Zhenxing Chen

Closed-form expressions for the symbol error probability of 3-D OFDM

In this letter, closed-form expressions for the symbol error probability of 3-D orthogonal frequency division multiplexing in additive white Gaussian noise channel are derived. When a 3-D 4-ary constellation is used as signal mapper, we calculate the upper and the lower bound for the error probability, and also provide its approximation. Since decision boundaries of 8- ary constellation form an extended regular hexahedron, an exact symbol error probability can be computed. It is verified that the theoretical error probabilities are very close to or almost the same as simulation results.

Construction of Higher-Level 3-D Signal Constellations and Their Accurate Symbol Error Probabilities in AWGN

A simple and straightforward method of constructing higher-level three-dimensional (3-D) signal constellations for a reliable digital communication system is proposed in this paper. The new method expands basic 8-ary constellation into 3-D signal space systematically so that it produces lattice configurations. We also derive accurate closed-form symbol error probability (SEP) of cross-lattice constellations in additive white Gaussian noise (AWGN). It is verified that the theoretical SEPs are almost the same as simulation results. Minimum Euclidean distance (MED) of the higher-level 3-D constellations is increased at least 49% in comparison with quadrature amplitude modulation (QAM). When the number of symbols is 256, the 3-D constellation has around 105% longer MED than the 2-D QAM. Due to increase in MED, the 3-D constellations have much improved error performance compared to the QAM configurations. It is, therefore, considered that the higher-level 3-D constellations are appropriate for high-quality digital communications.

Probability of symbol error of OFDM system with 3-Dimensional signal constellations

In this paper, symbol error probabilities of orthogonal frequency division multiplexing (OFDM) with 3-Dimensional (3-D) signal constellations over additive white Gaussian noise is computed and analyzed. We present the exact closed-form expressions of the symbol error probabilities of the OFDM system with 3-D 8-ary and 32-ary constellations. In the case of 16-ary constellation, an approximation symbol error probability is computed. The higher level 3-D constellations can be built by extension of a basic structure consisting of the regular hexahedron. Simulation result verifies that the theoretical error performance found in this paper matches well with the experimental values. It is also noted that the OFDM systems with 3-D constellation have much lower symbol error probability than general OFDM systems.

Multi-envelope 3-dimensional constellations for polarization shift keying modulation

In this paper, multi-envelope 3-dimensional (3-D) constellations for polarization shift keying modulation (POLSK) are introduced. Signal points of the constellations are on the surfaces of two concentric spheres. In the receiver, two kinds of demodulation schemes are exploited. One is the conventional coherent detection (CD) of the Stokes parameters. The other is based on the maximum-likelihood (ML) algorithm. As a result of simulation, the 16-ary cube-in-cube (CIC) constellation with the ML receiver shows the best error performance in the additive white Gaussian noise (AWGN) environment.

Multistage waveform coding for voice communication over Zigbee networks

Zigbee standard includes no technical references for voice communication. Since the Zigbee standard has very limited size of data payload, high compression with good waveform recovery capability is essential to realize voice communication. This paper presents a voice coding scheme based on discrete wavelet transform (DWT) for Zigbee. Theoretical analysis and simulation verify that 2-stage DWT-based scheme is considered as a feasible method for voice communication over Zigbee networks.

Three-Dimensional Modulation Formats with Constant Power for Optical Communications

In this paper, a new method of constructing three-dimensional modulation formats with constant power is introduced. Constellations designed by the method have slightly larger minimum Euclidean distances (MEDs) than the conventional ones. No repetitive algorithm to maximize MED is used so that the new method has little computational complexity. Since signal points in the new formats are distributed regularly and symmetrically, an error control coding with systematic set-partition is applicable. We also present theoretical symbol error probability (SEP) of the new constellations in an additive white Gaussian noise environment, and demonstrate that the theoretical results are accurate. As the new modulation formats have almost the same or slightly lower SEPs than the conventional ones, they are appropriate for implementing a highly reliable optical communication system.

An FPGA implementation of 3-D signal transmission system

A 3-dimensinal (3-D) signal transmission system is implemented on field programmable gate array (FPGA) in this paper. We exploit 3-D 8-ary and 32-ary signal constellations to map input binary data, and Gram-Schmidt orthogonalization procedure (GSOP) to generate transmitted signals. The prototypes of function modules such as encoder and demapper are implemented by means of Verilog hardware description language (VHDL). The modules are synthesized and emulated using FPGA tools. Emulation based on the fixed-point format demonstrates that the system has almost the same symbol error rate (SER) as a software test-bed. Hence, it is considered that the implemented system operates correctly.

A hybrid decoding of Reed–Muller codes

In this article, a hybrid decoding algorithm for Reed–Muller codes is presented. Unlike the conventional algorithm, the presented algorithm ends recursive decomposition when R ( 1 , m ) and R ( m − 1 , m ) appeared. A simplified maximum-likelihood algorithm based on fast Hadamard transform is also exploited to decode the systematic code through its special structure. As a result, the presented hybrid decoding algorithm reduces the number of floating-point multiplications significantly as compared with the conventional algorithms. In addition, the new algorithm has better error performance than the conventional ones.

Performance analysis of 3-D data transmission system in the presence of impulsive noise

In this paper, we investigate performance of a three-dimensional (3-D) data transmission system in the presence of impulsive noise. Symmetric α-stable (SαS) distribution is exploited to model an impulsive noise environment. Computer simulation demonstrates that power spectral density (PSD) of the received signals tends to concentrate on the main lobe with decrease of α. In addition, average symbol error rate (SER) of the 3-D data transmission system is lower than that of the conventional system with 2-D signal constellation.

Performance of Typical 3-D Signal Constellations in Rayleigh Fading Channel

In this paper, symbol error probability (SEP) of typical 3-dimensional (3-D) signal constellations in Rayleigh fading channel is derived. Simulation confirms that average SEP of the constellations is very accurate. Thus, the theoretical SEP derived can be exploited as a performance reference for future development of wireless communication systems with 3-D constellations.