On Walsh code assignment

We consider the problem of orthogonal variable spreading Walsh code assignments. The aim 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 partitioning of all users into several pools. Each pool can use its own codes, which 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 $n\times k$ matrix $\boldsymbol M$ where $n$ is the number of users and $k$ is the number of Walsh codes in the pool. A solution to the problem is given as a construction of a matrix $\boldsymbol M$ which has the assignment property defined in the paper. Two constructions of such $\boldsymbol M$ 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 $\boldsymbol M$ with the assignment property. In addition, we propose a simple algorithm of optimal assignment for the first construction.