Performance evaluation and mathematical analysis of direct sequence and frequency hopping spread spectrum systems under wideband interference

Spread Spectrum Multiple Access (SSMA) is one of the Multiple Access techniques in communication systems, that works by expanding the transmitted signal bandwidth to be larger than the bandwidth of the data signal [1]. Previous works discussing theory [2], techniques [3], and the developments of Spread Spectrum system [4] have been published since three decades ago. Spread Spectrum was originally applied to military communication system [5]. Currently, Spread Spectrum techniques have been widely used in many communication systems [6] such as GLOBALSTAR satellite communications system [5], Low Earth Orbiting (LEO) satellite communications network systems [7], GPS for satellite navigation system [8], Wireless Local Area Networks (WLAN) IEEE 802.11 system [8], optical codes for Fiber-optic Local Area Networks (LAN) [9], digital cellular radio system IS-95 for mobile voice communication [8], Wideband-CDMA for third-generation mobile communication system [8], wireless communication and control systems in Unmanned Aerial Vehicles (UAV) [10], underwater acoustic communication system [11]. This spread spectrum system is now developed for multiple access techniques on fifth generation (5G) cellular telecommunication system [12]. Spread Spectrum systems have been used in many other applications such as digital watermarking for copyright protection of audio, image and video, and multimedia data [13]-[15], digital watermarking for telemedicine [16], DC / DC converter circuit [17], LLC Resonant [18], and 3rd Generation Attachment Series (SATA-III) for reducing electromagnetic interference (EMI) problems [19]. ARTICL E INFO ABSTRACT


Introduction
Spread Spectrum Multiple Access (SSMA) is one of the Multiple Access techniques in communication systems, that works by expanding the transmitted signal bandwidth to be larger than the bandwidth of the data signal [1].Previous works discussing theory [2], techniques [3], and the developments of Spread Spectrum system [4] have been published since three decades ago.Spread Spectrum was originally applied to military communication system [5].Currently, Spread Spectrum techniques have been widely used in many communication systems [6] such as GLOBALSTAR satellite communications system [5], Low Earth Orbiting (LEO) satellite communications network systems [7], GPS for satellite navigation system [8], Wireless Local Area Networks (WLAN) IEEE 802.11 system [8], optical codes for Fiber-optic Local Area Networks (LAN) [9], digital cellular radio system IS-95 for mobile voice communication [8], Wideband-CDMA for third-generation mobile communication system [8], wireless communication and control systems in Unmanned Aerial Vehicles (UAV) [10], underwater acoustic communication system [11].This spread spectrum system is now developed for multiple access techniques on fifth generation (5G) cellular telecommunication system [12].Spread Spectrum systems have been used in many other applications such as digital watermarking for copyright protection of audio, image and video, and multimedia data [13]- [15], digital watermarking for telemedicine [16], DC / DC converter circuit [17], LLC Resonant [18], and 3rd Generation Attachment Series (SATA-III) for reducing electromagnetic interference (EMI) problems [19].

A R T I C L E I N F O
A B S T R A C T Spread Spectrum systems have been used in various fields due to their characteristics that can solve interference problems.Characteristics of the Spread Spectrum systems offering advantages for communication systems have been described in [20].Simulation study by using Matlab software as a digital signal processing tool has been done in [21].The advantages of the Spread Spectrum systems compared to the FDMA and TDMA systems have been ddiscussed in [22].In general, there are two methods of Spread Spectrum, namely: Direct Sequence Spread Spectrum (DSSS) and Frequency Hopping Spread Spectrum (FHSS).Several works addressing a thorough study of those two systems have been done in [23][24][25][26][27][28][29][30].In [23] and [24], design and simulation of both systems have been done on Matlab platform.In [25], a comparison study was done by changing the used signal bandwidth.Performance analysis by varying the pseudo noise (PN) sequence and modulation technique has been conducted in [26].In [27], comparative analysis based on the resulting modulated signal form has been presented.In [28], both systems are analyzed for their ability to avoid interference based on the maximum number of users for the same receiver.McCune [29] and Shayesteh [30] studied the performance of Spread Spectrum systems against interference with narrowband frequency.This research aims to simulate and analyse DSSS and FHSS performances when both systems are subject to wideband interference.The comparison analysis will be done based on the robustness of both systems against this type of interference.The used interference signal has similar spectrum behaviour to the transmitted signals of DSSS and FHSS systems.In other words, the generated interference signal employs similar frequency channel to DSSS and FHSS systems.BER parameter is used to determine the ability of each system to recover the data signal.This performance evaluation and mathematical analysis are important in the development of new multiple-access techniques, which are more resistant to wideband interference.This paper is structured as follows; Section 1 introduces the principle, the applications, and the previous works on Spread Spectrum system.Section 2 describes an overview of Spread Spectrum System covering the signal processing techniques on DSSS and FHSS systems, and presents the methodology covering the design procedure for simulation.Section 3 describes the simulation results and mathematical analysis, then followed by remarks.Section 4 concludes the paper.

Overview
Spread Spectrum is one of the multiple-access techniques that operates by expanding the transmitted signal bandwidth to be larger than the data signal [1].Spread Spectrum systems are generally divided into two techniques: DSSS and FHSS.DSSS transmits signals at a single frequency but on very wide bands, while FHSS transmits signals with narrow bands, but quickly jumps from one frequency to the next.Fig. 1 illustrates the difference between the spectrum of DSSS and FHSS.

Direct Sequence Spread Spectrum
DSSS is most widely used type of Spread Spectrum, due to it is easier to implement and also has a high data rate.DSSS is a method to transmit data where the sending and receiving systems are on a wide frequency band.This wide channel allows the device to transmit more information at a higher data rate.Fig. 2 shows the signal processing steps on both transmitter and receiver of DSSS system.DSSS works by modulating the data signal with the carrier signal, then spreading it with a spreading signal (pseudorandom signal) whose frequency is greater than the frequency of the data signal (bitrate).In the receiver, the despreading signal is generated from multiplication by the carrier signal and the same spreading signal on the transmitter, reversing the encoding process on the transmitter [3].The last process on the receiver is filtering to eliminate other signals, while keeping data signal.The mathematical model of the transmitted signal from the transmitter of DSSS has the following equation [1]: where   () is transmitted signal of DSSS system, () is data signal, () is function of the spreading signal, and () is function of the carrier signal.
The signals (), (), and () are formulated respectively as follow: where   is data series,   is data signal period,   is pseudo noise series,   is spreading signal period,  is carrier signal amplitude,  is carrier signal phase,   is spreading signal frequency, and ( − ) is the delayed impulse unit function.
The delayed impulse unit function ( − ) is simply given by

Frequency Hopping Spread Spectrum
In FHSS, the frequency of the spreading signal will continue to change or hopping at predetermined time intervals [27].The transmitter selects the frequency to be used based on the spreading frequency series.Fig. 3 shows the block diagram of transmitter and receiver of FHSS system.From Fig. 3, we can notice the main difference between DSSS and FHSS system.In FHSS system, the data signal is firstly modulated with the carrier signal, then spreading it with spreading signal whose frequency is constantly changing.The frequency of a spreading signal is selected from a predetermined range of frequencies, and it is known only to the system users.Therefore, the communication process is difficult to disturb if the used frequency of spreading signal is unknown [3].The mathematical equation of the transmitted signal of FHSS is given by [1]: where   () is transmitted signal of FHSS system, () is data signal, () is function of the spreading signal, and () is function of the carrier signal.
The data signal () is like DSSS's data signal, while carrier signal () and spreading signal () are different as they are formulated by where   is data signal frequency, ℎ() is hopping frequency given by: Hopping frequency ℎ() is a function of ℎ  , in which ℎ  refers to spreading frequency series.

Design Procedure for Simulation
There are two main contributions in this research works i.e.; (1) Simulation and (2) Mathematical analysis.Simulation is performed to simulate the process of sending and receiving signals for both DSSS and FHSS, while Mathematical analysis is done to verify that generated signal at each process is matched with the given mathematical model.The mathematical analysis is also used to justify the performance of both systems when wideband interference is added.
In the simulation, two main signals are generated.The first signal is data signal and the second signal is interference.Simulation procedure for comparing DSSS and FHSS is shown in Fig. 4, and it is called as Comparison program.Comparison program consists of single program that is used to generate Biterror rate (BER) data for each system, in which the program is run 5000 times to get an accurate average of BER data.The output of this program is BER data for every variation of spreading frequency.
BER is defined as the number of high-value digital bits in transmission networks interpreted as low, or otherwise, then divided by the number of bit received or processed over several predefined periods.

Results and Discussion
Simulation results comparing the performance of DSSS and FHSS are obtained by running the Comparison Program shown in Fig. 4. By keeping the bitrate at 10 Hz and varying the spreading frequency, the generated BER for each system will be recorded.

DSSS System
Table 1 shows the simulation results of DSSS system when the bitrate is kept at 10 Hz, while spreading frequency is varied from 40 Hz to 250 Hz.  1 indicates that there is a change in BER when spreading frequency is varied.When the spreading frequency is increased, the BER value tends to decrease.This behaviour can be explained from the mathematical analysis below.As mentioned before, there are two signals   () and   () generated from Transmitter 1 and 2 respectively.  () is transmitted signal without interference, while   () is interference signal.Fig. 5 demonstrates signal processing steps at the receiver for spreading frequency 40 Hz, while Fig. 6 shows the spectrum of the transmitted signal   () at 3 different spreading frequencies, i.e. 40 Hz, 100 Hz, and 200 Hz.where () is carrier signal shown in (4), ′() and ′() are interference data signal and interference spreading signal shown as The interfered data signal of DSSS system is given by: () =   () +   () = ()()() +  ′ () ′ ()()   The interfered data signal () becomes the received signal at the receiver.Then, the received signal passes through demodulation and de-spreading processes in order to obtain signal   () as follows: The signal   () after demodulation and despreading processes will be filtered by using FFT low-pass filter () shown in (16).To recover data signal (), the filter bandwidth of () is set to   =   .
The filtered signal in frequency domain is obtained from: where   () is   () in frequency domain, and () is filter function.
Thus, signal components having frequency greater than data frequency  >   or having period smaller than data period  <   , will be eliminated by the filter.
Given the conditions that   ≠   ′ and   >   , the obtained filtered signal   () is The filtered signal   () with  = 1 will be amplified with gain 2 to obtain signal function that is similar to the data signal () However, there may be other signal components that can pass through the filtering process, if the following conditions occur: 1.If   =   and   ≠   ′ , then signal components that can pass through the filtering process: 2. If   = 0.5  and   ≠   ′ , the filtered signal   () is 3. If   >   and   ′ =   , the filtered signal   () is From the mathematical analysis above, it can be noted that the required conditions for DSSS system to be robust against wideband interference   () are: 1)   >   , and 2)   ′ ≠   .
The larger spreading frequency   compared to bitrate   will have better robustness due to signal components other than  2  2 () will have small chance to pass the filtering process.This mathematical analysis matches with the simulation results shown in Table 1, where the greater the spreading frequency   to be larger than the bitrate   , then the smaller BER of the system to be obtained.

FHSS System
In the simulation of FHSS system, 6 variations of spreading frequency are simulated.The bitrate is kept at 10 Hz.The largest spreading frequency used in FHSS is equal to the highest spreading frequency used in the DSSS system.Table 2 is the BER results for simulated FHSS system.There are two hopping frequencies where one of them is kept at 20 Hz, while the other one is increasingly varied to 250 Hz.From Table 2, there is also a change in BER when hopping frequency is increased.When hopping frequency is increased, the BER value becomes smaller.We can also notice that BER of FHSS system is smaller than BER of DSSS system.Fig. 7 shows the signal processing steps at the receiver's side of FHSS.Fig. 7(f) indicates that data signal is recovered at the end of the process.
Let   () is transmitted signal of FHSS system without interference, while   () is interference signal.  () is given by: where () is carrier signal, ′() is interference data signal, and ′() is interference spreading signal.
The interfered data signal of FHSS system is given by: () =   () +   () = ()()() +  ′ ()() ′ ()   The received signal at the receiver is the interfered data signal ().The received signal passes through de-spreading followed by demodulation process.Then, the following signal   () is obtained: For FHSS system, the filtered signal   () with  = 1 will be amplified with gain 4 to recover the data signal ().
() ≈ 4  () ≈ ()   Like DSSS system, there may be other signal components that can pass through the filtering process, if the following conditions happen:

Conclusion
In this paper, performance evaluation and mathematical analysis of DSSS and FHSS systems subject to wideband interference have been presented.Simulation has been performed to evaluate the performance of both systems when the spreading frequencies are varied.Simulation results demonstrate that BER of both systems are decreased, when spreading frequencies are increased.Mathematical analysis verifies the performance of each system, where the optimum conditions for each system has also been demonstrated.It has been proposed that DSSS requires two conditions, while FHSS requires 4 conditions, to meet its optimum condition against wideband interference.Based on simulation results and mathematical analysis, FHSS is more optimal than DSSS, especially when the system is subject to wideband interference.

Fig. 2 .
Fig. 2. Block diagram of the (a) transmitter and (b) receiver of the DSSS system

Fig. 3 .
Fig. 3. Block diagram of the (a) transmitter and (b) receiver of the FHSS system

Table 1 .
BER of DSSS system

Table 2 .
BER of FHSS system