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1、一种基于信噪比最大化的信号恢复方法王心怡，苗晟，郝铁伟（昆明船舶设备研究试验中心，昆明，650051）摘 要：本文针对平稳噪声下的信号恢复问题，提出一种信噪比最大化指标函数，利用混合信号中噪声的协方差矩阵先验知识，通过多通道信号的线性组合，恢复出需要检测的信号，并使其信噪比最大化。本文对方法进行了推导，并进行仿真，结果表明，这种基于信噪比最大化的信号恢复方法能够在信号和噪声频谱有较大重叠的情况下，增强信号同时抵消噪声，以最大信噪比恢复出需要的信号，效果明显，具有良好的实际应用价值。关键词：信号恢复；噪声抵消；信噪比中图分类号：TP274文献标识码：A文章编号：1000-8829（2011）期数
2、-XXXX-XXA Signal Recovery Method based on SNR Maximization Wang Xinyi, Miao Sheng, Hao Tiewei（Kunming shipbuilding Equipment Research and Test Center, Kunming, 650051）Abstract: A signal recovery method based on SNR maximization is proposed in this paper, this method use a priori knowledge of the cov
3、ariance matrix of noise in the mixed signal, recover the required signal and maximize the SNR by linear combination of multi-channel received signal. The method is derived and simulated in this paper, the result shows that the signal recovery method based on SNR maximization can enhance signal and c
4、ancel noise in the circumstance that signal and noise have overlapped spectrum, and the recovered signal has maximal SNR, the method has a obviously good performance and good application value. Key words: signal recovery; noise canceling; signal-to-noise ratio收稿日期：2011-XX-XX作者简介：王心怡(1983-), 男, 汉族, 硕
5、士,工程师, 研究方向为水下电磁场、水声信号处理。在噪声环境下，恢复信号波形，对信号检测，信号参数估计等都是重要的。当噪声与信号的频谱有较大重叠时，通常的滤波降噪方法效果不理想；有些情况下，能够在采集信号的同时采集到与噪声相关的参考信号，可以采用自适应抵消的方法1。但是很多情况下，噪声和信号是混合在一起被检测到的，例如在有电磁噪声干扰的环境内检测外部电磁信号，就无法同时采集到与电磁噪声相关，而与外部信号不相关的参考信号，不具备自适应干扰抵消的使用条件。利用噪声的统计特性先验知识，对混合信号中的噪声成分进行抵消，恢复出需要检测的信号，是一项很有实际应用价值的研究。在封闭环境内，同一位置的电磁噪声
6、可以看作是平稳的，通常这也符合实际情况，其功率谱的分布特征是不变的，可以利用这个条件，在没有外部信号时，事先采集环境中的噪声，估计噪声的某些统计特性，以消除混合信号中的噪声成分。在频域中进行谱减法是常用的一种方法2，但在信号与噪声频谱重叠较多的情况下，将噪声成分减掉，有可能影响信号的频谱，并且由于信号采集长度很短，使频率分辨间隔较大，许多噪声成分淹没在真实信号的谱峰中，无法识别，会对信号参数估计结果产生影响。利用事先获得的外部信号及噪声的某些先验知识，可以通过参考独立分量分析等方法提取出需要的信号3，但很多情况下是无法获得检测信号先验知识的，并且经常存在独立噪声源数目较多，使混合信号中的独立分
7、量数目大于传感器通道数的情况，给信号提取带来很大困难。对于电磁信号，不同位置的传感器或同一个传感器的不同通道，检测的信号不存在时延，因此每个通道的检测信号都可以看作是噪声与外部信号的线性混合，并且不同通道检测信号中的噪声成分具有相干的部分，使用多个传感器，或一个传感器的多个通道进行联合检测，可以通过每个通道检测信号的线性组合，将噪声抵消，恢复出需要检测的信号。如果每个通道中的噪声不是完全相干的，将不能被完全抵消，恢复出的信号中将含有部分噪声，本文通过研究，利用混合信号的协方差矩阵以及噪声协方差矩阵含有的先验知识，提出一种使恢复出的信号的信噪比最大化的方法，文中推导了该算法，给出了结果，并通过仿
8、真对信号恢复效果进行验证。1 信噪比最大化准则基于信噪比最大化的信号恢复方法，要求混合信号为信号和噪声的线性混合，噪声是平稳的，不同传感器接收的噪声可以分为相干的部分和相互独立的部分，噪声的相干性在一段时间内保持不变。设待恢复的原始信号为，个传感器通道的噪声分为和两部分，为相干的部分，为相互独立的部分，并且与也是相互独立的，这通常也符合实际情况，则传感器接收的维混合信号为，其中为维混合向量，表示信号被传感器个通道接收的权值。信号恢复的目的是求出一个向量，恢复出信号，并使其信噪比最大化，即，和分别为恢复出的信号中原始信号和噪声的功率，为方便叙述，下文的推导中将维噪声记为。2 基于信噪比最大化的信
9、号恢复算法信号的功率可以用二阶统计量来表示，即用样本的协方差来度量， （1）其中为多通道接收噪声的协方差矩阵。然而实际上恢复出信号的仍然是原始信号的估计与线性组合噪声的混合信号，无法直接获得信噪比，需要选择另外一个可以直接进行计算的指标函数。由于噪声的能量和功率谱在一段时间内基本不变，可以使用事先采样的噪声样本估计，选择指标函数为混合信号与事先采样噪声的功率比，即 （2）其中为多通道接收混合信号的协方差矩阵。与相互独立，则与也是相互独立的，有（3）因此最大化信噪比，可以通过最大化指标函数来实现。协方差矩阵是对称、正定的，可以通过奇异值分解计算出方根和逆方根，令，则指标函数， （4）其中。则指标
10、函数可以看作矩阵的Rayleigh商， 可以计算的梯度为 （5）则对应于的极值点处，满足 （6）可以约束为单位长度，即，若是对应于最大特征值的单位长度特征向量，则可以满足，且取极大值，。由此可以得到恢复出的信号为 （7）达到的最大信噪比为 （8）3 仿真验证为了直观地表示出本文方法的信号恢复效果，这里对单频正弦信号的恢复进行仿真，通过恢复信号的参数估计结果来验证方法的有效性。设通道数为3，需要检测的原始信号为信号的混合向量。噪声为谐波信号加白噪声，每个通道的噪声含有相互独立的白噪声成分，噪声中的谐波信号含有个频率成分，每个频率成分对应一个独立分量，在每个通道中，不同频率成分之间的相对幅度有所不
11、同。用表示第个通道的噪声的相干成分，为采样点，即，在仿真中，取，原始信号和噪声中频率成分（Hz）参数如下，幅度采用归一化表示，混合信号的采样点数为2048，采样率，每个通道的混合信号的波形和幅度谱如图1所示。a)b)c)图1 混合信号的波形及幅度谱局部可以看出，需要恢复的正弦信号淹没在噪声中，从幅度谱上无法分辨出来。采用单频正弦信号的参数估计方法处理每个通道的混合信号4，得到的频率估计结果为，可见该噪声对正弦信号的参数估计结果影响严重，主要是由于噪声中与真实信号邻近的频率成分造成的。采用本文的方法对正弦信号进行恢复，事先采样的每个通道噪声的波形和幅度谱如图2所示a)b)c)图2 事先采集噪声的
12、波形及幅度谱局部使用该段噪声估计，恢复出的原始信号的波形和幅度谱如图3所示。图3 恢复信号的波形及幅度谱局部可以看出，噪声中相干的部分基本上已被抵消，恢复出的信号为原始信号加白噪声，以及部分未被完全抵消的谐波信号。对恢复的信号进行频率估计，得到结果为可见，采用本文方法能够恢复出噪声中的正弦信号，在参数估计等应用场合，可以有效消除噪声中邻近频率成分的影响。本文方法的一个使用条件是，噪声中谐波的每个频率成分至少出现在两个通道中，否则，如果某些频率成分只在一个通道的混合信号中出现，那么该频率成分将无法通过多通道信号的线性组合被抵消。需要注意的是，平稳噪声的协方差矩阵理论上是不变的，但实际上由于样本的
13、采样点数有限，因此使用事先采集的噪声样本估计的并不能完全代表混合信号中的噪声协方差，尤其是当样本的采样点数较少时，随时间变化更加显著，影响信号恢复效果。在条件允许时，可以采集更多点数的噪声样本估计，使其尽可能接近期望值。4 结论本文针对平稳噪声下，瞬时线性混合信号中独立分量数目大于传感器数目，或是混合信号中含有白噪声而无法实现信号有效分离的情况，在噪声的协方差矩阵先验知识能够获得的条件下，提出一种基于信噪比最大化准则的信号恢复方法，根据噪声和混合信号的协方差矩阵，通过多通道混合信号的线性组合，得到信噪比最大化的恢复信号。仿真结果表明，该方法能够有效增强信号，抵消噪声，具有较好的实用性和推广前景
14、。参考文献：1 申晓红, 赵宝珍, 王海燕. 基于ALE的高分辨频率估计新方法研究J. 探测与控制学报, 2007, 29(1): 5-8.2 Boll S F. Suppression of Acoustic Noise in Speech Using Spectral SubtractionJ. IEEE Trans on Acoustics, Speech & Signal Processing, 1979, 27(2): 113-120. 3 陈寿齐, 沈越泓, 马明等. 基于峭度的稳健特定信号盲提取J. 系统仿真学报, 2008, 20(22): 4 H.Renders, J.Sch
15、oukens, and G.Vilain. High-accuracy spectrum analysis of sampled discrete frequency signals by analytical leakage compensationJ. IEEE Trans.Instrum.Meas., 1984, vol.1M-33,pp, 287-292.Editors note: Judson Jones is a meteorologist, journalist and photographer. He has freelanced with CNN for four years
16、, covering severe weather from tornadoes to typhoons. Follow him on Twitter: jnjonesjr (CNN) - I will always wonder what it was like to huddle around a shortwave radio and through the crackling static from space hear the faint beeps of the worlds first satellite - Sputnik. I also missed watching Nei
17、l Armstrong step foot on the moon and the first space shuttle take off for the stars. Those events were way before my time.As a kid, I was fascinated with what goes on in the sky, and when NASA pulled the plug on the shuttle program I was heartbroken. Yet the privatized space race has renewed my chi
18、ldhood dreams to reach for the stars.As a meteorologist, Ive still seen many important weather and space events, but right now, if you were sitting next to me, youd hear my foot tapping rapidly under my desk. Im anxious for the next one: a space capsule hanging from a crane in the New Mexico desert.
19、Its like the set for a George Lucas movie floating to the edge of space.You and I will have the chance to watch a man take a leap into an unimaginable free fall from the edge of space - live.The (lack of) air up there Watch man jump from 96,000 feet Tuesday, I sat at work glued to the live stream of
20、 the Red Bull Stratos Mission. I watched the balloons positioned at different altitudes in the sky to test the winds, knowing that if they would just line up in a vertical straight line we would be go for launch.I feel this mission was created for me because I am also a journalist and a photographer
21、, but above all I live for taking a leap of faith - the feeling of pushing the envelope into uncharted territory.The guy who is going to do this, Felix Baumgartner, must have that same feeling, at a level I will never reach. However, it did not stop me from feeling his pain when a gust of swirling w
22、ind kicked up and twisted the partially filled balloon that would take him to the upper end of our atmosphere. As soon as the 40-acre balloon, with skin no thicker than a dry cleaning bag, scraped the ground I knew it was over.How claustrophobia almost grounded supersonic skydiverWith each twist, yo
23、u could see the wrinkles of disappointment on the face of the current record holder and capcom (capsule communications), Col. Joe Kittinger. He hung his head low in mission control as he told Baumgartner the disappointing news: Mission aborted.The supersonic descent could happen as early as Sunday.T
24、he weather plays an important role in this mission. Starting at the ground, conditions have to be very calm - winds less than 2 mph, with no precipitation or humidity and limited cloud cover. The balloon, with capsule attached, will move through the lower level of the atmosphere (the troposphere) wh
25、ere our day-to-day weather lives. It will climb higher than the tip of Mount Everest (5.5 miles/8.85 kilometers), drifting even higher than the cruising altitude of commercial airliners (5.6 miles/9.17 kilometers) and into the stratosphere. As he crosses the boundary layer (called the tropopause), h
26、e can expect a lot of turbulence.The balloon will slowly drift to the edge of space at 120,000 feet (22.7 miles/36.53 kilometers). Here, Fearless Felix will unclip. He will roll back the door.Then, I would assume, he will slowly step out onto something resembling an Olympic diving platform.Below, th
27、e Earth becomes the concrete bottom of a swimming pool that he wants to land on, but not too hard. Still, hell be traveling fast, so despite the distance, it will not be like diving into the deep end of a pool. It will be like he is diving into the shallow end.Skydiver preps for the big jumpWhen he
28、jumps, he is expected to reach the speed of sound - 690 mph (1,110 kph) - in less than 40 seconds. Like hitting the top of the water, he will begin to slow as he approaches the more dense air closer to Earth. But this will not be enough to stop him completely.If he goes too fast or spins out of cont
29、rol, he has a stabilization parachute that can be deployed to slow him down. His team hopes its not needed. Instead, he plans to deploy his 270-square-foot (25-square-meter) main chute at an altitude of around 5,000 feet (1,524 meters).In order to deploy this chute successfully, he will have to slow
30、 to 172 mph (277 kph). He will have a reserve parachute that will open automatically if he loses consciousness at mach speeds.Even if everything goes as planned, it wont. Baumgartner still will free fall at a speed that would cause you and me to pass out, and no parachute is guaranteed to work highe
31、r than 25,000 feet (7,620 meters).It might not be the moon, but Kittinger free fell from 102,800 feet in 1960 - at the dawn of an infamous space race that captured the hearts of many. Baumgartner will attempt to break that record, a feat that boggles the mind. This is one of those monumental moments I will always remember, because there is no way Id miss this.
