## 3 Proposed SQRD Algorithm with a Novel Modified RVD
### Proposed Modified RVD
The elimination process of the \(k\)th column zeros the complex-valued elements below the \(k\)th row and turns the element in the \(k\)th row into a real number, which contains two steps. Step 1, zero the imaginary parts of all the \(N-k+1\) complex-valued elements to be processed of the \(k\)th column. For the elimination process of every complex-valued element to be processed, one CORDIC operation for vectoring mode and \(N-k\) CORDIC operations (rotation operations for the subsequent \(N-k\) elements in the corresponding row) for rotation mode are needed. Thus, the number of CORDIC operations cost in step 1 is \((N-k+1)(1+N-k)\). Step 2, the first row of the \(k\)th column is selected as pivot row to nullify all the \(N-k\) real-valued elements in the subsequent rows of the \(k\)th column. For the elimination operation of every real-valued element in the subsequent rows, one CORDIC operation for vectoring mode and \(2(N-k)\) CORDIC operations (rotation operations for the subsequent \(N-k\) paired complex-valued elements in the corresponding rows) for rotation mode are needed. Thus, the number of CORDIC operations cost in step 2 is \((N-k)(1+2(N-k))\). For all the elimination processes of \(N\) columns in \(\mathbf{H}\), the number of CORDIC operations is totally \(\sum\limits_{k=1}^{N}\left((N-k+1)(N-k+1)+(N-k)(1+2(N-k))\right)=N^{3}\). ## References

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