Low Complexity Iterative Parallel Interference Cancellation Detection Algorithms for Massive MIMO Systems
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摘要: 基于干扰消除思想该文提出一种适用于大规模MIMO系统上行链路的低复杂度迭代并行干扰消除算法，在算法实现中避免了线性检测算法所需的高复杂度
$({\cal O}({K^3}))$ 矩阵求逆运算，将复杂度保持在$({\cal O}({K^2}))$ 。在此基础上，引入噪声预测机制，提出一种基于噪声预测的迭代并行干扰消除算法，进一步提高了硬判决检测性能。考虑天线间残留干扰，将干扰消除思想运用到软判决中，最后提出一种基于迭代并行干扰消除的低复杂度软输出信号检测算法。仿真结果表明：提出的信号检测方法的复杂度优于MMSE检测算法，经过几次简单的迭代，算法即快速收敛并获得接近甚至优于MMSE检测算法的误码率性能。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. -
表 1 基于迭代并行干扰消除算法(IPIC)
算法1 基于迭代并行干扰消除算法(IPIC) 输入: ${{H}},{{y}},{\sigma ^2},K,{T_{{\rm{iter}}}};$ 初始化： (1) ${{G}} = {{{H}}^{\rm{H}}}{{H}},{{b}} = {{{H}}^{\rm{H}}}{{y}},{{\hat{ s}}^{(0)}} = {{{D}}^{ - 1}}{{{H}}^{\rm{H}}}$ ${{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 输出 ${\hat{ s}} = {{\hat{ s}}^{({T_{{\rm{iter}}}})}}$ 
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表 2 基于噪声预测的迭代并行干扰消除算法(NP-IPIC)
算法2 基于噪声预测的迭代并行干扰消除算法(NP-IPIC) 输入: ${{H}},{{y}},{\sigma ^2},K,{T_{{\rm{iter}}}};$ 初始化： (1) ${{G}} = {{{H}}^{\rm{H}}}{{H}},{{b}} = {{{H}}^{\rm{H}}}{{y}}$, ${{D}} = {\rm{diag}}({{G}} + {\sigma ^2}{{{I}}_K})$ ${{\hat{ s}}^{(0)}} = Q({{{D}}^{ - 1}}{{{H}}^{\rm{H}}}{{y}}) = \{ \hat s_1^{(0)},\hat s_2^{(0)}, ·\!·\!· ,\hat s_K^{(0)}\}$ (2) 对 ${{H}}$列范数进行降序排序，
$o = \arg {\rm{sort}}({\tau _1},{\tau _2}, ·\!·\!· ,{\tau _K}),\ {\tau _k} = \left\| {{{{h}}_k}} \right\|_2^2,\ \forall k = 1,2, ·\!·\!· ,K$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) 判断 $i$是否等于1，如果为1，则计算 $\bar s_{o(1)}^{(t)} = Q\left(\hat s_{o(1)}^{(t)}\right)$, 噪声
采样 $\hat n_{o(1)}^{(t)} = \hat s_{o(1)}^{(t)} - \bar s_{o(1)}^{(t)} = \hat s_{o(1)}^{(t)} - \mathbb{Q}\left(\bar s_{o(1)}^{(t)}\right)$, 如果 $i > 1$，跳过
本步骤，执行下一步；
(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) 根据 ${{\hat{ s}}^{({T_{{\rm{iter}}}})}}$中下标进行重新排序得到 ${{\hat{ s}}^{{\rm{final}}}}$ 输出 ${\hat{ s}} = {{\hat{ s}}^{{\rm{final}}}}$
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表 3 基于迭代并行干扰消除的软输出算法(S-IPIC)
算法3 基于迭代并行干扰消除的软输出算法(S-IPIC) 输入: ${{H}},{{y}},{\sigma ^2},K,{T_{{\rm{iter}}}};$ 初始化： (1) ${G}={H}^{\rm H}{H}, {b}={H}^{\rm H}{y}$, ${{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) 估计方差 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 估计发送信号并计算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) 计算等效信道增益和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) 计算SINR ${{\rm Y}_i} = {{\mu _i^2} / {{{(\nu _i^{(t)})}^2}}}$ (9) $i = i + 1$ end for (10) $t = t + 1$ end for 输出
${L_{i,b}} = {{\rm Y} _i}\left( {\mathop {\min }\limits_{a \in {\cal{O}}_b^0} {{\left| {\frac{{\hat s_i^{(t)}}}{{{\mu _i}}} - a} \right|}^2} - \mathop {\min }\limits_{a' \in {\cal{O}}_b^1} {{\left| {\frac{{\hat s_i^{(t)}}}{{{\mu _i}}} - a'} \right|}^2}} \right)$
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