Neumann series


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Neumann series

[′nȯi‚män ‚sir·ēz]
(mathematics)
References in periodicals archive ?
Truncated Neumann series in [11,12] was proposed to obtain near-optimal performance.
In this paper, we propose a new joint Newton iteration and Neumann series method, where Newton iteration method is utilized to provide an efficient searching direction for the Neumann series.
Then, the new joint Newton iteration and Neumann series method is proposed in Section 3.
In this section, the system model, the Neumann series, and Newton iteration method are introduced.
The main computation complexity for ZF precoding lies in the inversion of KxK matrix W, so several approximated approaches including the Neumann series have been investigated recently, which are shown in Section 1.
K] and the Neumann series converges when N and K grow to infinity.
It is worth pointing out that, in order to guarantee the convergence of the Neumann series with [THETA] = [Z.
For downlink massive MIMO systems, the Neumann series with [THETA] = [Z.
By (15), the maximum value of K can be calculated for a specific N to achieve a high convergence probability for the Neumann series with [THETA] = [Z.
As seen in Figure 1, the joint Newton iteration and Neumann series method can achieve a very high probability of convergence under the condition of (15), with the convergence probability as high as 0.
For the two typical downlink massive MIMO configurations N x K = 256 x 16 and = 256 x 32 with [alpha] = 16 and [alpha] = 8, respectively [9], by Lemma 2, it can be concluded that the new joint Newton iteration and Neumann series method is convergent in both of these scenarios.
Note that, for different [THETA] and L [greater than or equal to] 2, the complexity of the Neumann series is 0([K.