Mapper Side Geometric Shaping for QAM Constellations in 5G MIMO Wireless Channel with Realistic LDPC Codes

In wireless communication systems, there are many stages for signal transmission. Among them, mapping and demapping convert a sequence of bits into a sequence of complex numbers and vice versa. This operation is performed by a system of constellations~ -- by a set of labeled points on the complex plane. Usually, the geometry of the constellation is fixed, and constellation points are uniformly spaced, e.g., the same quadrature amplitude modulation (QAM) is used in a wide range of signal-to-noise ratio (SNR). By eliminating the uniformity of constellations, it is possible to achieve greater values of capacity. Due to the current standard restrictions, it is difficult to change the constellation both on the mapper or demapper side. In this case, one can optimize the constellation only on the mapper or the demapper side using original methodology. By the numerical calculating of capacity, we show that the optimal geometric constellation depends on SNR. Optimization is carried out by maximizing mutual information (MI). The MI function describes the amount of information being transmitted through the channel with the optimal encoding. To prove the effectiveness of this approach we provide numerical experiments in the modern physical level Sionna simulator using the realistic LDPC codes and the MIMO 5G OFDM channels.