The major drawback of the differential chaos shift keying (DCSK) system is that equal time and energy are spent on the reference and data signal. This paper presents the design and performance analysis of a short reference multifold rate DCSK (SRMR-DCSK) system to overcome the major drawback. The SRMR-DCSK system is proposed to enhance the data rate of the short reference differential chaos shift keying (SR-DCSK) system. By recycling each reference signal in SR-DCSK, the data slot carries N bits of data and by P times. As a result, compared with SR-DCSK, the proposed system has a higher data transmission rate and evaluates the energy efficiency with respect to the conventional DCSK system. To further improve the bit-error-rate (BER) performance over Rayleigh fading channels, the multiple-input single-output SRMR-DCSK (MISO-SRMR-DCSK) is also studied. The BER expression of the proposed system is derived based on Gaussian approximation (GA), and simulations in Rayleigh fading channels are performed. Simulation results show a perfect match with the analytical expression.

CHAOS signals are suitable for spread spectrum communications due to broadband and nonperiodic characteristics. In the past few decades, the coherent and noncoherent algorithms of various chaotic communication systems have been proposed [

In this work, we propose a novel DCSK modulation scheme based on the SR-DCSK system, named short reference multifold rate differential chaos shift keying (SRMR-DCSK). In this system, a data frame is composed of the reference slot and the data slot, and the data slot can transmit

The rest of this paper is organized as follows: In Section

In the modulation of the DCSK system, each bit represents the same length of two chaotic sequences in the frame. The first time slot transmits a chaotic sequence as the reference sequence, and the second one transmits the chaotic sequence of the modulated data as data sequence. If +1 is transmitted, the reference sequence is equal to the data sequence, and if −1 is transmitted, the reverse reference sequence is transmitted as a data sequence. The spreading factor in the DCSK system is defined as the number of chaotic samples used to spread each transmitted bit and is presented by

DCSK transmitter.

DCSK receiver.

In the SISO-SRMR-DCSK system, the length of the reference signal and the length of the data signal are different. This is different from the traditional DCSK. For the SISO-SRMR-DCSK system, the length of the reference signal changes from

DCSK frame and SISO-SRMR-DCSK frame.

DCSK frame

SISO-SRMR-DCSK frame

Figure

SISO-SRMR-DCSK transmitter.

For the design of the frame structure, the duration of the corresponding frame is changed from

The above would be simplified to (

The SRMR-DCSK system can be used to describe the bit energy savings compared to the DCSK system in the same way:

Equations (

The simulation curve in Figure

Bit energy enhancement percentages of SRMR-DCSK compared to DCSK for the spreading factor

Figure

SISO-SRMR-DCSK receiver.

As the MISO-SRMR-DCSK system, there are two transmission antennas (

In the text, each antenna uses two independent paths of Rayleigh quasi-static block fading channels; the channel model is shown in Figure

Two-ray Rayleigh quasi-static block faded channel model.

At the receiver, the receiver signal can be given by

In this section, the performance of the MISO-SRMR-DCSK system is analyzed on the AWGN channel and the multipath Rayleigh fading channel. The mean and variance of this system are derived. In the text, the normalized logistic chaotic map is adopted, that is,

The decision variable

Here,

Since the sidelobe of the chaotic map is zero, (

The information bit

From the above description, it can be concluded that the terms of the decision variable in (

The mean and variance that can be obtained by (

The BER of the system can be expressed as

The BER of the MISO-SRMR-DCSK system can be expressed as

Here,

From formulas (

In the channel parameters

The effect of the reference signal length on the bit error rate and the derivation of the optimal reference signal length corresponding to the minimum BER will be analyzed in this part.

Firstly, we define

Next,

Then,

Finally, the solution for (

In order to validate the BER performance of the MISO-SRMR-DCSK scheme and compare it with SR-DCSK and HE-DCSK, the theoretic BER expressions are verified and well justified by simulation results under AWGN and multipath fading channels. In the next part, the simulation diagram will be introduced and explained.

In this part, we will compare the analytical expression of the BER performance in the AWGN channel to simulation results. From Figure

Simulation and analytical BER performance of MISO-SRMR-DCSK in AWGN channels for

BER performance of SISO-SRMR-DCSK, SR-DCSK, and HE-DCSK for

BER performance of MISO-SRMR-DCSK for

The effect of the reference signal length

Simulation of the BER for a data signal length of

Simulation of the BER performance for the effect of optimal reference sequence length and general reference signal length of MISO-SRMR-DCSK in the AWGN channel for

In this part, we will compare the analytical expression of the BER performance in the Rayleigh fading channel to simulation results in the two following cases:

The average channel gain of the first channel is equal to the average channel gain of the second channel

The average channel gain of the first channel is 3 dB higher than the average channel gain of the second channel

In the simulation, we assume that the delay of the multipath channel is

Simulation and analytical BER performance of MISO-SRMR-DCSK in Rayleigh fading channels for

Figure

Simulation and analytical BER performance of MISO-SRMR-DCSK in Rayleigh fading channels for

In the paper, MISO-SRMR-DCSK is introduced and analyzed. This system on the basis of the original DCSK system improves the data transmission rate and reduces the bit transmitted power. At the transmitter, two antennas are used to transmit data, in which the length of the reference signal in each frame of data is shortened to

For the complexity of the system, the MISO-SRMR-DCSK system requires multiple transmission antennas, but the system improves spectrum utilization and transmission rates, so the complexity of the sacrifice system is worthwhile.

The data used to support the findings of this study are available from the corresponding author upon request.

The authors declare that they have no conflicts of interest.

This work was supported in part by the National Natural Science Foundation of China under Grant 61771085 and 61371164, and in part by the Research Project of Chongqing Educational Commission under Grant KJ1600427 as well as by the Chongqing Distinguished Youth Foundation under Grant CSTC2009CA2003.