On Walsh code assignment

TL;DR

This paper addresses Walsh code assignment for orthogonal variable spreading, proposing combinatorial constructions that minimize code usage per user while avoiding signaling complexity and detection issues.

Contribution

It introduces two combinatorial constructions for Walsh code assignment that optimize code usage and satisfy the assignment property, with one being proven optimal.

Findings

Two constructions of Walsh code assignment matrices are presented.

One construction is proven to be optimal in minimizing codes per user.

An algorithm for optimal assignment in the first construction is provided.

Abstract

The paper considers the problem of orthogonal variable spreading Walsh-code assignments. The aim of the paper is to provide assignments that can avoid both complicated signaling from the BS to the users and blind rate and code detection amongst a great number of possible codes. The assignments considered here use a partition of all users into several pools. Each pool can use its own codes that are different for different pools. Each user has only a few codes assigned to it within the pool. We state the problem as a combinatorial one expressed in terms of a binary n x k matrix M where is the number n of users, and k is the number of Walsh codes in the pool. A solution to the problem is given as a construction of M, which has the assignment property defined in the paper. Two constructions of such M are presented under different conditions on n and k. The first construction is optimal in the sense that it gives the minimal number of Walsh codes assigned to each user for given n and k. The optimality follows from a proved necessary condition for the existence of M with the assignment property. In addition, we propose a simple algorithm of optimal assignment for the first construction.