基于迭代并行干擾消除的低復(fù)雜度大規(guī)模MIMO信號(hào)檢測(cè)算法

申濱; 趙書鋒; 金純

doi:10.11999/JEIT180111

基于迭代并行干擾消除的低復(fù)雜度大規(guī)模MIMO信號(hào)檢測(cè)算法

doi: 10.11999/JEIT180111 cstr: 32379.14.JEIT180111

重慶郵電大學(xué)移動(dòng)通信重點(diǎn)實(shí)驗(yàn)室 ??重慶 ??400065

基金項(xiàng)目: 重慶市科委重點(diǎn)產(chǎn)業(yè)共性關(guān)鍵技術(shù)創(chuàng)新專項(xiàng)(cstc2015zdcy-ztzx40008)

詳細(xì)信息

作者簡(jiǎn)介:
申濱：男，1978年生，教授，研究方向?yàn)檎J(rèn)知無線電、大規(guī)模MIMO等

趙書鋒：男，1991年生，碩士生，研究方向?yàn)榇笠?guī)模MIMO信號(hào)檢測(cè)

金純：男，1966年生，教授，研究方向?yàn)闊o線通信信號(hào)處理、物聯(lián)網(wǎng)等

通訊作者:
申濱　 shenbin@cqupt.edu.cn

中圖分類號(hào): TN929.5
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- 被引次數(shù): 0
出版歷程
- 收稿日期: 2018-01-25
- 修回日期: 2018-05-29
- 網(wǎng)絡(luò)出版日期: 2018-08-14
- 刊出日期: 2018-12-01

Low Complexity Iterative Parallel Interference Cancellation Detection Algorithms for Massive MIMO Systems

Chongqing Key Laboratory of Mobile Communications, Chongqing University of Posts and Telecommunications, Chongqing 400065, China

Funds: The Innovation Project of the Common Key Technology of Chongqing Science and Technology Industry (cstc2015zdcy-ztzx40008)

摘要

摘要: 基于干擾消除思想該文提出一種適用于大規(guī)模MIMO系統(tǒng)上行鏈路的低復(fù)雜度迭代并行干擾消除算法，在算法實(shí)現(xiàn)中避免了線性檢測(cè)算法所需的高復(fù)雜度 $({\cal O}({K^3}))$ 矩陣求逆運(yùn)算，將復(fù)雜度保持在 $({\cal O}({K^2}))$ 。在此基礎(chǔ)上，引入噪聲預(yù)測(cè)機(jī)制，提出一種基于噪聲預(yù)測(cè)的迭代并行干擾消除算法，進(jìn)一步提高了硬判決檢測(cè)性能?？紤]天線間殘留干擾，將干擾消除思想運(yùn)用到軟判決中，最后提出一種基于迭代并行干擾消除的低復(fù)雜度軟輸出信號(hào)檢測(cè)算法。仿真結(jié)果表明：提出的信號(hào)檢測(cè)方法的復(fù)雜度優(yōu)于MMSE檢測(cè)算法，經(jīng)過幾次簡(jiǎn)單的迭代，算法即快速收斂并獲得接近甚至優(yōu)于MMSE檢測(cè)算法的誤碼率性能。
- 大規(guī)模MIMO /
- 低復(fù)雜度 /
- 迭代并行干擾消除 /
- 噪聲預(yù)測(cè) /
- 軟輸出
Abstract: Based on interference cancellation method, a low complexity Iterative Parallel Interference Cancellation (IPIC) algorithm is proposed for the uplink of massive MIMO systems. The proposed algorithm avoids the high complexity matrix inversion required by the linear detection algorithm, and hence the complexity is maintained only at $({\cal O}({K^2}))$ . Meanwhile, the noise prediction mechanism is introduced and the noise-prediction aided iterative parallel interference cancellation algorithm is proposed to improve further the detection performance. Considering the residual inter-antenna interference, a low-complexity soft output signal detection algorithm is proposed as well. The simulation results show that the complexity of all the proposed signal detection methods are better than that of the MMSE detection algorithm. With only a small number of iterations, the proposed algorithm achieves its performance quite close to or even surpassing that of the MMSE algorithm.
- Massive MIMO /
- Low-complexity /
- Iterative Parallel Interference Cancellation (IPIC) /
- Noise-prediction /
- Soft output

HTML全文

圖 1 算法復(fù)雜度對(duì)比

下載: 全尺寸圖片幻燈片

圖 3 $128 \times 32$ MIMO系統(tǒng)下BER性能(硬判決)

下載: 全尺寸圖片幻燈片

圖 2 $128 \times 16$ MIMO系統(tǒng)下BER性能(硬判決)

下載: 全尺寸圖片幻燈片

圖 4 信道估計(jì)誤差下算法BER性能(硬判決)

下載: 全尺寸圖片幻燈片

圖 6 $128 \times 16$ MIMO系統(tǒng)中各算法軟輸出BER性能

下載: 全尺寸圖片幻燈片

圖 5 $128 \times 32$ MIMO系統(tǒng)中各算法軟輸出BER性能

下載: 全尺寸圖片幻燈片

表 1 基于迭代并行干擾消除算法(IPIC)

　算法1　基于迭代并行干擾消除算法(IPIC)

　輸入: ${{H}},{{y}},{\sigma ^2},K,{T_{{\rm{iter}}}};$

　初始化：

　(1) ${{G}} = {{{H}}^{\rm{H}}}{{H}},{} = {{{H}}^{\rm{H}}}{{y}},{{\hat{ s}}^{(0)}} = {{{D}}^{ - 1}}{{{H}}^{\rm{H}}}$ ${{y}} = \{ \hat s_1^{(0)},\hat s_2^{(0)}, ·\!·\!· ,\hat s_K^{(0)}\} $

　 For $t = 1:{T_{{\rm{iter}}}};$

　　 For $i = 1:K$;
　(2) 更新 $\hat s_i^{(t)} = \hat s_i^{(t - 1)} + \frac{{{b_i} - \displaystyle\sum\nolimits_{j = 1}^{i - 1} {{G_{ij}}} \hat s_j^{(t)} - \displaystyle\sum\nolimits_{j = i}^K {{G_{ij}}} \hat s_j^{(t - 1)}}}{{{G_{ii}}}}$

　(3) 更新 ${{\hat{ s}}^{(t)}} = {\left[ {\hat s_1^{(t)},\hat s_2^{(t)}, ·\!·\!· ,\hat s_{i - 1}^{(t)}}, {Q(\hat s_i^{(t)})}, {\hat s_{i + 1}^{(t - 1)},\hat s_{i + 2}^{(t - 1)}, ·\!·\!· ,\hat s_K^{(t - 1)}}\right]^{\rm{T}}}$

　(4)　　 $i = i + 1$

end for

　(5)　　 $t = t + 1$

　　　end for

　輸出 ${\hat{ s}} = {{\hat{ s}}^{({T_{{\rm{iter}}}})}}$

下載: 導(dǎo)出CSV

表 2 基于噪聲預(yù)測(cè)的迭代并行干擾消除算法(NP-IPIC)

　算法2　基于噪聲預(yù)測(cè)的迭代并行干擾消除算法(NP-IPIC)

　輸入: ${{H}},{{y}},{\sigma ^2},K,{T_{{\rm{iter}}}};$

　初始化：

　(1) ${{G}} = {{{H}}^{\rm{H}}}{{H}},{} = {{{H}}^{\rm{H}}}{{y}}$, ${{D}} = {\rm{diag}}({{G}} + {\sigma ^2}{{{I}}_K})$

　　　 ${{\hat{ s}}^{(0)}} = Q({{{D}}^{ - 1}}{{{H}}^{\rm{H}}}{{y}}) = \{ \hat s_1^{(0)},\hat s_2^{(0)}, ·\!·\!· ,\hat s_K^{(0)}\}$

　(2) 對(duì) ${{H}}$列范數(shù)進(jìn)行降序排序，
$o = \arg {\rm{sort}}({\tau _1},{\tau _2}, ·\!·\!· ,{\tau _K}),\ {\tau _k} = \left\| {{{{h}}_k}} \right\|_2^2,\ \forall k = 1,2, ·\!·\!· ,K$

　　　For $t = 1:{T_{{\rm{iter}}}}$;

　　　　For $i = 1:K$;

　(3) 更新
$\hat s_{o(i)}^{(t)} = \hat s_{o(i)}^{(t - 1)} + \frac{{{b_{o(i)}} - \displaystyle\sum\limits_{j = 1}^{i - 1} {{G_{o(i)o(j)}}} \hat s_{o(j)}^{(t)} - \displaystyle\sum\limits_{j = i}^K {{G_{o(i)o(j)}}} \hat s_{o(j)}^{(t - 1)}}}{{{G_{o(i)o(i)}}}}$

　(4) 判斷 $i$是否等于1，如果為1，則計(jì)算 $\bar s_{o(1)}^{(t)} = Q\left(\hat s_{o(1)}^{(t)}\right)$, 噪聲
采樣 $\hat n_{o(1)}^{(t)} = \hat s_{o(1)}^{(t)} - \bar s_{o(1)}^{(t)} = \hat s_{o(1)}^{(t)} - \mathbb{Q}\left(\bar s_{o(1)}^{(t)}\right)$, 如果 $i > 1$，跳過
本步驟，執(zhí)行下一步；
　(5) 更新 ${\hat{ n}} = \frac{{{{a}}_{o(i - 1)}^{\rm{H}}}}{{{{\left\| {{{{a}}_{o(i - 1)}}} \right\|}^2}}}\hat n_{o(i - 1)}^{(t)}$

　(6) $\hat n_{o(i)}^{(t)} = {{{a}}_{o(i)}}{\hat{ n}}$, $\bar s_{o(i)}^{(t)} = Q\left(\hat s_{o(i)}^{(t)} - \hat n_{o(i)}^{(t)}\right)$

　(7) 更新
${{\hat{ s}}^{(t)}} = {[ {\hat s_{o(1)}^{(t)},\hat s_{o(2)}^{(t)}, ·\!·\!· ,\hat s_{o(i - 1)}^{(t)}}, {\bar s_{o(i)}^{(t)}}, {\hat s_{o(i + 1)}^{(t - 1)},\hat s_{o(i + 2)}^{(t - 1)}, ·\!·\!· ,\hat s_{o(K)}^{(t - 1)}}]^{\rm{T}}}$

　(8)　　　 $i = i + 1$

　　　　end for

　(9)　　 $t = t + 1$

　　　end for

　(10) 根據(jù) ${{\hat{ s}}^{({T_{{\rm{iter}}}})}}$中下標(biāo)進(jìn)行重新排序得到 ${{\hat{ s}}^{{\rm{final}}}}$

　輸出 ${\hat{ s}} = {{\hat{ s}}^{{\rm{final}}}}$

下載: 導(dǎo)出CSV

表 3 基于迭代并行干擾消除的軟輸出算法(S-IPIC)

　算法3　基于迭代并行干擾消除的軟輸出算法(S-IPIC)

　輸入: ${{H}},{{y}},{\sigma ^2},K,{T_{{\rm{iter}}}};$

　初始化：

　(1) ${G}={H}^{\rm H}{H}, ={H}^{\rm H}{y}$,

${{D}} = {\rm{diag}}({{G}} + {\sigma ^2}{{{I}}_K}) {{\hat{ s}}^{(0)}} = {{{D}}^{ - 1}}{{{H}}^{\rm{H}}}{{y}} = \{ \hat s_1^{(0)},\hat s_2^{(0)}, ·\!·\!· ,\hat s_K^{(0)}\} $

　(2) 估計(jì)方差

　　　For $i = 1:K;$
　(3) $V_i^{(0)} = \sum\limits_{{\alpha _n} \in {\cal{Q}}} \Bigr| {\alpha _n} - \hat s_i^{(0)}{\Bigr|^2}P({s_i} = {\alpha _n})$

　　　end for

　　　估計(jì)發(fā)送信號(hào)并計(jì)算NPI方差

　　　For $t = 1:{T_{{\rm{iter}}}};$

　　　　For $i = 1:K;$
　(4) 更新
　　　　 $\hat s_i^{(t)} = {\rm{ }}\hat s_i^{(t - 1)} + \frac{{{b_i} - \displaystyle\sum\limits_{j = 1}^{i - 1} {{G_{ij}}} \hat s_j^{(t)} - \displaystyle\sum\limits_{j = i}^K {{G_{ij}}} \hat s_j^{(t - 1)}}}{{{G_{ii}}}}$

　(5) 更新 ${{\hat{ s}}^{(t)}} = {\left[ {\hat s_1^{(t)},\hat s_2^{(t)}, ·\!·\!· ,\hat s_{i - 1}^{(t)}}, {\hat s_i^{(t)}}, {\hat s_{i + 1}^{(t - 1)},\hat s_{i + 2}^{(t - 1)}, ·\!·\!· ,\hat s_K^{(t - 1)}}\right]^{\rm T}}$

　(6) 更新
　　　　 $V_i^{(t)} = \sum\limits_{{\alpha _n} \in {\cal{O}}} | {\alpha _n} - \hat s_i^{(t)}{|^2}P({s_i} = {\alpha _n})$

　(7) 計(jì)算等效信道增益和NPI方差

　　 ${\mu _i} = 1$,
　　 ${(\nu _i^{(t)})^2}{\rm{ }} = \frac{1}{{G_{ii}^2}}\left( {\sum\limits_{j = 1}^{i - 1} | {G_{ij}}{|^2}V_j^{(t)} + \sum\limits_{j = i + 1}^K | {G_{ij}}{|^2}V_j^{(t - 1)}} \right) + \frac{{{\sigma ^2}}}{{{G_{ii}}}}$

　(8) 計(jì)算SINR ${{\rm Y}_i} = {{\mu _i^2} / {{{(\nu _i^{(t)})}^2}}}$

　(9)　　　 $i = i + 1$

　　　　end for

　(10)　　 $t = t + 1$

　　　end for

　輸出
　　　　 ${L_{i,b}} = {{\rm Y} _i}\left( {\mathop {\min }\limits_{a \in {\cal{O}}_b^0} {{\left| {\frac{{\hat s_i^{(t)}}}{{{\mu _i}}} - a} \right|}^2} - \mathop {\min }\limits_{a' \in {\cal{O}}_b^1} {{\left| {\frac{{\hat s_i^{(t)}}}{{{\mu _i}}} - a'} \right|}^2}} \right)$

下載: 導(dǎo)出CSV

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