Hexagonal constellations for small cell communication

We describe novel algorithms to enable the use of hexagonal constellations in practical high-rate communication systems. The first algorithm aims at optimizing the codewords assignment to the constellation points of a hexagonal grid to minimize the average Hamming distance between adjacent codewords. This codeword assignment is critical for the bit error rate performance that is usually more relevant than symbol error rate in coded schemes. We describe an efficient dynamic programming algorithm to solve this assignment problem. Then, we study the construction of the hexagonal grid that exploits the inherent redundancy in the hexagonal grid where the available constellation points for a given peak power are usually more than the grid size. Finally, we describe computationally efficient procedures for hard and soft decoding of hexagonal constellations. The proposed algorithms are shown to provide significant improvement for the bit error rate performance for both coded and uncoded schemes.