How can I apply a custom sort rule to a WPF DataGrid?

When the user does a column sort in my DataGrid, I want all null or empty cells to be sorted to the bottom, rather than the top.

I wrote an IComparer<T> that makes sure blanks are always sorted downward, but I can't figure out how to apply it to the columns of my DataGrid. Note that the initial sort of the DataGrid, which I'm doing with the LINQ OrderBy() method, works great. The problem is that all subsequent sorts performed by the user sort the blanks to the top.

Comparer Code

public class BlankLastStringComparer : IComparer<string>
{
    public int Compare(string x, string y)
    {
        if (string.IsNullOrEmpty(x) && !string.IsNullOrEmpty(y))
            return 1;
        else if (!string.IsNullOrEmpty(x) && string.IsNullOrEmpty(y))
            return -1;
        else
            return string.Compare(x, y);
    }
}

Questions

How do I get the DataGridColumn to use my comparer? Or if this is not possible, can you offer a workaround? I'm hoping for an MVVM friendly solution if possible.