Near-Optimal Partial Hadamard Codebook Construction Using Binary Sequences Obtained From Quadratic Residue Mapping

摘要

In this paper, a new class of $(N,K)$ near-optimal partial Hadamard codebooks is proposed. The construction of the proposed codebooks from Hadamard matrices is based on binary row selection sequences, which are generated by quadratic residue mapping of $p$ -ary $m$ -sequences. The proposed codebooks have parameters $N=p^{n}$ and $K=({p-1}/{2p})(N+sqrt{N})+1$ for an odd prime $p$ and an even positive integer $n$ . We prove that the maximum magnitude of inner products between the code vectors of the proposed codebooks asymptotically achieves the Welch bound equality for sufficiently large $p$ and derive their inner product distribution.