CN101179291B

CN101179291B - Condition maximum likelihood estimation based ultra-wideband communication system synchronization method

Info

Publication number: CN101179291B
Application number: CN2007100474065A
Authority: CN
Inventors: 曾晓洋; 麦浪; 彭延杰; 王易因
Original assignee: Fudan University
Current assignee: Fudan University
Priority date: 2007-10-25
Filing date: 2007-10-25
Publication date: 2012-11-21
Anticipated expiration: 2027-10-25
Also published as: CN101179291A

Abstract

The invention belongs to the technical field of wireless communication, and in particular relates to a method for synchronizing an ultra-wideband (UWB) communication system based on conditional maximum likelihood estimation. Using the cyclostationarity of the UWB symbol structure, the frame-level noise suppression processing is performed on the received waveform to construct the noise template required for synchronization, and then the parameter A _ξ representing the energy of a frame is obtained by using the invented noise template cross-correlation estimation. The parameter is used to estimate and characterize the frame-level timing offset n _f ; finally, the proposed sliding correlation search is used for fine synchronization to obtain the intra-frame timing offset ξ. The first two improvements proposed by the present invention can more effectively suppress the influence of noise components in the parameter estimation process, improve the performance of the synchronization mean square error in the case of low signal-to-noise ratio; and reduce the synchronization mean square error in the case of high signal-to-noise ratio Lower performance limit.

Description

Synchronization Method for UWB Communication System Based on Conditional Maximum Likelihood Estimation

技术领域technical field

本发明属于无线通信技术领域，具体涉及一种应用于脉冲体制超宽带(IR-UWB)通信系统的同步方法。The invention belongs to the technical field of wireless communication, and in particular relates to a synchronization method applied to a pulse system ultra-wideband (IR-UWB) communication system.

背景技术Background technique

超宽带(Ultra-wideband，UWB)技术已成为近些年学术界和工业界极为关注的无线通信技术之一。其中，IR-UWB(Impulse Radio UWB)方案采用亚纳秒或皮秒级的脉冲序列直接进行基带传输，避免了载波频偏(carrier frequency offset，CFO)所引起的性能下降，同时系统复杂度也因无需作载波处理而大大降低。此外，良好的多径可辨性削弱了室内多径衰减所引起的能量损耗，使得UWB信号以低发射功率进行传播并与其他通信方式共享频谱成为可能。更值得一提的是，通过香农公式的计算，作为正统超宽带信号的极窄脉冲承诺了极高的信道容量，为短距离高速无线通信提供了一条新的途径。然而，正由于采用了极窄脉冲进行传输，UWB通信系统的设计面临着极大的挑战。其中，定时同步环节的设计尤其重要。研究表明，即使是极小的定时误差都有可能引起较大误码率性能下降。传统的UWB同步根据信道估计获得的参数在本地生成模板，并通过信号与模板的滑动相关来获得码元同步。从硬件实现的角度来评估这类算法可以发现，由DSP完成精确的信道估计，系统将引入采样率高达数GHz的ADC，使其对脉宽不到1纳秒的脉冲进行高速采样；同时，大量的滑动相关对DSP的运算能力也是一个不小的考验。有研究者[1]提出了一种数据辅助(Data-aided，DA)方式的基于条件最大似然估计(Conditional MaximumLikelihood，CML)算法。该算法显著的优点是滑动相关仅在符号层面进行即可获得帧层面的定时同步。借助接收信号形成NT(Noise Template，NT)，并基于通用似然比测试的准则(Generalized likelihood ratio tests，GLRT)进行CML的估计，从而获得帧级的定时偏差量。然而原算法存在两方面的问题。首先，该算法在低信噪比的情况下，由于噪声抑制并非十分有效，因而均方估计性能并不理想；其次，在高信噪比的情况下，由于算法未引入精同步环节，故均方误差不可能随信噪比的提高而进一步减小，理论上存在下限(low bound)。Ultra-wideband (UWB) technology has become one of the wireless communication technologies that academic circles and industrial circles pay close attention to in recent years. Among them, the IR-UWB (Impulse Radio UWB) scheme uses sub-nanosecond or picosecond pulse sequences for direct baseband transmission, avoiding the performance degradation caused by carrier frequency offset (CFO), and reducing the system complexity. It is greatly reduced because there is no need for carrier processing. In addition, good multipath discrimination weakens the energy loss caused by indoor multipath attenuation, making it possible for UWB signals to propagate with low transmit power and share spectrum with other communication methods. What's more worth mentioning is that through the calculation of Shannon's formula, the ultra-narrow pulse as an orthodox ultra-wideband signal promises a very high channel capacity, providing a new way for short-distance high-speed wireless communication. However, due to the use of extremely narrow pulses for transmission, the design of UWB communication systems is facing great challenges. Among them, the design of the timing synchronization link is particularly important. Studies have shown that even small timing errors can cause large bit error rate performance degradation. Traditional UWB synchronization generates templates locally according to the parameters obtained by channel estimation, and obtains symbol synchronization through sliding correlation between signals and templates. Evaluating this type of algorithm from the perspective of hardware implementation, it can be found that the accurate channel estimation is completed by DSP, and the system will introduce an ADC with a sampling rate as high as several GHz, so that it can perform high-speed sampling of pulses with a pulse width of less than 1 nanosecond; at the same time, A large number of sliding correlations is also a big test for the computing power of DSP. Some researchers [1] proposed a Data-aided (DA) method based on Conditional Maximum Likelihood (CML) algorithm. The obvious advantage of this algorithm is that the sliding correlation can only be performed at the symbol level to obtain the timing synchronization at the frame level. The NT (Noise Template, NT) is formed with the help of the received signal, and the CML is estimated based on the generalized likelihood ratio tests (GLRT), so as to obtain the frame-level timing deviation. However, the original algorithm has two problems. First of all, in the case of low signal-to-noise ratio, the mean square estimation performance is not ideal because the noise suppression is not very effective; secondly, in the case of high signal-to-noise ratio, because the algorithm does not introduce fine synchronization, the average The square error cannot be further reduced with the increase of the signal-to-noise ratio, and there is a lower limit (low bound) in theory.

原CML估计同步方法存在几方面的缺点：The original CML estimation synchronization method has several shortcomings:

1.原CML估计算法其波形平均操作的周期为符号周期，没有充分利用有限的训练序列，由此影响到NT的形成，受噪声影响较大。1. The cycle of the waveform averaging operation of the original CML estimation algorithm is the symbol period, which does not make full use of the limited training sequence, which affects the formation of NT and is greatly affected by noise.

2.由NT和接收信号相关得到一帧能量的估计值，然后接收信号未进行噪声抑制处理，从而影响到帧级定时偏差量的估计。2. An estimated value of a frame energy is obtained by correlating the NT with the received signal, and then the received signal is not subjected to noise suppression processing, thus affecting the estimation of the frame-level timing offset.

3.原CML估计算法仅包含粗同步环节，未考虑精同步问题。3. The original CML estimation algorithm only includes the coarse synchronization link, and does not consider the fine synchronization problem.

发明内容Contents of the invention

本发明的目的在于提供一种基于CML估计的新型超宽带系统同步方法，以便更有效抑制噪声影响，并提供一级精同步环节，进一步缩小定时误差。The purpose of the present invention is to provide a new ultra-wideband system synchronization method based on CML estimation, so as to more effectively suppress the influence of noise, and provide a first-level fine synchronization link to further reduce timing errors.

本发明提供的基于CML估计的超宽带系统同步方法，属于数据辅助方式(Data-aided)。因此，首先要构造一组训练序列，该训练序列由前同步序列和后同步序列两部分组成(如图3(b)所示)，其中前同步序列(Preamble)M₁+M₂(M₁＝M₂)用于噪声模板(Noise Template，NT)的生成，后同步序列(Post-amble)M₃用于估计帧级定时偏差量n_f。The ultra-wideband system synchronization method based on CML estimation provided by the present invention belongs to the data-aided method. Therefore, firstly, a set of training sequences should be constructed, which consists of two parts, the preamble and the postamble (as shown in Figure 3(b)), where the preamble (Preamble) M ₁ +M ₂ (M ₁ =M ₂ ) is used for generating a noise template (Noise Template, NT), and a post-amble sequence (Post-amble) M ₃ is used for estimating the frame-level timing offset n _f .

同步过程分以下几个步骤：The synchronization process consists of the following steps:

(1)利用前同步序列中的前M₁个符号序列构造噪声模板NT₁，通过帧级的波形平均运算抑制噪声产生的影响。噪声模板NT₁构造式如下：(1) The noise template NT ₁ is constructed by using the first M ₁ symbol sequences in the preamble sequence, and the impact of the noise is suppressed through the frame-level waveform averaging operation. The noise template NT ₁ construction formula is as follows:

${p p}_{r r {f f}_{11}} ((t t)) = = \frac{11}{{M m}_{11} {N N}_{f f}} {Σ Σ}_{k k = = 00}^{{M m}_{11} {N N}_{f f} - - 11} r r ((t t + + k k {T T}_{f f})) {W W}_{f f} ((t t)),, t t &Element; &Element; [[00,, {T T}_{f f}))$

其中 $W_{f} (t) = \{\begin{matrix} 1 & t &Element; [0, T_{f}) \\ 0 & t &Element; (- \infty, 0) \cup [T_{f}, + \infty) \end{matrix},$ N_f为单个符号内的帧数，T_f为帧间隔，r(t)为载入定时偏差的接收波形，t为时间变量。in $W_{f} (t) = \{\begin{matrix} 1 & t &Element; [0, T_{f}) \\ 0 & t &Element; (- \infty, 0) \cup [T_{f}, + \infty) \end{matrix},$ N _f is the number of frames in a single symbol, T _f is the frame interval, r(t) is the received waveform loaded with timing deviation, and t is the time variable.

然后将

以T_f为周期进行延拓，扩展成长度为T_s的NT₁。新构造的NT₁如下式：Then

Carry out continuation with T _f as period, and expand into NT ₁ with length T _s . The newly constructed NT ₁ is as follows:

${p p}_{N N {T T}_{11}} ((t t)) = = {p p}_{r r {f f}_{11}} ((t t mod mod {T T}_{f f})),, t t &Element; &Element; [[00,, {T T}_{s the s}))$

其中T_s＝N_f×T_f，表示单个符号间隔。Where T _s =N _f ×T _f represents a single symbol interval.

(2)再利用前同步序列中的后M₂(通常M₁＝M₂)个符号序列构造噪声模板NT₂，通过帧级的波形平均运算抑制噪声产生的影响。模板NT₂构造式如下：(2) Construct a noise template NT ₂ by using the last M ₂ (usually M ₁ =M ₂ ) symbol sequences in the preamble sequence, and suppress the impact of noise through frame-level waveform averaging operations. The template NT ₂ constructor is as follows:

${p p}_{r r {f f}_{22}} ((t t)) = = \frac{11}{{M m}_{22} {N N}_{f f}} {Σ Σ}_{k k = = {M m}_{11} {N N}_{f f}}^{(({M m}_{11} + + {M m}_{22})) {N N}_{f f} - - 11} r r ((t t + + k k {T T}_{f f})) {W W}_{f f} ((t t)),, t t &Element; &Element; [[00,, {T T}_{f f}))$

其中 $W_{f} (t) = \{\begin{matrix} 1 & t &Element; [0, T_{f}) \\ 0 & t &Element; (- \infty, 0) \cup [T_{f}, + \infty) \end{matrix}$ in $W_{f} (t) = \{\begin{matrix} 1 & t &Element; [0, T_{f}) \\ 0 & t &Element; (- \infty, 0) \cup [T_{f}, + \infty) \end{matrix}$

然后将p_rf2(t)以T_f为周期进行延拓，扩展成长度为T_s的NT₂。构造新的NT₂如下式：Then p _rf 2(t) is extended with period T _f as _NT ₂ . Construct new NT ₂ as follows:

${p p}_{N N {T T}_{22}} ((t t)) = = {p p}_{r r {f f}_{22}} ((t t mod mod {T T}_{f f})),, t t &Element; &Element; [[00,, {T T}_{s the s}))$

(3)对生成的NT₁和NT₂，进行平均从而获得噪声模块NT，如下式所示：(3) Average the generated NT ₁ and NT ₂ to obtain the noise module NT, as shown in the following formula:

${p p}_{NT NT} ((t t)) = = \frac{{p p}_{N N {T T}_{11}} ((t t)) + + {p p}_{N N {T T}_{22}} ((t t))}{22}$

(4)对生成的NT₁和NT₂进行噪声模板互相关估计，获得表征一帧能量的参数A_ξ，如下式所示：(4) Carry out noise template cross-correlation estimation on the generated NT ₁ and NT ₂ , and obtain the parameter A _ξ that characterizes the energy of a frame, as shown in the following formula:

${\overset{^^}{A A}}_{ξ ξ} = = \frac{11}{{N N}_{f f}} {&Integral; &Integral;}_{00}^{{T T}_{S S}} {p p}_{N N {T T}_{11}} ((t t)) {p p}_{N N {T T}_{22}} ((t t)) dt dt$

(5)根据CML算法，利用估计所得A_ξ、所构造的NT、后同步序列(Post-amble)M3和其他已知参数计算帧级定时偏差量n_f，如下式所示：(5) According to the CML algorithm, use the estimated A _ξ , the constructed NT, the post-amble sequence (Post-amble) M3 and other known parameters to calculate the frame-level timing offset n _f , as shown in the following formula:

其中 $y [n] : = {&Integral;}_{0}^{T_{s}} r (t + {nT}_{s}) p_{NT} (t) dt;$ in $the y [no] : = {&Integral;}_{0}^{T_{the s}} r (t + n_{the s}) p_{NT} (t) dt;$

(6)在获得帧级定时偏差量

的基础上增加区域滑动相关搜索(Regional SlideCorrelation Search，RSCS)，通过捕捉相关峰对应的τ值来估计ξ，即：(6) When obtaining the frame-level timing offset

Add Regional Slide Correlation Search (RSCS) on the basis of , and estimate ξ by capturing the value of τ corresponding to the correlation peak, namely:

$\overset{^^}{ξ ξ} = = arg arg \underset{τ τ &Element; &Element; [[- - {T T}_{f f},, {T T}_{f f}))}{max max} {&Integral; &Integral;}_{00}^{{T T}_{s the s}} r r ((t t + + (({M m}_{11} + + {M m}_{22} + + {M m}_{33})) {T T}_{s the s} + + τ τ + + {\overset{~ ~}{τ τ}}_{00})) {p p}_{NT NT} ((t t + + τ τ {+ + \overset{^^}{τ τ}}_{00})) dt dt$

其中τ在的前后跨度为2T_f区域内步进搜索，步进大小Δτ(Δτ∈(0，T_f])根据精度的要求进行调整；而对于噪声模板NT来说，采用步进循环移位来配合相关窗口在r(t)上的滑动，以实现滑动相关运算。where τ is in The front and rear spans of 2T _f step search in the region, and the step size Δτ(Δτ∈(0, T _f ]) is adjusted according to the accuracy requirements; and for the noise template NT, a step cyclic shift is used to match the correlation The sliding of the window on r(t) to realize the sliding correlation operation.

(7)最终得到总延时估计 ${\hat{τ}}_{total} = T_{f} {\hat{n}}_{f} + \hat{ξ} .$ (7) Finally, the total delay estimate is obtained ${\hat{τ}}_{total} = T_{f} {\hat{no}}_{f} + \hat{ξ} .$

本发明中，前同步序列可由一组全“+1”序列构成：“+1，+1，…”，后同步序列由一组“+1和-1”交替排列的序列构成：“+1，-1，+1，-1…”。In the present invention, the preamble sequence can be composed of a set of all "+1" sequences: "+1, +1, ...", and the postamble sequence is composed of a set of alternately arranged sequences of "+1 and -1": "+1 , -1, +1, -1...".

有益效果Beneficial effect

本发明提供的同步方法采用的基于CML估计的新型超宽带系统同步方法充分利用了有限的训练序列进行能量的估计，采用帧级噪声抑制手段，在很大程度上改进了低信噪比情况下的参数估计精度，从而有效地改进了均方误差性能；此外，增加一级精同步，大大降低了均方误差性能的下限。The new ultra-wideband system synchronization method based on CML estimation adopted by the synchronization method provided by the present invention makes full use of the limited training sequence to estimate the energy, and adopts the frame-level noise suppression method, which greatly improves the low signal-to-noise ratio. The parameter estimation accuracy can effectively improve the mean square error performance; in addition, adding a level of fine synchronization greatly reduces the lower limit of the mean square error performance.

附图说明Description of drawings

图1：信噪比E_b/N₀＝6dB的时域信号波形比较。(a)用800个符号作波形平均；(b)用100个符号作波形平均；(c)无噪声抑制。Figure 1: Comparison of time-domain signal waveforms with a signal-to-noise ratio E _b /N ₀ =6dB. (a) Waveform averaging with 800 symbols; (b) Waveform averaging with 100 symbols; (c) No noise suppression.

图2：信噪比E_b/N₀＝6dB的时域信号波形比较，M₁＝50，N_f＝20。(a)经过信道未加噪声的信号波形；(b)经帧级平均后的信号波形；(c)经符号级平均后的信号波形；(d)无噪声抑制。Fig. 2: Comparison of time-domain signal waveforms with SNR E _b /N ₀ =6dB, M ₁ =50, N _f =20. (a) Signal waveform without noise added through the channel; (b) Signal waveform after frame-level averaging; (c) Signal waveform after symbol-level averaging; (d) No noise suppression.

图3：训练序列配置方案的比较。(a)原训练序列配置方案；(b)噪声模板互相关估计的训练序列配置方案。Figure 3: Comparison of training sequence configuration schemes. (a) Original training sequence configuration scheme; (b) Training sequence configuration scheme for noise template cross-correlation estimation.

图4：给出的是在IEEE802.15.3a的CM1信道下，累加三种不同技术和原算法的归一化均方误差性能比较。Figure 4: Shows the performance comparison of the normalized mean square error of accumulating three different technologies and the original algorithm under the CM1 channel of IEEE802.15.3a.

具体实施方式Detailed ways

在PAM-TH的IR-UWB系统中，每个信息比特由一个符号(symbol)来传输，每个符号包括N_f帧(frame)，其中每帧包含一个脉冲，帧间隔为T_f，脉冲宽度T_p＜＜T_f。因此符号间隔为T_s：＝N_fT_f。当引入跳时码(Time-hopping code，TH code)，每一帧又被划分为N_c个码片，码片间隔为T_c。TH码表示为c_j∈[0，N_c-1]，

j∈[1，N_f]，故单个符号波形为In the IR-UWB system of PAM-TH, each information bit is transmitted by a symbol (symbol), and each symbol includes N _f frames (frame), where each frame contains a pulse, the frame interval is T _f , and the pulse width T _p << T _f . The symbol interval is thus T _s := N _f T _f . When a time-hopping code (TH code) is introduced, each frame is further divided into N _c chips, and the chip interval is T _c . The TH code is expressed as c _j ∈ [0, N _c -1],

j∈[1, N _f ], so the waveform of a single symbol is

${p p}_{s the s} ((t t)) = = {Σ Σ}_{j j = = 00}^{{N N}_{f f} - - 11} p p ((t t - - j j {T T}_{f f} - - c c {T T}_{c c})) - - - - - - ((11))$

其中p(t)是脉宽为T_p的极窄脉冲波形。Among them, p(t) is a very narrow pulse waveform with pulse width T _p .

本发明主要针对二进制PAM调制，符号表示为s[n]∈{±1}，独立等概率出现，能量为ε_s。故UWB发射波形为：The present invention is mainly aimed at binary PAM modulation, the symbol is expressed as s[n]∈{±1}, independent equal probability occurs, and the energy is ε _s . Therefore, the UWB transmission waveform is:

$u u ((t t)) = = \sqrt{{ϵ ϵ}_{s the s}} {Σ Σ}_{n no = = - - \infty \infty}^{\infty \infty} s the s [[n no]] {p p}_{s the s} ((t t - - n no {T T}_{s the s})) - - - - - - ((22))$

信号u(t)经过L径的多径衰落信道，每径的衰耗和延时分别表示为{α_l}和{τ_l}，其中τ₀＜τ₁＜…＜τ_L-1。而定时同步最为关心的参数就是第一径的到达时间τ₀。因而信道的表达式可写成：The signal u(t) passes through L-path multipath fading channels, and the attenuation and delay of each path are expressed as {α _l } and {τ _l } respectively, where τ ₀ <τ ₁ <...<τ _L-1 . The most concerned parameter of timing synchronization is the arrival time τ ₀ of the first path. Thus the expression for the channel can be written as:

$h h ((t t)) = = {Σ Σ}_{l l = = 00}^{L L - - 11} {α α}_{l l} δ δ ((t t - - {τ τ}_{l l,, 00})) - - - - - - ((33))$

其中τ_l，0：＝τ_l-τ₀定义为每条多径的相对延时。Among them, τ _l,0 :=τ _l -τ ₀ is defined as the relative delay of each multipath.

由此，信号u(t)经过信道后的波形为：Therefore, the waveform of the signal u(t) after passing through the channel is:

${g g}_{s the s} ((t t)) = = {Σ Σ}_{l l = = 00}^{L L - - 11} {α α}_{l l} {p p}_{s the s} ((t t - - {τ τ}_{l l,, 00})) - - - - - - ((44))$

从而，完整的接收端信号波形为：Thus, the complete receiver signal waveform is:

$r r ((t t)) = = \sqrt{{ϵ ϵ}_{s the s}} {Σ Σ}_{n no = = - - \infty \infty}^{\infty \infty} s the s [[n no]] {g g}_{s the s} ((t t - - n no {T T}_{s the s} - - {τ τ}_{00})) + + w w ((t t)) - - - - - - ((55))$

其中，w(t)是服从均值为0、方差为σ²的加性高斯白噪声(Additive White GaussianNoise，AWGN)。Among them, w(t) is an additive white Gaussian noise (AWGN) with a mean value of 0 and a variance of ^σ2 .

不失一般性地假设τ₀∈[0，T_s)，因而可以定义τ₀：＝n_fT_f+ξ，其中n_f：＝

τ₀/T_f

，而余量ξ∈[0，T_f)。Assuming without loss of generality τ ₀ ∈ [0, T _s ), it is thus possible to define τ ₀ :=n _f T _f +ξ, where n _f :=

τ ₀ /T _f

, while the margin ξ∈[0, T _f ).

于是载入延时信息的接收端波形为：So the waveform of the receiver loading the delay information is:

$r r ((t t)) = = \sqrt{{ϵ ϵ}_{s the s}} {Σ Σ}_{n no = = - - \infty \infty}^{\infty \infty} s the s [[n no]] {g g}_{s the s} ((t t - - n no {T T}_{s the s} - - {n no}_{f f} {T T}_{f f} - - ξ ξ)) + + w w ((t t)) - - - - - - ((66))$

CML算法[1]本质上通过收集训练序列(Training Sequence，TS)的能量，从中算取定时误差，找到一帧的起始位置。因而能量收集将直接影响估计的准确性。通过接收信号与模板的相关来得到符号的能量，即The CML algorithm [1] essentially collects the energy of the training sequence (Training Sequence, TS), calculates the timing error from it, and finds the starting position of a frame. Thus energy harvesting will directly affect the accuracy of the estimation. The energy of the symbol is obtained by correlating the received signal with the template, namely

$y the y [[n no]] : : = = {&Integral; &Integral;}_{00}^{{T T}_{s the s}} r r ((t t + + {nT n}_{s the s})) {p p}_{rs rs} ((t t)) dt dt - - - - - - ((77))$

由能量的定义可知，理想模板是与r(t)完全匹配的波形。传统同步通过信道估计来生成相关模板，但密集多径条件下信道估计代价极高，故提出NT代替信道估计完成模板的构造。具体地，在训练序列的第一部分发送一组全“+1”序列，由于全“+1”序列不存在符号调制问题，故 $E {r (t)} = \sqrt{ϵ_{s}} Σ_{n = - \infty}^{\infty} g_{s} (t - n T_{s} - τ_{0}),$ 由此对连续M₁个长度为T_s的训练序列进行平均，即可获得近似的理想模板，如下式From the definition of energy, an ideal template is a waveform that completely matches r(t). Traditional synchronization uses channel estimation to generate correlation templates, but the cost of channel estimation is extremely high under dense multipath conditions, so NT is proposed to replace channel estimation to complete the construction of templates. Specifically, a set of full "+1" sequences is sent in the first part of the training sequence, since there is no symbol modulation problem in the full "+1" sequences, so $E. {r (t)} = \sqrt{ϵ_{the s}} Σ_{no = - \infty}^{\infty} g_{the s} (t - no T_{the s} - τ_{0}),$ In this way, the approximate ideal template can be obtained by averaging the continuous M ₁ training sequences of length T _s , as shown in the following formula

${\overset{~ ~}{p p}}_{rs rs} ((t t)) = = \frac{11}{{M m}_{11}} {Σ Σ}_{k k = = 00}^{{M m}_{11} - - 11} r r ((t t + + k k {T T}_{s the s})) {W W}_{s the s} ((t t)),, t t &Element; &Element; [[00,, {T T}_{s the s})) - - - - - - ((88))$

$= = x x ((t t)) + + \frac{11}{{M m}_{11}} {Σ Σ}_{k k = = 00}^{{M m}_{11} - - 11} w w ((t t)) {W W}_{s the s} ((t t))$

其中， $x (t) = \{\begin{matrix} g_{s} (t - τ_{0}) & t &Element; [τ_{0}, T_{s}) \\ g_{s} (t + T_{s} - τ_{0}) & t &Element; [0, τ_{0}) \end{matrix}$

in,

x (t) = \{\begin{matrix} g_{the s} (t - τ_{0}) & t &Element; [τ_{0}, T_{the s}) \\ g_{the s} (t + T_{the s} - τ_{0}) & t &Element; [0, τ_{0}) \end{matrix}

被称为噪声模板(Noise Template)，原因在于

包含了多径的各条分支、延时τ₀以及噪声分量。 It is called the noise template (Noise Template) because the

Contains each branch of multipath, time delay τ ₀ and noise component.

经过平均之后，噪声分量的方差降为σ²/M₁，随着M₁的增加，NT则趋近于理想模板。After averaging, the variance of the noise component decreases to σ ² /M ₁ , and with the increase of M ₁ , NT approaches the ideal template.

然而，观察信噪比相对较低时的波形(如图1(a))发现即使是M₁＝100，都无法有效地抑制噪声；尝试用800个符号作平均(如图1(b))才部分抑制了噪声。而实际通信当中，用800个符号完成一次同步代价相当大，很大程度上限制了波特率。考虑到平均运算是建立在接收信号的周期性之上，因而缩短平均运算的周期将大大增加平均运算的次数，使模板受噪声影响更小。为此，本发明提出帧级噪声抑制(Frame-level Noise Suppression，FNS)概念。帧级噪声抑制是将平均运算的周期降至帧级，此时训练序列比特不能引入TH码。分析TH码在UWB通信中的三大功能：1)为信息比特提供多址接入(Multi-access，MA)；2)白化频谱以减小对其他通信方式的干扰；3)支持数据的低截获率(Low Probability ofInterception，LPI)。由于训练序列只占整个比特流的很小一部分，因此这种方案将不会对上述三点产生影响。However, observing the waveform when the signal-to-noise ratio is relatively low (as shown in Figure 1(a)), it is found that even M ₁ =100 cannot effectively suppress the noise; try to use 800 symbols for averaging (as shown in Figure 1(b)) The noise is only partially suppressed. In actual communication, the cost of completing a synchronization with 800 symbols is quite high, which limits the baud rate to a large extent. Considering that the average operation is based on the periodicity of the received signal, shortening the period of the average operation will greatly increase the number of average operations, making the template less affected by noise. For this reason, the present invention proposes the concept of frame-level noise suppression (Frame-level Noise Suppression, FNS). Frame-level noise suppression is to reduce the period of the average operation to the frame level, and at this time, the training sequence bits cannot be introduced into the TH code. Analyze the three major functions of TH codes in UWB communication: 1) Provide multiple access (Multi-access, MA) for information bits; 2) Whiten spectrum to reduce interference to other communication methods; 3) Support data low Interception rate (Low Probability of Interception, LPI). Since the training sequence only occupies a very small part of the whole bit stream, this scheme will not affect the above three points.

通过帧级噪声抑制方式构造NT如下式所示：Constructing NT by frame-level noise suppression is shown in the following formula:

${\overset{~ ~}{p p}}_{rf rf} ((t t)) = = \frac{11}{{M m}_{11} {N N}_{f f}} {Σ Σ}_{k k = = 00}^{{M m}_{11} {N N}_{f f} - - 11} r r ((t t + + k k {T T}_{f f})) {W W}_{f f} ((t t)),, t t &Element; &Element; [[00,, {T T}_{f f})) - - - - - - ((99))$

其中

in

随后将

以T_f为周期进行延拓如下式，扩展成长度为T_s的NT，即可进行能量的收集。新构造的NT如下式will subsequently

Taking T _f as the period to extend the following formula, the NT with the length of T _s can be expanded to collect energy. The newly constructed NT is as follows

${\overset{~ ~}{P P}}_{NT NT} ((t t)) = = {\overset{~ ~}{p p}}_{rf rf} ((t t mod mod {T T}_{f f})),, t t &Element; &Element; [[00,, {T T}_{s the s})) - - - - - - ((1010))$

若采用M₁个符号进行平均，每个符号包含N_f帧，则符号级平均方式下，噪声方差为σ²/M₁；而帧级平均可使噪声方差下降至σ²/(M₁N_f)，由图2，可以看到在较低信噪比的环境中，帧级平均运算的噪声抑制能力比符号级平均运算强很多。If M ₁ symbols are used for averaging, and each symbol contains N _f frames, then in symbol-level averaging, the noise variance is σ ² /M ₁ ; while frame-level averaging can reduce the noise variance to σ ² /(M ₁ N _f ), from Figure 2, it can be seen that in an environment with a lower SNR, the noise suppression capability of the frame-level averaging operation is much stronger than that of the symbol-level averaging operation.

NT构造完成以后，便可以开始利用前同步序列和NT进行参数估计。除了之前提到的M₁个用来构建NT的全“+1”序列之外，为了参数估计的需要，还另外配置了一组后同步序列由两个互斥的子集构成：S₊：＝{s[n]＝s[n-1]}和S_-：＝{s[n]＝-s[n-1]}，其中M₂和M₃分别为集合S₊和S_-的势。After the NT is constructed, the preamble and the NT can be used for parameter estimation. In addition to the previously mentioned M ₁ full "+1" sequences used to construct NT, for the needs of parameter estimation, an additional set of post-synchronization sequences is configured consisting of two mutually exclusive subsets: S ₊ : ={s[n]=s[n-1]} and S _- :={s[n]=-s[n-1]}, where M ₂ and M ₃ are the potentials of sets S ₊ and S _- respectively .

根据[1]附录A中的推导得到y[n]的显性表达式为：According to the derivation in Appendix A of [1], the explicit expression of y[n] is:

y[n]＝A_ξ(s[n](N_f-n_f-λ_ξ)+s[n-1](n_f+λ_ξ))+w[n] (11)y[n]=A _ξ (s[n](N _f -n _f -λ _ξ )+s[n-1](n _f +λ _ξ ))+w[n] (11)

其中 $A_{ξ} : = \sqrt{ϵ_{s}} {&Integral;}_{0}^{T_{f}} g_{s} (t + T_{f} - ξ) p_{rf} (t) dt$ 表示一帧的能量。(11)表明由于延时的存在，y[n]收集到的能量是前后两个连续符号的能量，而CML算法正是利用前后两部分能量来估计延时。in $A_{ξ} : = \sqrt{ϵ_{the s}} {&Integral;}_{0}^{T_{f}} g_{the s} (t + T_{f} - ξ) p_{rf} (t) dt$ Represents the energy of a frame. (11) shows that due to the existence of delay, the energy collected by y[n] is the energy of two consecutive symbols before and after, and the CML algorithm uses the two parts of energy before and after to estimate the delay.

[5]通过CML的方法推导得到参数A_ξ估计的解析表达式为：[5] The analytical expression of parameter A _ξ estimated by derivation by CML method is:

${\overset{^^}{A A}}_{ξ ξ} = = \frac{11}{{N N}_{f f} {M m}_{22}} \underset{n no &Element; &Element; {S S}_{+ +}}{Σ Σ} y the y [[n no]] s the s [[n no]]$

观察上式发现，对于A_ξ的估计，本质上是利用集合S₊内的全“+1”序列估计得到一帧的能量。估计A_ξ的精确与否又直接影响到n_f的估计精度。由此本发明提出噪声模板互相关估计(NT Cross-correlation Estimation，NTCE)的方式来估计A_ξ，进一步抑制噪声的影响。Observing the above formula, it is found that the estimation of A _ξ essentially uses all "+1" sequences in the set S ₊ to estimate the energy of one frame. The accuracy of estimating A _ξ directly affects the estimation accuracy of n _f . Therefore, the present invention proposes a noise template cross-correlation estimation (NT Cross-correlation Estimation, NTCE) method to estimate A _ξ to further suppress the influence of noise.

噪声模板互相关估计方法如图3(b)所示，利用前同步序列产生两个噪声无相关性的模板NT₁和NT₂，并采用NT的互相关来估计A_ξ，即The noise template cross-correlation estimation method is shown in Fig. 3(b). The preamble sequence is used to generate two noise-free correlation templates NT ₁ and NT ₂ , and the cross-correlation of NT is used to estimate A _ξ , namely

${\overset{^^}{A A}}_{ξ ξ}^{* *} = = \frac{11}{{N N}_{f f}} {&Integral; &Integral;}_{00}^{{T T}_{s the s}} {\overset{~ ~}{p p}}_{{NT NT}_{11}} ((t t)) \overset{~ ~}{{p p}_{N N {T T}_{22}}} ((t t)) dt dt - - - - - - ((1313))$

可以看出，改变了估计器的设计之后，相关操作的两个分量均经过帧级噪声抑制的处理，而原CML算法的A_ξ估计，见式(12)，其中y[n]只经过少量的符号级噪声抑制处理，因此A_ξ的估计性能明显不如噪声模板互相关估计。It can be seen that after changing the design of the estimator, the two components of the related operation are processed by frame-level noise suppression, while the A _ξ estimation of the original CML algorithm is shown in formula (12), where y[n] only undergoes a small amount of The symbol-level noise suppression processing of , so the estimation performance of _Aξ is significantly inferior to the noise template cross-correlation estimation.

A_ξ估计完成之后代入到n_f估计的表达式中即可获得粗同步的延时估计，即After the _Aξ estimation is completed, it can be substituted into the expression of n _f estimation to obtain the delay estimation of coarse synchronization, that is

原CML算法在信噪比高于一定水平以后，均方误差存在性能下限，究其原因是因为最终获得的延时估计 ${\hat{τ}}_{0} = T_{f} {\hat{n}}_{f}$ 为T_f的整数倍，因而ξ不可避免地成为了估计器的系统误差。为了进一步改善高信噪比环境下的估计精度，增加一级基于滑动相关搜索(SlideCorrelation Search，SCS)的精同步算法，通过捕捉相关峰对应的τ值来估计ξ，即After the original CML algorithm has a higher signal-to-noise ratio than a certain level, the mean square error has a performance lower limit. The reason is that the final delay estimate ${\hat{τ}}_{0} = T_{f} {\hat{no}}_{f}$ is an integer multiple of T _f , so ξ inevitably becomes the systematic error of the estimator. In order to further improve the estimation accuracy in high SNR environment, a fine synchronization algorithm based on Slide Correlation Search (SCS) is added to estimate ξ by capturing the value of τ corresponding to the correlation peak, namely

$\overset{^^}{ξ ξ} = = arg arg \underset{τ τ &Element; &Element; [[- - {T T}_{f f},, {T T}_{f f}))}{max max} {&Integral; &Integral;}_{00}^{{T T}_{s the s}} r r ((t t + + (({M m}_{11} + + {M m}_{22} + + {M m}_{33})) {T T}_{s the s} + + {\overset{~ ~}{τ τ}}_{00} + + τ τ)) {\overset{~ ~}{p p}}_{NT NT} ((t t + + \overset{~ ~}{{τ τ}_{00}} + + τ τ)) dt dt - - - - - - ((1515))$

其中τ在

的前后2T_f范围内步进搜索，采用怎样的步进来搜索该区域可以根据精度的要求进行调整；而对于NT来说，采用步进循环移位来配合相关窗口在r(t)上的滑动，以实现滑动相关运算。where τ is in

Step search in the range of 2T _f before and after, what step to use to search this area can be adjusted according to the accuracy requirements; and for NT, step cyclic shift is used to match the relative window on r(t) Swipe to implement sliding related operations.

最终得到总延时估计 ${\tilde{τ}}_{total} = T_{f} {\hat{n}}_{f} + \hat{ξ} .$ Finally, the total delay estimate is obtained ${\tilde{τ}}_{total} = T_{f} {\hat{no}}_{f} + \hat{ξ} .$

同步完成之后，通过

可以确定符号的起始位置，同时，将载入帧级噪声模板对其进行帧内部的时域校正，并引入跳时延拓即可构造出带TH码的解调模板。考虑到TH码所引入的帧间干扰(Inter-frame Interference，IFI)，对于每一帧模板的构造都需要累加前一帧甚至是前两帧的影响(视信道长度而定，这里假设

τ_{L} + T_{c} \max_{k &Element; [1, N_{f})} (c_{k}) \leq 2 T_{f}) .

于是构造解调NT的方法如下所示。After synchronization is complete, pass

The starting position of the symbol can be determined, and at the same time, the The demodulation template with TH code can be constructed by loading the frame-level noise template to correct it in the time domain within the frame, and introducing time-hopping extension. Considering the inter-frame interference (Inter-frame Interference, IFI) introduced by the TH code, the construction of each frame template needs to accumulate the influence of the previous frame or even the previous two frames (depending on the channel length, it is assumed here that

τ_{L} + T_{c} \max_{k &Element; [1, N_{f})} (c_{k}) \leq 2 T_{f}) .

Then the method of constructing the demodulation NT is as follows.

首先引入对

进行循环移位，则first import right

Perform a cyclic shift, then

${\overset{~ ~}{p p}}_{rf rf} ((t t;; \overset{^^}{ξ ξ})) = = \{\begin{matrix} {\overset{~ ~}{p p}}_{rf rf} ((t t - - \overset{^^}{ξ ξ})) & t t &Element; &Element; [[\overset{^^}{ξ ξ},, {T T}_{f f})) \\ {\overset{~ ~}{p p}}_{rf rf} ((t t + + {T T}_{f f} - - \overset{^^}{ξ ξ})) & t t &Element; &Element; [[00,, \overset{^^}{ξ ξ})) \end{matrix} - - - - - - ((1616))$

再对

进行跳时处理，由于需考虑当前和之前一帧的影响，故again

For time-hopping processing, since the influence of the current and previous frames needs to be considered,

${\overset{~ ~}{p p}}_{rf rf - - TH TH}^{((k k))} ((t t;; \overset{^^}{ξ ξ})) = = \{\begin{matrix} {\overset{~ ~}{p p}}_{rf rf} ((t t - - {c c}_{k k} {T T}_{c c};; \overset{^^}{ξ ξ})) & t t &Element; &Element; [[{c c}_{k k} {T T}_{c c},, {c c}_{k k} {T T}_{c c} + + {T T}_{f f})) \\ 00 & t t &Element; &Element; [[00,, {c c}_{k k} {T T}_{c c})) \cup \cup t t &Element; &Element; [[{c c}_{k k} {T T}_{c c} + + {T T}_{f f},, 22 {T T}_{f f})) \end{matrix} k k &Element; &Element; [[11,, {N N}_{f f})) - - - - - - ((1717))$

最后进行时域展开，得到Finally, the time-domain expansion is carried out to obtain

${p p}_{NT NT - - De De mod mod} ((t t)) = = \{\begin{matrix} {\overset{~ ~}{p p}}_{rf rf - - TH TH}^{((11))} ((t t;; \overset{^^}{ξ ξ})) & t t &Element; &Element; [[00,, {T T}_{f f})) \\ {\overset{~ ~}{p p}}_{rf rf - - TH TH}^{((22))} ((t t - - {T T}_{f f};; \overset{^^}{ξ ξ})) + + {\overset{~ ~}{p p}}_{rf rf - - TH TH}^{((11))} ((t t;; \overset{^^}{ξ ξ})) & t t &Element; &Element; [[{T T}_{f f},, 22 {T T}_{f f})) \\ . . \\ . . \\ . . \\ {\overset{~ ~}{p p}}_{rf rf - - TH TH}^{((k k))} ((t t - - ((k k - - 11)) {T T}_{f f};; \overset{^^}{ξ ξ})) + + {\overset{~ ~}{p p}}_{rf rf - - TH TH}^{((k k - - 11))} ((t t - - ((k k - - 22)) {T T}_{f f};; \overset{^^}{ξ ξ})) & t t &Element; &Element; [[((k k - - 11)) {T T}_{f f},, k k {T T}_{f f})) \\ . . \\ . . \\ . . \\ {\overset{~ ~}{p p}}_{rf rf - - TH TH}^{(({N N}_{f f}))} ((t t - - (({N N}_{f f} - - 11)) {T T}_{f f};; \overset{^^}{ξ ξ})) + + {\overset{~ ~}{p p}}_{rf rf - - TH TH}^{(({N N}_{f f} - - 11))} ((t t - - (({N N}_{f f} - - 22)) {T T}_{f f};; \overset{^^}{ξ ξ})) & t t &Element; &Element; [[(({N N}_{f f} - - 11)) {T T}_{f f},, {T T}_{s the s})) \end{matrix} - - - - - - ((1818))$

针对BPSK-UWB系统进行MATLAB仿真。采用改进型S-V模型中CM₁信道(LOS 0-4m)，信道参数为(1/Λ，1/λ，Γ，γ)＝(43，0.4，7.1，4.3)ns。所用脉冲波形为单位能量的高斯二阶脉冲，脉冲宽度为1ns。基本参数如下：N_f＝20，T_f＝50ns。配置训练序列M₁＝M₂＝M₃＝20。加入SCS算法时，令步进长度Δ＝T_f/20。将本文三种改进方案逐一加载到CML算法上进行优化，采用归一化均方误差(Normalized MSE， $NMSE = E {{| ({\hat{τ}}_{0} - τ_{0}) / T_{s} |}^{2}})$ 分析其同步性能，仿真结果如图4所示。Perform MATLAB simulation for BPSK-UWB system. Using the CM ₁ channel (LOS 0-4m) in the improved SV model, the channel parameters are (1/Λ, 1/λ, Γ, γ) = (43, 0.4, 7.1, 4.3) ns. The pulse waveform used is a second-order Gaussian pulse with unit energy, and the pulse width is 1 ns. The basic parameters are as follows: N _f =20, T _f =50 ns. Configure the training sequence M ₁ =M ₂ =M ₃ =20. When adding the SCS algorithm, let the step length Δ=T _f /20. Load the three improvement schemes in this paper to the CML algorithm one by one for optimization, and use the normalized mean square error (Normalized MSE, $NMSE = E. {{| ({\hat{τ}}_{0} - τ_{0}) / T_{the s} |}^{2}})$ Analyze its synchronization performance, and the simulation results are shown in Figure 4.

仿真结果表明，FNS和NTCE确实在一定程度上改善了低信噪比情况下的同步精度，然而在高信噪比下算法的目标是粗同步，精度在一帧范围左右，因此FNS和NTCE并没有能力突破理论上存在的下限；当追加一级SCS精同步估计，均方性能下限被突破一个数量级左右。然而，从图4中可以发现，SCS无法优化低信噪比情况下的均方性能，原因在于总的延时估计 ${\hat{τ}}_{0} = T_{f} {\hat{n}}_{f} + \hat{ξ},$ 其中

占了很大的比重，一旦

出现较大的偏差，

的精确与否对总延时的估计贡献不大，故启用SCS的前提是帧级已获得正确的延时估计。The simulation results show that FNS and NTCE do improve the synchronization accuracy in the case of low SNR to a certain extent, but the goal of the algorithm is coarse synchronization under high SNR, and the accuracy is about one frame, so FNS and NTCE do not There is no ability to break through the theoretical lower limit; when an additional level of SCS fine synchronization estimation is added, the lower limit of the mean square performance is broken by about an order of magnitude. However, it can be seen from Fig. 4 that SCS cannot optimize the mean square performance in the case of low SNR because the total delay estimate

{\hat{τ}}_{0} = T_{f} {\hat{no}}_{f} + \hat{ξ},

in

accounted for a large proportion, once

There is a large deviation,

The accuracy of the frame rate does not contribute much to the estimation of the total delay, so the premise of enabling SCS is that the correct delay estimate has been obtained at the frame level.

以上所述为本发明的较佳的具体实施方式，但本发明的保护范围并不局限于此，任何熟悉本领域的技术人员在本发明说明的技术范围内，可轻易想到的变化或替换，都应涵盖在本发明的保护范围之内。因此，本发明的保护范围应该以权利要求书的保护范围为准。The above description is a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto, any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention, All should be covered within the protection scope of the present invention. Therefore, the protection scope of the present invention should be determined by the protection scope of the claims.

参考文献references

[1]Zhi Tian and G B.Giannakis，“A GLRT Approach to Data-Aided Timing Acquisitionin UWB Radios-Part I：Algorithms”，IEEE Transactions on wireless communications，Vol.4，No.6，pp.2956-2967，Nov.2005[1] Zhi Tian and G B. Giannakis, "A GLRT Approach to Data-Aided Timing Acquisition in UWB Radios-Part I: Algorithms", IEEE Transactions on wireless communications, Vol.4, No.6, pp.2956-2967, Nov.2005

Claims

1. A method for synchronizing an ultra-wideband communication system based on conditional maximum likelihood estimation, characterized in that: at first one group of training sequences will be constructed, and this training sequence is made up of two parts, a preamble sequence and a postamble sequence, wherein the preamble sequence M ₁ + M ₂ is used for the generation of noise template NT, the post-synchronization sequence, and M ₃ is used for estimating the frame-level timing offset n _f ;

The specific steps of the synchronization process are as follows:

(1) The noise template NT ₁ is constructed by using the first M ₁ symbol sequences in the preamble sequence, and the influence of noise is suppressed through the frame-level waveform averaging operation. The construction formula of the noise template NT ₁ is as follows:

in

N _f is the number of frames in a single symbol, T _f is the frame interval, r(t) is the received waveform loaded with timing deviation, and t is the time variable;

Then

The extension is carried out with T _f as the period, and it is expanded into NT ₁ with a length of T _s . The newly constructed NT ₁ is as follows:

Where T _s =N _f ×T _f represents a single symbol interval;

(2) Use the last M ₂ symbol sequences in the preamble sequence to construct the noise template NT ₂ , and suppress the influence of noise through the frame-level waveform averaging operation. The template NT ₂ construction formula is as follows:

in

Then

Extending with T _f as the period, expanding into NT ₂ with a length of T _s , the constructed NT ₂ is as follows:

(3) Average the generated NT ₁ and NT ₂ to obtain the noise template NT, as shown in the following formula:

(4) Carry out noise template cross-correlation estimation on the generated NT ₁ and NT ₂ to obtain a parameter estimation representing the energy of a frame As shown in the following formula:

(5) According to the CML algorithm, use the estimation obtained in (4)

The noise template NT constructed in (3), the post-synchronization sequence M3 and other known parameters calculate the estimated value of the frame-level timing deviation

As shown in the following formula:

in

s[n]∈{±1} is the transmitted information symbol; S- is a subset of the transmitted information symbol, and satisfies the opposite condition of adjacent information symbols S-:={s[n]=-s[n- 1]};

(6) When obtaining the estimated value of the frame-level timing offset

based on the definition

And increase the regional sliding correlation search, and estimate ξ by capturing the ξ value corresponding to the correlation peak, namely:

where ξ is in

The front and rear spans of 2T _f step search in the region, and the step size Δτ, Δτ∈(0, T _f ] is adjusted according to the accuracy requirements; and for the noise template NT, a step cyclic shift is used to match the correlation window Sliding on r(t) to realize sliding correlation operation;

(7) Finally, the total delay estimate is obtained

2. the UWB communication system synchronization method based on conditional maximum likelihood estimation as claimed in claim 1, is characterized in that in described step (1), preamble sequence is made of one group of full "+1" sequence, modulation The method is BPSK.

3. the ultra-wideband communication system synchronization method based on conditional maximum likelihood estimation as claimed in claim 1, is characterized in that in described step (6), post-synchronization sequence is by the sequence that one group of +1 and-1 are alternately arranged Composition: "+1, -1, +1, -1...". the