預編碼技術和大數量天線系統通常會被使用於毫米波系統中來減緩減訊號的衰減。然而，若將預編碼處理全部實現在數位端，那麼高耗能和高複雜度的射頻前端和類比數位轉換器將是不可避免的，因此，射頻/基頻預編碼技術就被提出，此技術利用毫米波的散射數較少的特性來有效降低射頻前端和類比數位轉換器的數量，然而，儘管複雜度已經有所降低，在於搜尋方向的部分複雜度還是很高。
這篇論文提出了了一個可以藉由部分更新的方式來有效的降低運算複雜度，並有兩個更新條件在此篇論文中被提出來決定是否進行更新，還有一個新的搜尋演算法被提出來有效的減少搜尋的個數，最後，模擬結果顯示利用所提出來的更新條件進行部分更新可以有效的減少運算複雜度。更甚之，使用新的收尋方法可以再進一步的降低運算複雜度。

The precoding and large scale antennas system are important technology in millimeter
wave for compensating the severe path loss [1–3]. However, the several high cost and high
power consumption of the analog-to-digital converters (ADC) in gigabit per second are
inevitable if the precoder and combiner are all implemented on baseband, because each
antenna should has one RF chain and ADC.Therefore, the hybrid precoding is proposed
to reduce the number of RF chain and ADC in [4–6] owing to the limited scatterings
in mmWave. Furthermore, the low complexity mixed-signal precoding algorithm is
proposed in [7] to reduce the complexity by simplifying the method to find out the
precoder in RF chain with the negligible performance degradation. However, despite
applying the low complexity algorithm, the computation complexity in searching the
bases vector is still high. The propose algorithm in this study can reduce the expected
value of computation complexity by keeping the unchanged precoder in RF chain and
partially updating the precoder in baseband owing to the high correlation between the
neighboring channel state information. The two update condition are also proposed to
make the condition to do the update and one searching algorithm is proposed to limit
the search range if the AoA and AoD change continually. In final, the simulation results
show that the expected value of computation complexity with proposed update condition
and proposed searching algorithm simulated in the extended SV channel model with
channel coefficient in Quadriga can reduce 27.0%∼31.7% in precoder and 52.2%∼58.1%
in combiner according to the different tracks or different velocities. Furthermore, theproposed searching algorithm can reduce 38.3%∼62.4% in precoder and 34.0%∼58.1%
in combiner also indifferent tracks or different velocities.

1 Introduction 1
1.1 Millimeter Wave MIMO Systems . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Research Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 Organization of This Thesis . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.4 Notations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2 Transceiver Design for the Millimeter Wave Single-User MIMO Chan-
nel 5
2.1 Millimeter Wave Channel Model . . . . . . . . . . . . . . . . . . . . . . . 6
2.1.1 Extended Saleh Valengeometric Millimeter Wave Channel Model . 6
2.1.2 Millimeter Wave Channel Model with Continuous Drifting . . . . 7
2.2 SVD-Based Precoding Method . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2.1 Singular Value Decomposition . . . . . . . . . . . . . . . . . . . . 10
2.2.2 SVD-Based Precoding Scheme . . . . . . . . . . . . . . . . . . . . 10
2.3 Joint RF/Baseband Precoding Scheme . . . . . . . . . . . . . . . . . . . 12
2.3.1 Joint RF/Baseband Precoding Scheme . . . . . . . . . . . . . . . 12
2.3.2 Precoder Reconstruction via Simultaneous Orthogonal Matching
Pursuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.3.3 Generation of Array Response Vectors . . . . . . . . . . . . . . . 16
2.4 Parallel-Index-Selection Matrix-Inversion-Bypass Simultaneous Orthogonal
Matching Pursuit Algorithm . . . . . . . . . . . . . . . . . . . . . . . 18
3 Proposed Algorithm for Beamforming Tracking 21
3.1 Partial Update of Parallel-Index-Selection Matrix-Inversion-Bypass Algorithm
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.2 Update Condition for RF Chain Precoder/Combiner . . . . . . . . . . . 25
3.2.1 Optimal Precoder/Combiner Correlation Condition . . . . . . . . 25
3.2.2 Predicted Baseband Precoder/Combiner Correlation Condition . . 30
3.3 Neighboring Search Method in Index Selection . . . . . . . . . . . . . . . 35
4 Simulation Results and Analysis 41
4.1 Simulation Environment and Some Assumptions . . . . . . . . . . . . . . 41
4.2 Optimal Precoder/Combiner Correlation Condition . . . . . . . . . . . . 48
4.3 Predicted Baseband Precoder/Combiner Correlation Condition . . . . . . 55
4.4 Neighboring Searching Index Selection via Simultaneous OrthogonalMatching
Pursuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
4.5 Comparison with Three Proposed Algorithm . . . . . . . . . . . . . . . . 69
5 Conclusion and Future Work 77
5.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
5.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

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