CN102571178A - Beam forming method used in equivalent isotropic radiated power limited systems - Google Patents

Abstract

The invention discloses a beam forming method in an EIRP limited system, which is proposed for solving the problem of low bit error rate performance of the existing beam forming method. The method of the invention first selects the antenna and compresses the initial beam vector, and then obtains a numerical solution through an exhaustive search method to approach the optimal solution. Compared with the prior art, the beamforming method of the present invention makes full use of the channel matrix information by selecting and utilizing more antennas, and can further reduce the power loss in the radiation peak direction. Compared with the smooth reduction scheme, the obtained The greater the received power, the better the bit error rate performance of the system. The beamforming method of the present invention is suitable for EIRP limited systems, not only for ultra-wideband systems, but also for 60GHz systems.

Description

A Beamforming Method in EIRP Constrained Systems

technical field

The invention belongs to the technical field of wireless communication, and in particular relates to a beamforming method in an Equivalent Isotropic Radiated Power (EIRP, Equivalent Isotropic Radiated Power) limited system.

Background technique

In the multi-antenna multi-carrier ultra-wideband (UWB) system, because the US Federal Communications Commission (FCC) has strict requirements on the power spectral density of the Orthogonal Frequency Division Multiplexing (OFDM, Orthogonal Frequency Division Multiple) multi-carrier UWB system, That is, for each subcarrier, the equivalent isotropic radiated power is not greater than -41.3dBm/MHz. Because the traditional ideal transmit beamforming algorithm (eigenbeamforming) uses channel eigenvalues to generate directional spatial beams, and simply limiting the total transmit power cannot make the power in all directions meet the EIRP limit, so the eigenbeam Shaping algorithms are not suitable for EIRP constrained systems. In view of the above problems, there are already some transmit beamforming schemes suitable for EIRP-limited ultra-wideband systems. These methods further limit the transmit power, including compressed eigenbeamforming schemes and antenna selection schemes, but these schemes make the system error Bit rate performance is poor. On the basis of compressed eigenbeamforming, a compression algorithm and a fast smoothing iterative algorithm are proposed to design the transmit beamforming vector and further improve the receive signal-to-noise ratio. Compared with compressive intrinsic beamforming schemes, these algorithms reduce bit error rate and improve system performance. For multi-carrier UWB systems, it is a challenging task to continuously improve system performance under EIPR-limited conditions.

Mathematical analysis on EIRP limitation: analyze the case where the antenna at the transmitting end is a uniform linear array (ULA). Suppose λ _c is the transmission carrier wavelength, the antenna spacing is d _T , the number of array elements is n _T , the array elements are arranged along the z-axis direction, and the included angle with the z-axis is θ. The n _T -element linear array is shown in Figure 1, and the antenna array vector $a\left(\mathrm{\&theta;}\right)={(1,e^{\mathrm{j\&Omega;}},{\mathrm{<figure-callout\; id="2"\; label="e\; j"\; filenames="HDA0000138991640000031.png,HDA0000138991640000041.png"\; state="\{\{state\}\}">e</figure-callout>}}^j,...,e^{j({\mathrm{no}}_T-1)\mathrm{\&Omega;}})}^h,$ where Ω=(2π/λ _c )d _T cos(θ). Suppose d _T ≥ λ _c /2, θ∈(-π, π], obviously Ω∈(-π, π]. Assume that the number of antennas at the receiving end is n _R = 1, and the channel state information is known at the transmitting end, that is, the kth The channel matrix information H _k on the subcarrier, the received signal on the kth subcarrier y _k =H _k w _k x _k +n _k , x _k is a complex scalar symbol with a mean value of 0 and a variance of 1, and n _k is a cyclic symmetric complex Gaussian noise vector, each element of n _k is independently and identically distributed, with a mean value of 0 and a variance of N ₀ . w _k represents the beam vector on the kth subcarrier.

(j＝1，2，…，K)。因此，r_k与w_k可以表示： $r_k={\mathrm{\&Theta;}}_{K\&times;n_T}{w}_k.$ 其中，The EIRP-limited normalization on the kth subcarrier can be expressed as: $P_{\mathrm{EIRP}}\left(\mathrm{\&theta;}\right)=\underset{\mathrm{\&theta;}\&Element;\left(\mathrm{0,2}\mathrm{\&pi;}\right]}{\max }\left|{a\left(\mathrm{\&theta;}\right)}^h{w}_k\right|\&le;1,$ The above formula can also be expressed as P(Ω)=|a(Ω) ^H w _k | ² ≤1. P(Ω) can be regarded as the square of the modulus of the inverse Fourier transform of w _k . For a uniform linear array, it can be regarded as a beam vector w _k for IDFT sampling. n _T ×1-dimensional beam vector w _k corresponds to the IDFT of length K as r _k =(r ₁ ,r ₂ ,…,r _K ) ^T , where

(j=1, 2, . . . , K). Therefore, r _k and w _k can express: $r_k={\mathrm{\&Theta;}}_{K\&times;{\mathrm{no}}_T}{w}_k.$ in,

${\mathrm{<span\; class="notranslate">\; \&Theta;</span>}}_{\mathrm{<span\; class="notranslate">\; K</span>}<span\; class="notranslate">\; \&times;</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; T</span>}}}<span\; class="notranslate">\; =</span>{\left[\begin{array}{cccc}\mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span>& \mathrm{<span\; class="notranslate">\; 1</span>}\\ \mathrm{<span\; class="notranslate">\; 1</span>}& {\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="e\; j"\; filenames="HDA0000138991640000031.png,HDA0000138991640000041.png"\; state="\{\{state\}\}">e</figure-callout></span><figure-callout\; id="2"\; label="e\; j"\; filenames="HDA0000138991640000031.png,HDA0000138991640000041.png"\; state="\{\{state\}\}">\; </figure-callout>}}^{\mathrm{<span\; class="notranslate">\; </span>}}& <span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span>& {\mathrm{<span\; class="notranslate">\; e</span>}}^{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="j"\; filenames="HDA0000138991640000031.png,HDA0000138991640000041.png"\; state="\{\{state\}\}">j</figure-callout></span>}\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; K</span>}}\\ \mathrm{<span\; class="notranslate">\; m</span>}& \mathrm{<span\; class="notranslate">\; m</span>}& \mathrm{<span\; class="notranslate">\; o</span>}& \mathrm{<span\; class="notranslate">\; m</span>}\\ \mathrm{<span\; class="notranslate">\; 1</span>}& {\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="e\; j"\; filenames="HDA0000138991640000031.png,HDA0000138991640000041.png"\; state="\{\{state\}\}">e</figure-callout></span><figure-callout\; id="2"\; label="e\; j"\; filenames="HDA0000138991640000031.png,HDA0000138991640000041.png"\; state="\{\{state\}\}">\; </figure-callout>}}^{\mathrm{<span\; class="notranslate">\; </span>}}& <span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span>& {\mathrm{<span\; class="notranslate">\; e</span>}}^{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="j"\; filenames="HDA0000138991640000031.png,HDA0000138991640000041.png"\; state="\{\{state\}\}">j</figure-callout></span>}\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; K</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; K</span>}}\end{array}\right]}_{\mathrm{<span\; class="notranslate">\; K</span>}<span\; class="notranslate">\; \&times;</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; T</span>}}}$

is the IDFT matrix corresponding to w _k , K represents the number of spatial directions taken, and the EIRP restriction is satisfied in the chosen direction. The value of K can be changed, the larger the value of K, the more accurate the calculation, but K must be a finite value.

Depend on $P_{\mathrm{EIRP}}\left(\mathrm{\&theta;}\right)=\underset{\mathrm{\&theta;}\&Element;\left(\mathrm{0,2}\mathrm{\&pi;}\right]}{\max }\left|{a\left(\mathrm{\&theta;}\right)}^h{w}_k\right|\&le;1$ can get ${\left|\right|{\mathrm{\&Theta;}}_{K\&times;{\mathrm{no}}_T}{w}_k\left|\right|}_{\&infin;}^2\&le;1.$ In order to improve the bit error rate performance of the system, it is necessary to consider how to design the transmitting beam vector w _k to improve the receiving SNR or maximize the SNR at the receiving end. The problem is equivalent to:

$\underset{{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}}{\mathrm{<span\; class="notranslate">\; max</span>}}\mathrm{<span\; class="notranslate">\; \&rho;</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; )</span>{<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}$

$\mathrm{<span\; class="notranslate">\; subject\; to</span>}{<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; \&Theta;</span>}}_{\mathrm{<span\; class="notranslate">\; K</span>}<span\; class="notranslate">\; \&times;</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; T</span>}}}{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>}_{<span\; class="notranslate">\; \&infin;</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; 1</span>}$

只有在取等号时，ρ(w_k)才会得到最优解。因此，because

Only when the equal sign is taken, ρ(w _k ) will get the optimal solution. therefore,

$\mathrm{<span\; class="notranslate">\; \&rho;</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{{<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; \&Theta;</span>}}_{\mathrm{<span\; class="notranslate">\; K</span>}<span\; class="notranslate">\; \&times;</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; T</span>}}}{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>}_{<span\; class="notranslate">\; \&infin;</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; .</span>$

其中

其方法详细描述可以参考文献：Cheran M.Vithanage，Steve C.J.Parker，Magnus Sandell.Antenna selection with phase precoding for high performance UWB communication with legacyWiMedia multi-band OFDM devices.Proc.IEEE Int.Conf.Communications，pp.3938-3942，May 2008。其优点在于：当发射天线数目为两个时，发射天线选择能够在EIRP限制条件下使系统误码率最小；当发射天线数超过两个时，天线选择方法易于实现，复杂度很低。其缺点在于：当发射天线数超过两个时，系统误码率性能较差。Antenna selection (Antenna Selection) includes the selection of the transmitting antenna and the selection of the receiving antenna, and the antenna selection criteria mainly include the maximum channel capacity criterion and the minimum reception bit error rate criterion. The transmit antenna selection method considered here selects the only antenna and adopts the minimum criterion of the receive bit error rate, ie the receive signal-to-noise ratio (SNR) is maximized. Antenna selection: the unit vector e _l indicates that the lth element is 1, and the beam vector in the antenna selection method

in

For a detailed description of the method, please refer to: Cheran M.Vithanage, Steve CJParker, Magnus Sandell.Antenna selection with phase precoding for high performance UWB communication with legacyWiMedia multi-band OFDM devices.Proc.IEEE Int.Conf.Communications, pp.3938- 3942, May 2008. The advantage is that: when the number of transmitting antennas is two, the selection of transmitting antennas can minimize the bit error rate of the system under the condition of EIRP restriction; when the number of transmitting antennas exceeds two, the antenna selection method is easy to implement and the complexity is very low. Its disadvantage is that when the number of transmitting antennas exceeds two, the performance of the bit error rate of the system is poor.

的最大特征值对应的特征向量，压缩后的波束矢量

能够适用于EIRP受限系统。该方法详细描述可以参考文献：C.M.Vithanage，Y.Wang，and J.P.Coon.Transmitbeamforming methods for improved received signal-to-noise ratio in equivalent isotropic radiatedpower-constrained systems.IET Communications，Vol.3，PP.38-47，2009。其缺点在于仅仅简单地限制发射功率而造成接收信噪比很小，从而使系统的误码率性能很差。Scaled Eigen-beamforming algorithm (Scaled Eigen-beamforming) compresses the eigenbeam vector so that the transmission power meets the EIRP limit requirement. The eigenbeam vector w _EB can be obtained by eigenbeamforming, and w _EB is

The eigenvector corresponding to the largest eigenvalue of , the compressed beam vector

Can be applied to EIRP restricted systems. For a detailed description of the method, please refer to: CMVithanage, Y.Wang, and JPCoon.Transmitbeamforming methods for improved received signal-to-noise ratio in equivalent isotropic radiatedpower-constrained systems.IET Communications, Vol.3, PP.38-47, 2009 . Its shortcoming is that the received signal-to-noise ratio is very small only by simply limiting the transmission power, so that the bit error rate performance of the system is very poor.

The smooth clipping method (Soft clipping method) is similar to applying the principle of suppressing the peak-to-average power ratio (PAPR) in the time-domain OFDM system to the space domain. This method first determines the radiation peak direction of the compressed eigenbeam vector, and then changes the peak direction, similar to the limiting filter technology of the OFDM system, transforms the beam vector in the frequency domain to the time domain, and then performs a certain adjustment on the amplitude of the corresponding time domain vector. Processing, that is, the peak-to-average power ratio of the amplitude is smoothed and iteratively compressed to meet specific requirements, and the time-domain vector after iterative processing is transformed into the frequency domain, and the frequency-domain vector is processed correspondingly to the radiation direction to obtain the beam vector of the smooth reduction scheme . The smooth curtailment scheme reduces the power loss in the radiation peak direction through multiple iterations, so as to obtain higher received power and improve system performance. For a more detailed description of this method, refer to: C.M.Vithanage, Y.Wang, and J.P.Coon.Transmit beamforming methods for improved receivedsignal-to-noise ratio in equivalent isotropic radiated power-constrained systems.IETCommunications, Vol.3, PP .38-47, 2009.

Overall, the BER performance of the above three methods cannot meet the requirements. The BER performance of the antenna selection method and the compressed intrinsic beamforming algorithm is relatively poor. Although the smooth reduction scheme improves the BER performance, the improved Not much.

Contents of the invention

The purpose of the present invention is to solve the problem of low bit error rate performance of the existing beamforming method, and propose a beamforming method in an EIRP limited system to further improve the system bit error rate performance on the basis of the smooth reduction scheme .

The technical solution of the present invention is: a beamforming method in an EIRP limited system, the specific flow diagram is shown in Figure 2, including the following steps:

其中，λ为天线T的权值系数，大小范围为：0＜λ≤1，则第i根天线的初始波束矢量1≤i≤n_T，(H_k)_i为第i根天线上第k个子载波上的信道增益，∠表示求相位运算，(·)_i表示取第i个元素；Step 1: Antenna selection: Select two antennas S and T corresponding to the largest and second largest channel gains from the n _T antennas in the EIRP limited system, where n _T > 2, the weights of antennas S and T They are: p, λp, the weights of all other n _T -2 antennas are 0, and the probability distribution of n _T antennas is recorded as

Among them, λ is the weight coefficient of the antenna T, and the size range is: 0<λ≤1, then the initial beam vector of the i-th antenna 1≤i≤n _T , (H _k ) _i is the channel gain on the kth subcarrier on the i-th antenna, ∠ means to calculate the phase operation, (·) _i means to take the i-th element;

其中，w_0，k对应的方向旋转矩阵

${\mathrm{\&Theta;}}_{K\&times;n_T}=\left[\begin{array}{cccc}1& 1& ...& 1\\ 1& e^{j2\mathrm{\&pi;}/K}& ...& e^{j2\mathrm{\&pi;}(n_T-1)/K}\\ M& M& O& M\\ 1& e^{j2\mathrm{\&pi;}(K-1)/K}& ...& e^{j2\mathrm{\&pi;}(n_T-1)(K-1)/K}\end{array}\right],$ K表示所取的空间方向数目，||||_∞表示无穷范数运算；得到k个子载波上的初始接收功率||||₂表示2范数运算；Step 2: Compress the initial beam vector: Select the compressed initial beam vector on the kth subcarrier

in, The direction rotation matrix corresponding to w _{0, k}

${\mathrm{\&Theta;}}_{K\&times;{\mathrm{no}}_T}=\left[\begin{array}{cccc}1& 1& ...& 1\\ 1& {\mathrm{<figure-callout\; id="2"\; label="e\; j"\; filenames="HDA0000138991640000031.png,HDA0000138991640000041.png"\; state="\{\{state\}\}">e</figure-callout>}}^j& <figure-callout\; id="2"\; label="...\; e\; j"\; filenames="HDA0000138991640000031.png,HDA0000138991640000041.png"\; state="\{\{state\}\}">.</figure-callout>..& e^j{2\mathrm{\&pi;}({\mathrm{no}}_T-1)/K}^{}\\ m& m& o& m\\ 1& {\mathrm{<figure-callout\; id="2"\; label="e\; j"\; filenames="HDA0000138991640000031.png,HDA0000138991640000041.png"\; state="\{\{state\}\}">e</figure-callout>}}^j& <figure-callout\; id="2"\; label="...\; e\; j"\; filenames="HDA0000138991640000031.png,HDA0000138991640000041.png"\; state="\{\{state\}\}">.</figure-callout>..& e^j{2\mathrm{\&pi;}({\mathrm{no}}_T-1)(K-1)/K}^{}\end{array}\right],$ K represents the number of spatial directions taken, |||| _∞ represents the infinite norm operation; get the initial received power on k subcarriers |||| ₂ means 2-norm operation;

λ_j为第j次循环时天线T的权值系数，w_0，k(λ_j)为第j次循环时第k个子载波上的压缩初始波束矢量，初始化循环变量m＝1；Step 3: Set the number of loop iterations J and M, initialize the loop variable j=1,

λ _j is the weight coefficient of the antenna T during the j-th cycle, w _{0, k} (λ _j ) is the compressed initial beam vector on the k-th subcarrier during the j-th cycle, and the initialization cycle variable m=1;

r_i＝(r_k，m)_i表示r_k，m的第i个元素，1≤i≤n_T，PAPR₀＝0，Δ＝|PAPR_m-PAPR_m-1|；Step 4: Calculate $r_{k,m}={\mathrm{\&Theta;}}_{{\mathrm{no}}_T\&times;{\mathrm{no}}_T}{w}_{m-1,k}\left({\mathrm{\&lambda;}}_j\right),$ Among them, r _{k, m} is a column vector of n _T × 1, and the peak-to-average power ratio of r _{k, m} amplitude is

r _i =(r _{k, m} ) _i means r _{k, the ith element of m} , 1≤i≤n _T , PAPR ₀ =0, Δ=|PAPR _m -PAPR _m-1 |;

得到

空间辐射的峰值方向由

值确定，

计算出

和 $\mathrm{\&rho;}\left(w_{m,k}\left({\mathrm{\&lambda;}}_j\right)\right)=\frac{{\left|\right|H_k{w}_{m,k}\left({\mathrm{\&lambda;}}_j\right)\left|\right|}_2^2}{{\left|\right|{\mathrm{\&Theta;}}_{K\&times;n_T}{w}_{m,k}\left({\mathrm{\&lambda;}}_j\right)\left|\right|}_{\&infin;}^2};$ 否则，w_m，k(λ_j)＝w_m-1，k(λ_j)， $\mathrm{\&rho;}\left(w_{m,k}\left({\mathrm{\&lambda;}}_j\right)\right)=\frac{{\left|\right|H_k{w}_{m,k}\left({\mathrm{\&lambda;}}_j\right)\left|\right|}_2^2}{{\left|\right|{\mathrm{\&Theta;}}_{K\&times;n_T}{w}_{m,k}\left({\mathrm{\&lambda;}}_j\right)\left|\right|}_{\&infin;}^2};$ If Δ>ε, where ε is the preset threshold, ${\left(r_{k,m+1}\right)}_i=\left(\right|{\left(r_{k,m}\right)}_i|-\frac{{\left|{\left(r_{k,m}\right)}_i\right|}^3}{3})\exp (j\&angle;{\left(r_{k,m}\right)}_i),$

get

The peak direction of space radiation is given by

value is determined,

Calculate

and $\mathrm{\&rho;}\left(w_{m,k}\left({\mathrm{\&lambda;}}_j\right)\right)=\frac{{\left|\right|h_k{w}_{m,k}\left({\mathrm{\&lambda;}}_j\right)\left|\right|}_2^2}{{\left|\right|{\mathrm{\&Theta;}}_{K\&times;{\mathrm{no}}_T}{w}_{m,k}\left({\mathrm{\&lambda;}}_j\right)\left|\right|}_{\&infin;}^2};$ Otherwise, w _m,k (λ _j )=w _m-1 ,k(λ _j ), $\mathrm{\&rho;}\left(w_{m,k}\left({\mathrm{\&lambda;}}_j\right)\right)=\frac{{\left|\right|h_k{w}_{m,k}\left({\mathrm{\&lambda;}}_j\right)\left|\right|}_2^2}{{\left|\right|{\mathrm{\&Theta;}}_{K\&times;{\mathrm{no}}_T}{w}_{m,k}\left({\mathrm{\&lambda;}}_j\right)\left|\right|}_{\&infin;}^2};$

和

若j＜J，则j＝j+1，m＝1，重复步骤4，否则，转到步骤6；Step 5: m=m+1, if m≤M, repeat step 4; otherwise, get

and

If j<J, then j=j+1, m=1, repeat step 4, otherwise, go to step 6;

其中 $\underset{x}{\arg \max }f\left(x\right):=\left\{x\right|\&ForAll;y:f\left(y\right)\&le;f\left(x\right)\};$ Step 6: Calculate

in $\underset{x}{\arg \max }f\left(x\right):=\left\{x\right|\&ForAll;\mathrm{the\; y}:f\left(\mathrm{the\; y}\right)\&le;f\left(x\right)\};$

则波束矢量为

否则，波束矢量为w_ASS＝w_AS，其中，w_AS为天线选择方法得到的波束矢量，ρ(w_AS)为波束矢量w_AS对应的接受功率。Step 7: If

Then the beam vector is

Otherwise, the beam vector is w _ASS =w _AS , where w _AS is the beam vector obtained by the antenna selection method, and ρ(w _AS ) is the received power corresponding to the beam vector w _AS .

In step 3, only a typical uniform search method is used as a reference, and other search methods that can reduce complexity such as dichotomy, unimodal function search (also known as golden section method or 0.618 method) can also be used. Because the above scheme is a uniform search for λ, the calculation complexity is relatively high. In order to reduce the number of calculations, the optimal λ for ρ(w _k (λ)) can be obtained through the binary method (that is, the half-search method). In this way, compared with the antenna subset selection scheme using the dichotomy method, the number of cycles in step 3 is significantly reduced. In step 3, because ρ(w _k (λ)) is a unimodal function in the interval 0<λ _j ≤1, using the unimodal function search method can guarantee the system performance while further reducing the computational complexity.

Taking the dichotomy as an example, the corresponding step 3 is modified as follows:

λ_j+1＝(λ_a+λ_b)/2，λ_j为第j次循环时天线T的权值系数，w_0，k(λ_j)为第j次循环时第k个子载波上的压缩初始波束矢量，初始化循环变量m＝1。Step 3: Set the number of loop iterations J and M, initialize the loop variable j=1, λ ₀ =0, λ ₁ =1,

λ _j+1 ＝(λ _a +λ _b )/2, λ _j is the weight coefficient of the antenna T in the j-th cycle, w _{0, k} (λ _j ) is the weight coefficient on the k-th subcarrier in the j-th cycle Compress the initial beam vector and initialize the loop variable m=1.

Beneficial effects of the present invention: the method of the present invention first selects the antenna and compresses the initial beam vector, and then obtains the numerical solution through the method of exhaustive search to approach the optimal solution, which can further reduce the power loss in the direction of the radiation peak, and smooth reduction scheme In comparison, the received power obtained is larger, and the bit error rate performance of the system is better. Compared with the prior art, the present invention has the following advantages:

(1) The beamforming method of the present invention makes full use of the channel matrix information by selecting and utilizing more antennas;

(2) The beamforming method of the present invention is suitable for EIRP limited systems, not only for ultra-wideband systems, but also for 60GHz systems.

Compared with the traditional method, the beamforming method of the present invention can further improve the system performance.

Description of drawings

FIG. 1 is a schematic diagram of an antenna array of an N-element linear array of the present invention.

Fig. 2 is a schematic flow chart of the beamforming method of the present invention.

Fig. 3 is a comparison diagram of the bit error performance between the beamforming method of the present invention and the traditional method under the CM3 channel environment of the ultra-wideband system.

FIG. 4 is a comparison diagram of the bit error performance of the beamforming method of the present invention using different search distances under the CM3 channel environment of the ultra-wideband system.

FIG. 5 is a schematic diagram of the bit error performance of the beamforming method of the present invention under the CM1 channel environment of the 60GHz system.

Detailed ways

Specific embodiments of the present invention will be given below in conjunction with the accompanying drawings. It should be noted that the parameters in the examples do not affect the generality of the present invention.

The channels used in Figure 3 and Figure 4 are both CM3 channels in the 802.15.3a standard channel model. For a more detailed description of this channel, please refer to the literature: IEEE P802.15 Working Group for Wireless Personal AreaNetworks, Channel Modeling Sub-committee Report Final, IEEE P802.15-02/368r5-SG3a, Dec.2002. The channel used in Figure 5 is the CM1 channel in the 802.15.3c standard channel model. For a more detailed description of this channel, refer to the literature: IEEE P802.15 Working Group for Wireless Personal Area Networks, TG3cChannel Modeling Sub-committee Report Final, IEEE 15-07-0584-01-003c, Sep. 2010.

λ_j值可以从0.1，0.2，0.3一直取到1，在BER＝10^-4时，其误比特性能与平滑削减方案相比改善了约0.7dB。As shown in FIG. 3 , in the ultra-wideband system CM3 channel environment, the bit error performance of the beamforming method of the present invention is compared with that of the traditional method. Wherein, the beamforming method adopts a uniform search method, the search interval is 0.1, and the number of searches is 10, that is, the maximum number of cycles is J=10. When the search distance is 0.1, at the jth cycle, the value of λ _j is

The value of λ _j can be taken from 0.1, 0.2, 0.3 to 1. When BER=10 ^-4 , its bit error performance is improved by about 0.7dB compared with the smooth reduction scheme.

As shown in Figure 4, under the CM3 channel environment of the ultra-wideband system, the bit error performance comparison of the beamforming method of the present invention when using different search distances, the different search distances adopted are respectively: 0.5, 0.2, 0.1, 0.05; The maximum number of cycles are 2, 5, 10, 20 respectively. With the narrowing of the search distance, the location of λ is more accurate, and the value of λ corresponding to the larger value of ρ(w _k (λ)) can be found, and the corresponding bit error performance of the system is better. It can be seen from the figure that when the search distance is 0.5, the value of _λj can only be 0.5 and 1, and its bit error performance is even worse than that of the smooth reduction scheme. However, when the search interval is 0.05, the value of λ _j can be taken from 0.05, 0.1, 0.15, 0.2 to 1. When BER=10 ^-4 , its bit error performance is improved by about 0.8dB compared with the smooth reduction scheme.

As shown in Figure 5, in the CM1 channel environment of the 60GHz system, the bit error performance diagram of the beamforming method using different search methods, wherein, ASS (uniform search method) means the beamforming method using uniform search method, ASS (dichotomy method ) represents the beamforming method using dichotomy.

The above example is only a preferred example of the present invention, and the use of the present invention is not limited to this example. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention should be included in this document. within the scope of protection of the invention.

Claims (2)

1. A beamforming method in an EIRP limited system, comprising the steps of: Step 1: Antenna selection: Select two antennas S and T corresponding to the largest and second largest channel gains from the n _T antennas in the EIRP limited system, where n _T > 2, the weights of antennas S and T They are: p, λp, the weights of all other n _T -2 antennas are 0, and the probability distribution of n _T antennas is recorded as

Among them, λ is the weight coefficient of the antenna T, and the size range is: 0<λ≤1, then the initial beam vector of the i-th antenna 1≤i≤n _T , (H _k ) _i is the channel gain on the kth subcarrier on the i-th antenna, ∠ means to calculate the phase operation, (·) _i means to take the i-th element; Step 2: Compress the initial beam vector: Select the compressed initial beam vector on the kth subcarrier

in,

The direction rotation matrix corresponding to w _{0, k}

${\mathrm{\&Theta;}}_{K\&times;{\mathrm{no}}_T}=\left[\begin{array}{cccc}1& 1& ...& 1\\ 1& e^{j2\mathrm{\&pi;}/K}& ...& e^{j2\mathrm{\&pi;}({\mathrm{no}}_T-1)/K}\\ m& m& o& m\\ 1& e^{j2\mathrm{\&pi;}(K-1)/K}& ...& e^{j2\mathrm{\&pi;}({\mathrm{no}}_T-1)(K-1)/K}\end{array}\right],$ K represents the number of spatial directions taken, |||| _∞ represents the infinite norm operation; get the initial received power on k subcarriers |||| ₂ means 2-norm operation; Step 3: Set the number of loop iterations J and M, initialize the loop variable j=1,

λ _j is the weight coefficient of the antenna T during the j-th cycle, w _{0, k} (λ _j ) is the compressed initial beam vector on the k-th subcarrier during the j-th cycle, and the initialization cycle variable m=1; Step 4: Calculate $r_{k,m}={\mathrm{\&Theta;}}_{{\mathrm{no}}_T\&times;{\mathrm{no}}_T}{w}_{m-1,k}\left({\mathrm{\&lambda;}}_j\right),$ Among them, r _{k, m} is a column vector of n _T × 1, and the peak-to-average power ratio of r _{k, m} amplitude is

r _i =(r _{k, m} ) _i means r _{k, the ith element of m} , 1≤i≤n _T , PAPR ₀ =0, Δ=|PAPR _m -PAPR _m-1 |; If Δ>ε, where ε is the preset threshold, ${\left(r_{k,m+1}\right)}_i=\left(\right|{\left(r_{k,m}\right)}_i|-\frac{{\left|{\left(r_{k,m}\right)}_i\right|}^3}{3})\exp (j\&angle;{\left(r_{k,m}\right)}_i),$

get The peak direction of space radiation is given by

value is determined,

Calculate

and $\mathrm{\&rho;}\left(w_{m,k}\left({\mathrm{\&lambda;}}_j\right)\right)=\frac{{\left|\right|h_k{w}_{m,k}\left({\mathrm{\&lambda;}}_j\right)\left|\right|}_2^2}{{\left|\right|{\mathrm{\&Theta;}}_{K\&times;{\mathrm{no}}_T}{w}_{m,k}\left({\mathrm{\&lambda;}}_j\right)\left|\right|}_{\&infin;}^2};$ Otherwise, w _m,k (λ _j )=w _m-1,k (λ _j ), $\mathrm{\&rho;}\left(w_{m,k}\left({\mathrm{\&lambda;}}_j\right)\right)=\frac{{\left|\right|h_k{w}_{m,k}\left({\mathrm{\&lambda;}}_j\right)\left|\right|}_2^2}{{\left|\right|{\mathrm{\&Theta;}}_{K\&times;{\mathrm{no}}_T}{w}_{m,k}\left({\mathrm{\&lambda;}}_j\right)\left|\right|}_{\&infin;}^2};$ Step 5: m=m+1, if m≤M, repeat step 4; otherwise,

get

and

If j<J, then j=j+1, m=1, repeat step 4, otherwise, go to step 6; Step 6: Calculate

in $\underset{x}{\arg \max }f\left(x\right):=\left\{x\right|\&ForAll;\mathrm{the\; y}:f\left(\mathrm{the\; y}\right)\&le;f\left(x\right)\};$ Step 7: If

Then the beam vector is

Otherwise, the beam vector is w _ASS =w _AS , where w _AS is the beam vector obtained by the antenna selection method, and ρ(w _AS ) is the received power corresponding to the beam vector w _AS . 2. A beamforming method in an EIRP limited system, comprising the steps of: Step 1: Antenna selection: Select two antennas S and T corresponding to the largest and second largest channel gains from the n _T antennas in the EIRP limited system, where n _T > 2, the weights of antennas S and T They are: p, λp, the weights of all other n _T -2 antennas are 0, and the probability distribution of n _T antennas is recorded as

Among them, λ is the weight coefficient of the antenna T, and the size range is: 0<λ≤1, then the initial beam vector of the i-th antenna 1≤i≤n _T , (H _k ) _i is the channel gain on the kth subcarrier on the i-th antenna, ∠ means to calculate the phase operation, (·) _i means to take the i-th element; Step 2: Compress the initial beam vector: Select the compressed initial beam vector on the kth subcarrier

in, The direction rotation matrix corresponding to w _{0, k}

${\mathrm{\&Theta;}}_{K\&times;{\mathrm{no}}_T}=\left[\begin{array}{cccc}1& 1& ...& 1\\ 1& e^{j2\mathrm{\&pi;}/K}& ...& e^{j2\mathrm{\&pi;}({\mathrm{no}}_T-1)/K}\\ m& m& o& m\\ 1& e^{j2\mathrm{\&pi;}(K-1)/K}& ...& e^{j2\mathrm{\&pi;}({\mathrm{no}}_T-1)(K-1)/K}\end{array}\right],$ K represents the number of spatial directions taken, |||| _∞ represents the infinite norm operation; get the initial received power on k subcarriers

|||| ₂ means 2-norm operation; Step 3: Set the number of loop iterations J and M, initialize the loop variable j=1, λ ₀ =0, λ ₁ =1,

λ _j+1 ＝(λ _a +λ _b )/2, λ _j is the weight coefficient of the antenna T in the j-th cycle, w _{0, k} (λ _j ) is the weight coefficient on the k-th subcarrier in the j-th cycle Compress the initial beam vector and initialize the loop variable m=1; Step 4: Calculate $r_{k,m}={\mathrm{\&Theta;}}_{{\mathrm{no}}_T\&times;{\mathrm{no}}_T}{w}_{m-1,k}\left({\mathrm{\&lambda;}}_j\right),$ Among them, r _{k, m} is a column vector of n _T × 1, and the peak-to-average power ratio of r _{k, m} amplitude is

r _i =(r _{k, m} ) _i means r _{k, the ith element of m} , 1≤i≤n _T , PAPR ₀ =0, Δ=|PAPR _m -PAPR _m-1 |; If Δ>ε, where ε is the preset threshold, ${\left(r_{k,m+1}\right)}_i=\left(\right|{\left(r_{k,m}\right)}_i|-\frac{{\left|{\left(r_{k,m}\right)}_i\right|}^3}{3})\exp (j\&angle;{\left(r_{k,m}\right)}_i),$

get

The peak direction of space radiation is given by

value is determined,

Calculate

and $\mathrm{\&rho;}\left(w_{m,k}\left({\mathrm{\&lambda;}}_j\right)\right)=\frac{{\left|\right|h_k{w}_{m,k}\left({\mathrm{\&lambda;}}_j\right)\left|\right|}_2^2}{{\left|\right|{\mathrm{\&Theta;}}_{K\&times;{\mathrm{no}}_T}{w}_{m,k}\left({\mathrm{\&lambda;}}_j\right)\left|\right|}_{\&infin;}^2};$ Otherwise, w _m,k (λ _j )=w _m-1,k (λ _j ), $\mathrm{\&rho;}\left(w_{m,k}\left({\mathrm{\&lambda;}}_j\right)\right)=\frac{{\left|\right|h_k{w}_{m,k}\left({\mathrm{\&lambda;}}_j\right)\left|\right|}_2^2}{{\left|\right|{\mathrm{\&Theta;}}_{K\&times;{\mathrm{no}}_T}{w}_{m,k}\left({\mathrm{\&lambda;}}_j\right)\left|\right|}_{\&infin;}^2};$ Step 5: m=m+1, if m≤M, repeat step 4; otherwise,

get

and

If j<J, then j=j+1, m=1, repeat step 4, otherwise, go to step 6; Step 6: Calculate in $\underset{x}{\arg \max }f\left(x\right):=\left\{x\right|\&ForAll;\mathrm{the\; y}:f\left(\mathrm{the\; y}\right)\&le;f\left(x\right)\};$ Step 7: If

Then the beam vector is

Otherwise, the beam vector is w _ASS =w _AS , where w _AS is the beam vector obtained by the antenna selection method, and ρ(w _AS ) is the received power corresponding to the beam vector w _AS .

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