and complex numbers for matrix'selements, with affecting it in telecommunication (Jassim et al., 2013), (Mohammed, 2012), then Code Hopping with FHSS Spread Spectrum will be (CHSS) the person who reads will realize on the finishing line of this section that yielded matrices will remain orthogonal matrices too and the processing thru the novel method is actual easy way.
The tensor product in this paperwill be Kronecker product, can be useful in different actions like in matrices, vectors, Algebras, topological vector, modules,andspacing calculations……etc., among many other forms or things (Jassim et al., 2013). The most common bilinear trick, in some frameworks, was the tensor product and is additionally referred to as outer matrices product. For linear algebra mapping action for together[A], [B] (represented by matrices here), then, the type of matrix tensor product for two or more matricesand there are many properties for tensor product, but in this paper, will represent ournovel and actualsuitable way also its important for create orthogonal code can use for (CHSS) implementation were Theorem 2 and 2.1 descript this way to find many orthogonal matrices using as codes but the full proof for this new theorem can find in both reference Theorem 2 If X:ℤ → ℤ and Y: ℤ → ℤ are not square orthogonal matrices, so any actthrough their tensor product by matrix form is given by (X⊗Y = C: ℤ → ℤ ) the resulting matrix C will be not square orthogonal too, which is the set for complex numbers including the vectors numbers.
Theorem 2.1 (Special form) If X:ℤ → ℤ and Y: ℤ → ℤ are square orthogonal matrices, then any action by their tensor product by matrix form is given by (X⊗Y = C: ℤ → ℤ ) the resulting matrix C will be square orthogonal too, which is the set for complex numbers including the vectors numbers.

Journal of Engineering
As from above in Eq. 25 it is can reachedlowest bandwidth for one chip in Eq. 23 and 24, the parameter requirement tostand in the impropersmallest length or dA must be smallestmodel and that can stand if and only if Codekremain in the minimum; yet it is so rigid and difficult to create and originatesmallest code, in this situation must remain orthogonal and only if the length of it will be at least is equal to number of users, therefor the condition equation designed Where at this point in Eq. 26, = (n: is serial to parallel ratiothrough1/n ratio). The future systems for JCDMA are accomplished, and how easy can be programing from severalfactor and features, the receiver will be at this point as the end user or for further general form as the down link scheme, or it is be able as with PNk=1 for all (k) or (users): If we want the receiver and the Eq. 27 as Fig.2 to work properly fordemodulation all signals for whichever user in Eq.27, it is be required tomeet the condition as in Eq. 28 below: The Phase Hopping will be appliedby Eq.10 to Eq. 11 and the block diagram for the all system will see in Fig. 3 where Control for Phase Shifting and Code Hopping, and the Code Hopping will be used by Eq. 12 to Eq. 20 with deference orthogonal Codes similar to Wavelet group and Slentlet and so on , see references (Jassim et al., 2013), (Mohammed, 2012) exactly how to createa lot of orthogonal metrics and applied as Codes for requesting in DS-JCDMA. Table 1 Shows most variables that can be programmable, and that will compare with same old system and with both Phasing Shift and Code Hopping Speared Spectrum but in same settings below, in the Table 1. , it is clearlyas of the table, it can get our scheme with great security if all schemes Frequency Hopping Speared Spectrum (FHSS) and both with PSH, CH combined gather together.

THE SUGGESTEDSCHEME FOR FHSS COMBINED WITH CH AND PSH
TheFig. 3 and Table. 1 will introduce our novel scheme with its parameters and features, that willbe intended toFHSS with PSH and CH althoughmoreover with CDMA therefor we will rename as PSHSS, CHSS. Fig. 3explains the total systemthat we previously proposed in this paper, all user data will be work as input for complex CDMA which is clearly described in (Mohammed, 2011), additionally in Fig. 2which is have PSH and CH controllers parametersalso we will use Eq. 25 for modulation and Eq. 27 for demodulation with, of certainly, Eq. 1 where u(t) will be here DS-JCDMA data as shown below in Eq. 29 where both Fhss(t) and c(t) find in Eq. 3 and Eq. 2respectively.

CONCLUSIONS AND DISCUSSION FOR FIGURES RESULTS
All figures The foremost Result as shown will be exposed to the viewer that, it imaginable to make the new scheme that proposed FHSS and PH or CH , the results above compare between the Phase Hopping and Code hopping in DS-JCDMA with FHSS in Additive White Gaussian Noise (AWGN) wireless channel, therefore the results enlighten that the Code Hopping with FHSS (CH-FHSS) is extra protected from the Phase Shift Hopping with FHSS (PSH-FHSS), and we can using together systems if its requirement extra protected scheme in the same time exclusive of growing physical layer.
SinceFig. 6to Fig.7, it can be considerate that in the primary CH-FHSS is equivalent FHSS without CH, but it is furthermore protected and secure, when transmittingthe wireless data. Also reviewer noticeably, from Fig. 6,which from it can be seen that from the results above, the outcome of shifting in phase angle will be few in to transmitted and some outcome more effect and so on when the Phase Shifting are increase there for the result acceptable and accumulationsupplementarysafety for this ourscheme.
Similarly, from Fig.7it realized that the using CH by changing transforms code in the transmitterand in the receiver but with orthogonal code instead on Walsh Hadamard in CDMA at the transmitter and by defaulting similarly Walsh Hadamard in the receiver. For example, Wavelet Transform matrix,Slantlet transform matrix, Safe matrix, Complex-Wavelet Transform matrix (WSafe2) and Fourier matrix FFT.The system's parametersat the Table 1. is programmable for customize techniques as imperative and as we will use in the future.
From figuresabove that the results atFig. 6 and Fig. 7 for the proposal scheme, it been realizing that it can be increasing bit rate not includingexpanding bandwidth for everyone"users" or single user split up.
Conclusively, It can be gotten that since the results exceeding, the proposed scheme can be functionedwith orthogonal matrix as code with complex numbers elements and orthogonal matrix with real number elements, which is mostly likely one, and that actualsignificant and respectable for having extra security in CH for physical layer if using Theorem 2 and Theorem 2.1 from as presented in outcome for Fig.7. The signal receiver SNR towardsnumber of BER for the new scheme is acceptable at 16QAM (DS-JCDMA) on the AWGN wireless channel, therefor we are inspired to continue the research. The new proposed system which is use in this paper pilot bits in addition using type channel estimator together with channel compensating, the result have beinginspiredus, and we sagest to use each above for WiFi or LTEA system integrated with JCDMA to improve security and BER to SNR. In the end as shown above, we have a system possible work like synthesized radio in both the code, the phase and frequency jointly without any complexity in one system, for many users with same bandwidth.