Spread-spectrum (SS) methods have long been used in communications systems to achieve certain levels of transmission efficiency and security. Unfortunately, traditional spread-spectrum approaches have typically employed pseudorandom sequences of codes characterized by an inherent periodicity which can be detected over time. As a solution, true random sequences generated by chaotic lasers can help achieve increased SS gain at a lower bit error rate (BER) than traditional SS systems based on pseudorandom bit sequences, while also improving the communications security.

In traditional SS systems, high-speed random codes are substituted for a 1-b source stream, making these transmissions more robust in the presence of interference. Typical techniques for spread spectrum communications are direct-sequence spread spectrum (DSSS), frequency-hopping spread spectrum (FHSS), time-hopping spread spectrum (THSS), and chirp modulation. Among them, pseudorandom sequences generated by an n-level m-sequence shift register with longest period of 2^{n }-1 are commonly adopted as SS codes. But theoretical studies have shown that this kind of SS spread spectrum communications systems based on pseudorandom sequences are prone to deciphering. Essentially, the m sequence can be determined when 2n b of m sequence transmission is received and decoded.^{1}

In traditional DSSS communications systems, the SS sequence cannot be changed during the process of communications, allowing hackers to use the inherent periodicity to acquire the SS codes.^{2} To enhance the anti-interference capabilities and the safety of SS systems, the codes should be varied. In 2005, Xingang Wang, et al.^{3} proposed a scheme to generate chaotic binary codes by using a chain of coupled chaotic maps. Those researchers demonstrated that the codes can be applied to baseband SS communications systems. Although the period of such chaotic codes is, in theory, infinitely long, the period is practically limited by the word length of the system's microprocessor and can still be deciphered.^{4} For true SS communications security, true random sequences are needed. Compared with the pseudorandom numbers as spreading codes, true random sequences have the characteristics of aperiodicity, unpredictability, and nonreplicability, and can only be deciphered with great difficulty.

There are many methods available for generating true random numbers. Traditional random-number generators are based on the thermal noise of circuits or resistances,^{5} the oscillation frequency of an oscillation circuit,^{6} the randomness of a quantum mechanics fundamental quantity,^{7,8} circuit chaos,^{9} or biological random characteristics.^{10} But the rates of these approaches above are limited by low bandwidths. Typically, the bandwidths of electric chaos effects are below 1 GHz and rarely reach a rate of 200 Mb/s.^{9}

Another kind of novel random-number generator is based on chaotic lasers. The high bandwidth of this approach supports the bandwidths at the current upper limits of electronic data processing. For example, in 2007, the current researchers proposed a patent for a fast true random-number generator using a wideband chaotic light source, realized by an optical-feedback semiconductor laser.^{11} In 2008, Uchida, et al.^{12,13} became the first to realize a 1.7-Gb/s random-number generator (RNG) by using chaotic lasers. That same year, the current authors demonstrated that the bandwidth of an optical-feedback semiconductor laser can achieve several tens of GHz by using continuous-wave (CW) optical injection.^{14} This indicates that true random numbers with higher rate can be accomplished.

In addition, Kanter and colleagues^{15} demonstrated a high speed, 12.5-Gb/s, random-number generator based on an optical-feedback chaotic laser with an 8-b analog-to-digital converter (ADC). The same researchers improved upon their work by achieving a faster random bit generator based on a chaotic semiconductor laser capable of a rate to 300 Gb/s.^{16} In 2010, the current researchers demonstrated an all-optical scheme of for a random-number generator (RNG), in which all signal processing is performed in the optical domain; this approach yielded 10-Gb/s random numbers.^{17}

From previous studies, it is known that true random-number generators have reached Gb/s rates. It is also known that a synchronization method for true random numbers has been realized,^{18} allowing their use in SS communications systems. To pursue that application, the current researchers propose the use of true random numbers for safe and efficient SS communications, using random numbers produced by chaotic semiconductor lasers. A schematic diagram of a true random-number generator based on chaotic lasers is shown in Fig. 1(a).

In this scheme, two semiconductor lasers are used for chaotic intensity. The intensity output of each laser is converted to an AC electrical signal by means of photodetectors. Following amplification, the AC electrical signals are converted to a binary signal by means of two comparators. Subsequently, the generated binary signal is converted into a random number, with its code rate controlled by the clock. The binary bit signals obtained from the lasers are combined by a logical exclusive-OR (XOR) operation to generate a single random bit sequence. Any processing that occurs after this point can be applied to improve the randomness of the sequence.

Figure 1(b) shows the authors' experimental setup for a chaotic laser using distributed-feedback (DFB) semiconductor lasers. A circuit for chaotic signals based on semiconductor lasers can be seen in ref. 14. In experiments, the feedback light from semiconductor laser, a model LMD5S752 from Wuhan Telecommunications Devices Co. (WTD), with center wavelength stabilized at 1550 nm and threshold current, I_{th}, set at 22.5 mA, is injected into the resonant oscillation cavity via a fiber reflection mirror. The intensity and polarization state of the optical feedback signals can be adjusted by a variable attenuator and a polarization controller, respectively. The intensity of the feedback light is monitored by an optical power meter. If the operating current of the laser is biased at 1.6 times more than I_{th}, at 22.5 mA, and the feedback intensity is 10%, the signal power of the chaotic laser from the DFB laser is 0.5 mW through a 40/60 optical fiber coupler. When the amplitude of optical signals is about 45 mV, the optical signals are converted to electrical signals through a photoelectric detector.

Figure 2 shows the RF spectrum of the generated chaotic light and the noise floor. As can be seen, the bandwidth of the chaotic laser is about 6 GHzconsiderably greater than a traditional entropy source, such as circuit chaos. The signal is sampled and stored by a real-time oscilloscope, a model TDS3052 from Tektronix, which has a bandwidth of 500 MHz and sampling rate of 5 GSamples/s. For improved randomness of the generated random sequence, a post-processing method was adopted, such as the use of a two-way exclusive-OR (XOR) for post-processing. This yields true random-number sequences at 1 Gb/s, which pass all standard tests for randomness according to the United States National Institute for Standards and Technology (NIST) and their Special Publication 800-22.^{19}

The "randomness" of the random sequence can be investigated by analyzing the self-similarity of the generated sequence. The similarity between two random sequences can be expressed by using the autocorrelation function, R_{ac}(m), and the cross-correlation function, R_{cc}(m). The expressions for these two functions are shown in Eqs. 1 and 2, respectively:

where:

x^{i} = the i-th bit value of the random sequence;

x_{i + m} = the i + m bit value of the random sequence;**x** = the mean value of the random sequence;

x_{li} = the i-th bit value of the first random sequence; and

x_{2(i + m)} = the (i + m) bit value of the second random sequence.

The autocorrelation coefficient and the cross-correlation coefficient are the normalization of the autocorrelation function and the cross-correlation function. Ideally, the value of the autocorrelation function and the value of the cross-correlation function for the true random-number sequence should be values of some d function and 0, respectively.

Figure 3(a) shows the autocorrelation function of a traditional m-sequence function. It reveals that the m-sequence function exhibits a strong periodicity. In comparison, the autocorrelation function of the random sequences generated by the chaotic lasers is shown in Fig. 3(b). From it, we can see that its shape is similar with an d function, indicating an improvement for these true random-numbers sequences compared to m sequences.

Figures 3(c) and 3(d) show cross-correlation functions of m sequences and true random numbers, respectively. They reveal a sharp pulse spiking in the cross-correlation function of m sequences, while the true random numbers present a relatively better cross-correlation function (and thus, their suitability as SS codes).

What is the impact of using random-number sequences on the capacities of different communications systems? In a traditional direct-sequence, code-division-multiple-access (DS-CDMA) communications system, the capacity of the system is determined by the available SS numbers. For example, if the spreading factor N is 1023, the available number of m sequences is only 60, which limits the capacity of the system. In contrast, if true random-number sequences are as SS codes, it can greatly enhance the capacity of the system. The true random-number sequence generated by chaotic semiconductor lasers is a kind of sequence with codes that are truly random and independent each other. The higher-order complexity of these codes enhances the anti-decryption and anti-interference characteristics of a SS system.

Figure 4 depicts a schematic diagram of a SS communication system. The transmitter converts an analog signal into a digital signal through an information source encoder. Following the SS operation, the signal is frequency modulated (FM) and transmitted via antennas. In this system, true random sequences are used for SS codes. In the receiver, the original signals can be recovered by following a reverse set of procedures.

The use of a true random-number sequence in a SS communications system greatly increases the anti-interference capability of the system. Such a system faces two main forms of interference: multipath and multiple-user. Multipath interference is associated with the autocorrelation of SS codes, while multiple-user interference is mainly relative to the cross-correlation of SS codes. It is possible to choose SS codes with good orthogonality to minimize relevance between codes. In addition, the authors' experiments have found that the autocorrelation and cross-correlation of a true random-number sequence will decrease with an increase in the length of the random-number sequence. With an appropriate SS code length, SS system interference can be reduced.

The performance levels versus multipath interference and multiple-user interference can be characterized respectively via the mean-square value of the autocorrelation sidelobe and the mean-square value of the cross-correlation sidelobe.^{4} The mean-square value of the autocorrelation sidelobe, d^{2}_{ac}(m), and the cross-correlation sidelobe, d^{2}_{cc}(m), can be written as Eqs. 3 and 4, respectively:

where:

R_{ac}(m) = the value of the autocorrelation of the m-th bit of the generated sequence and

R_{cc}(m) = the value of the cross-correlation of the m-th bit of the generated sequence.

Figure 5 shows a curve of the mean-square value of the generated random-number sequence. It can be seen that the mean-square value of the autocorrelation and cross-correlation sidelobes decrease with an increase in the length of the random-number sequence. When the random-number sequence length increases to 2000, the mean-square value of the autocorrelation and cross-correlation sidelobes will be less than 0.6 10^{-3}.

To analyze this further, a simulation was performed using MATLAB Simulink simulation software from The MathWorks, choosing 2000 to 5000 b random sequences as SS codes. Simulink was used to build a simulation model of a DSSS communications system, as shown in Fig. 6. The binary random signal source is multiplied by the input true random-number sequences following polarity-reversal, to realize a SS communications system. Subsequently, the signal passes through an additive-white-Gaussian-noise (AWGN) channel. In the receiver, the signal multiplies the true random sequences to complete the dispreading process. Following that point, the signal will become binary random sequences though polarity reversal. During the simulation, an error bit analyzer is used to compare the transmitted binary random codes with the despreaded random codes in order to calculate the bit-error ratio.

Figure 7 shows the relationship among the information rate, spread spectrum gain, and bit-error ratio. When the information rate is constant, the SS gain increases with a decrease in the bit-error ratio. When signal noise ratio (SNR) is -20 dB, increasing the SS gain can effectively reduce the system bit-error ratio. It can be seen from Fig. 7 that the SS gain is 0 in this system, while the bit-error ratio is 0.4623 when the information bandwidth is 2 MHz. If the information rate is also 2 MHz and the SS gain is 10 dB, the system bit-error ratio will be 0.3765. When the SS gain is 20 dB, the system bit-error ratio will be 0.1567. In essence, the influence of the information rate on the bit-error ratio is minimal. The channel bandwidth is enhanced when the information rate increases. Therefore, it is possible to reduce the bit-error ratio by increasing the SS gain in a practical SS communications system. In this system with true random-number sequences, a section of the sequence is used to represent digital "1" values, while a different section is used to represent digital "0" values. This processing method can double the noise margin of a SS communications system compared to one using orthogonal code.

In summary, the inherent periodicity of the pseudorandom sequences used in traditional SS communications systems limits the capacities of those systems. In the proposed SS scheme, improved capacity and security can be achieved.

**ZHANG ZHAO-XIA**, Lecturer, College of Physics and Optoelectronics, Taiyuan University of Technology, Taiyuan 030024, People's Republic of China, and State Key Laboratory of Millimeter Waves, Southeast University, Nanjing 210096, People's Republic of China; (+86) 13803436295.

**TONG HAI-LI**, Postgraduate Student, College of Information Engineering, Taiyuan University of Technology, Taiyuan 030024, People's Republic of China.

**ZHANG JIAN-ZHONG**, Lecturer, College of Physics and Optoelectronics, Taiyuan University of Technology, Taiyuan 030024, People's Republic of China.

**XIAO BAO-JIN**, Professor, College of Information Engineering, Taiyuan University of Technology, Taiyuan 030024, People's Republic of China.

**Acknowledgments**

This project was supported by the Special Funds of the National Natural Science Foundation of China (Grant No. 60927007) and the National Natural Science Foundation of China (Grant No. 60872019), and was an open subject of the State Key Laboratory of Millimeter Waves (Grant No: K201108).

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