Background

The current 5G systems adopt conventional uniform quadrature-amplitude modulation (QAM) with signal points on the rectangular grid, which results in a theoretical 1.53 dB gap to the Shannon capacity. To address these challenges, the non-uniform constellations (NUCs) relax this restriction by employing constellation-shaping techniques to approach the Shannon capacity for extremely high spectral efficiency, emerging as one of the promising technologies for the physical layer communication evolution. The constellation shaping solutions for NUCs can be categorized into two types [1]: 1) probabilistic shaping by tackling the symbol probabilities with a shaping encoder; 2) geometrical shaping by optimizing the positions of the constellations. Probabilistic shaping solutions require a shaping decoder at receiver side, which increases the overall complexity and is not suitable for commercial deployment. Geometrical shaping solutions only require a new set of constellation points and the quantization in hardware implementations, which is superior

To address these issues, we integrate the biological observation into the constellation design. The idea is quiet interesting that the constellation arrangement is regarded as the progress of the seed growth. In order to obtain the enough sunlight and energy, the adjacent seeds are moving away as far as from each other possible which naturally solves the key challenge in the constellation design: how to maximize the Euclidean distances among the constellations. Specifically, we transform the conventional constellation design problem into a seed arrangement problem within a circular region. The proposed constellations, called ‘CirNUC’, adopt the contact-pressure model and utilize the centroidal Voronoi tessellation (CVT) method to maximize the average constellation point distance, which results in robust performance. Next, the particle swarm optimization (PSO) algorithm is proposed to minimize averaged bit error probability (ABEP), which is regarded as the lower bound of the bit error rate (BER) performance.

System Setup

We consider a point-to-point communication system with single antenna. The transmit symbols are randomly selected from an M-point constellation set with the normalized power. The symbols are associated to the bits at the input of the modulator by a one-to-one mapping. We employ two metrics to design the constellations: symbol error probability (SEP) and the averaged bit error probability (ABEP). The goal of our work is to arrange the locations of constellations s = [s₁, s₂, …, s_M]^T for minimizing SEP and minimizing ABEP.

Proposed CirNUC

A. SEP minimization

We transform the conventional constellation design problem to a seed growth problem. The circle-shape constellations, called “CirNUC-SEP”, are proposed to enlarge the Euclidean distances among the constellations. The constellation initialization and the constellation optimization are corresponds to the seed birth and seed growth, which is introduced as follows:

Seed Birth: We select a circle with radius r and initialize {s_m }^M_m=1 in Ω, which can be regarded as the birth of the seeds and the generators of the Voronoi tessellation.

Seed Growth: Next, the seeds grow up to occupy more space for obtaining enough sunlight and energy. The CVT method is introduced to model this progress, where the mass centroid c_m of V_m is computed to represent the evolution of the growth, which is given by

where ρ(v) is the density function of the region. For the uniform density, the Voronoi region can be viewed as the polygon and calculate its coordinate of the mass centroid. Then, we employ the centroid as the updated constellation and the new generator of the Voronoi region. By the iteration of the centroid and the Voronoi region, the adjacent points move away from each other resulting in the increase of the Euclidean distance until the convergence. In addition, the Voronoi regions can also be extended to weighted Voronoi regions, which can approximate a Gaussian distribution on the two-dimensional plane, which benefits the received signals with a Gaussian distribution to approach the Shannon capacity. An example of the proposed 64 points CirNUC with golden angle modulation (GAM) as the initialization is shown in Figure 1.

B. ABEP minimization

We jointly consider the constellation Euclidean distance and hamming distance of its bit labelling to minimize the BER. Since the joint design of the bit labeling and constellation design is a NP-hard problem, we propose “CirNUC-ABEP” that employs the CVT method to enlarge the Euclidean distances among the constellations and then uses the PSO algorithm to further minimize ABEP in (4), which is described in the following: First, we utilize the QAM constellations and its gray labeling as the initialization, and perform the CVT method for K times and find the constellations with the minimum ABEP. Next, the PSO algorithm is applied to further optimize the constellations with the ABEP fitness function.

C. MLP-based demodulation

We propose a light-weight MLP-based demodulator to reduce the complexity caused by the asymmetric of constellations. The total framework of the proposed modulation and demodulation is shown in Figure 2.

Experiments

The SER and BER performance is evaluated for the proposed CirNUC and benchmarks which is shown in Figure 3. (a) SER performance for M =256. The proposed CirNUC-SEP scheme outperforms the QAM and GAM schemes for approximately 0.6dB and 0.3dB, respectively. (b): BER performance for M = 32. The code rate is 0.5 with low-density parity-check code. The GAM employs the bit labeling method in [2] and the QAM employs the gray mapping. The proposed scheme achieves 0.7dB and 1.6dB gain compared to QAM and GAM due to the ABEP minimization in our solution.

Conclusion

This paper investigated the modulation and demodulation in the wireless communication network and proposed a transceiver solution. We found the answer from the biology and contributed to enlarging the constellation distances, which provides a high spectral efficiency compared to the current QAM-based network. The ramification of this paper is that it provides a new perspective for the NUCs design to replace the current modulation, which performs a candidate for the standardization and the upcoming products.

Link to the paper

https://ieeexplore.ieee.org/document/10901255