本論文提出5個極座標中空間調變多輸入多輸出偵測演算法，分別有極座標中的最大似然偵測器 (PML ), 極座標中的梯度偵測器 (PGML ), 一階候選解選擇偵測器(OCS ), 兩階候選 解選擇偵測器(TCS) 和進化兩階候選解選擇偵測器(MTCS) 。我們先在極座標推導出最大 似然的偵測解，求得極座標的演算法複雜度小於直角座標系的 最大似然偵測解。我們在數學空間中求得兩件事情。一是偵測解在空間中只有唯一的解；二是當空間點距離偵測解 越遠 ，距離 會單調 遞增。透過將偵測解的詮釋從最小距離解改為最小梯度解，我們 設計出 極座標中的梯度偵測器(PGML)，其演算法 複 雜度 比最大似 然偵測器來得小且BER 表現也很接近最佳解。從最小梯度解中推導出一階候選解選擇偵測器(OCS )。其中利用 角度 的資訊在所有空間調變和訊號調變的組合中選出候選解的組合。為了增加選擇候選解 的能力 ，我們多增加了半徑量值的資訊衍伸出兩階候選解選擇偵測器的設計。這樣會衍伸出 運算上以及流程上 的複雜度，因此我們利用角度和半徑量值域上最大似然函數有凸涵數的性質，提出進化兩階候選解選擇偵測器(MTCS)可以有效減少演算法的複雜度。在模擬結果中，我們可 以看到所有在極座標的偵測演算法 論是最佳解或是次佳解的BER 表現都很接近 且 次佳解 的演算法複雜度和直角座標系的次佳解是相似的甚至更小。在所有演算法中，進化兩階候選解選擇偵測器(MTCS)有最小的複雜度。

The thesis proposed 5 algorithms for spatial modulation detector in polar coordinate.
There are maximum likeliood detector in polar coordinate(PML), gradient detector in polar coordinate(PGML), one-stage candidate selection(OCS), two-stage candidate selection(TCS) and modified two-stage candidate selection(MTCS).
We derived the maximum likelihood detector in polar coordinate(PML) and find that the complexity is lower than in rectangular coordinate.
With the mathematical proof of only single local minimum in maximum likelihood distance formula and the slope of distance is monotonically increasing from the local minimum, we reinterpret the maximum likelihood solution from minimum distance to minimum slope summation.
The interpretation leads to the PGML and it has lower complexity and the performance is near optimal.
From the formula of slope summation, we proposed OCS algorithm by using part of the information: phase as parameter to select candidates from all the combinations of spatial and symbol index.
To enhance the power of candidate selection, we proposed the TCS algorithm by adding the magnitude information which requires more complexity.
With the property of convex in phase and magnitude domain, we proposed the MTCS algorithm which reduced the complexity efficiently.
In the simulation result, we can see that the BER performance of sub optimal detectors in polar coordinate are near to optimal detector and the complexity are comparable to the sub optimal detector in rectangular coordinate.
Among all the detectors, MTCS algorithm has the lowest complexity.

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