Theoretical Research On Four-dimensional Wireless Modulator And Demodulator

In this paper, a four-dimensional (4-D) wireless modulator and demodulator, which can simultaneously carry information via the amplitude, phase, auxiliary polarization angle, and polarization difference angle of electromagnetic (EM) waves, are proposed. On the basis of the mathematical description of the EM fields impinging on vector sensors/antennae (vector sensor), we describe the general principle of modulating and demodulating the 4-D parameters of EM waves.At the transmitter (i.e. modulator), according to the field distribution radiated by small linear and circular wires, we introduce a method to generate 4-D modulated signals via a pair of dipole and loop from a vector sensor. Besides, the specific configuration under both single-user and multi-user scenarios are given.As for the receiver (i.e. demodulator), a geometric algebra approach, in conjunction with vector sensor (or its array), is employed to demodulate the signals. During the demodulation process, the direction of arrival (DOA) parameters of the 4-D modulated signals need to be estimated first. Thanks to their superiority of complexity, performance and data storage memory over other DOA estimators, the optimal weighted inner product algorithm and the multiple signal classification algorithm under the geometric algebra model are respectively applied to estimate the DOAs of the received signals under single-user and multi-user scenarios. After achieving the DOA parameters, the detection of the four modulated parameters for each signal is realized via a least squares method to complete the 4-D demodulation.The theoretical symbol error probabilities (SEP) of our proposed 4-D wireless modulator and demodulator for both single-user and multi-user scenarios are derived. The simulations are conducted to validate the effectiveness of the theoretical results. Both the theoretical and simulation results show that the 4-D wireless modulator and demodulator enjoy a higher data rate and a lower error probability than the traditional ones.To further implement the 4-D wireless modulator and demodulator, a lattice based optimal programming approach to the construction of multi-dimensional signal constellations has also been proposed in this paper.The constellation figure of merit (CFM), in terms of lattice theory, can be separated into the coding gain of a lattice and the shaping gain of the boundary of a constellation. In this paper, maximizing the CFM of multi-dimensional signal constellations is formulated as a series of optimization problems. The geometric characteristics of signal constellations are taken as the constraints of such problems. Since the desirable signal constellations can be achieved by solving the optimization problems, our approach can serve as a general method of the construction of multi-dimensional signal constellations. In comparison with the fact that existing methods can only be applied when the number of signal points is small, the proposed approach can construct large constellations with ease. The simulation results show that the SEPs of small constellations built by our approach are very close to the optimum and that the proposed large constellations have better SEPs than the traditional constellations generated by integer lattices.