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1、文章编号：1009-8119（2006）07-0034-02基于四阶累量的PSK信号信噪比估计高效算法田 阳 杨 杰（北京理工大学电子工程系，北京 100081）摘 要 在无线数字通信中，许多算法都需要知道信噪比以获得最优性能。提出一种基于四阶累量的PSK信号信噪比估计算法，该算法具有较好的性能和较低的运算复杂度，可以满足软件无线电系统对信噪比估计精度和实时性的要求。关键词 PSK调制，四阶累量，信噪比估计A High Efficiency Algorithm of SNR Estimation for PSK Signals Using Fourth Order MomentsTian Ya
2、ng Yang Jie （Dept. of Electronic and Egnineering, Beijing Institute of Technology, Beijing 100081）Abstract In wireless digital communications, many algorithms require knowledge of the signal-noise-ratio (SNR) for optimal performance. An SNR algorithm for PSK signals using fourth order moments was de
3、veloped and this algorithm bears better performance and lower operation complexity, which could satisfy precision of estimation and real time of processing in software radio system.Keywords PSK modulation，Fourth order moments，SNR estimation1 引 言通信信号的信噪比估计一直是无线通信领域一个重要的研究课题，在无线通信中信噪比是衡量信道质量最主要的指标，也是实
4、现功率控制、自适应调制切换、自适应均衡处理的前提条件。在文献1中提出了一种在AWGN和有训练序列的慢衰落信道下QPSK信号信噪比估计的简易算法，在文献2中介绍了四种QPSK信噪比估计方法并进行了比较，在文献3中使用二阶统计量、数据拟合及对QPSK信号实部和虚部分开考虑的方法，得到了一种比较精确的QPSK信号的信噪比估计方法。本文结合各文献的分析方法，提出了一种基于四阶累量的信噪比估计算法，该算法巧妙地避免了复数运算，具有较好的性能和较低的运算复杂度。2 PSK信号二阶及其四阶累量介绍对一个具有零均值的平稳复随机时间序列X，有如下定义的2阶及4阶累量： （1） （2） （3） （4） （5）对于
5、PSK信号，I、Q两路分别视为实部和虚部，因此PSK信号也是一个具有零均值的平稳复随机时间序列。在无噪声情况下，可推出如表1所示的不同阶数PSK信号二阶及四阶累量，E代表信号能量。表1 BPSK、QPSK、8PSK基带信号的二阶和四阶累量BPSKE-2-2-2QPSK0E0-8PSK0E00-计算以上各累量，大多需要进行复数运算，运算量大，因此，在进行信噪比估计时，应间接使用以上高阶累量，以避免复数运算。由于高斯随机过程的奇数阶矩为零，偶数阶矩不为零。其高阶累量（）恒等于零。因此，存在高斯噪声时信号四阶累量不受噪声影响，部分二阶累量受噪声影响。分别用 和表示接收信号中信号的能量及高斯白噪声的能
6、量，通过推导可以得到： （6） 3 信噪比估计新方法及理论推导（1）新方法的提出计算，k为信噪比估计值的倒数，最后求得信噪比估值：。虽然X为复信号，即，但是和不涉及复数运算，算法易于实现并可大大减少运算量。（2）新算法的理论推导首先，利用二阶及四阶累量替换公式中的变量 （7）由二阶、四阶累量与信号、噪声能量的关系可得： （8）所以，。 （9）4 性能仿真及算法测试图1为不同算法（本文提出的新算法称为算法1，文献1、文献2和文献3提出的算法分别称为算法2、算法3和算法4）针对QPSK信号在数据样本长度为500时的估计标准误差。与其它算法比较可以看出，本文提出的新算法的估计均值更加接近真实值，并具
7、有较小的估计标准误差，尤其在低信噪比时，也具有较好的性能。采用Monte Carlo方法，对新算法进行仿真以验证其性能。信噪比的变化范围是-2 ,16dB，每种信号（BPSK、QPSK或8PSK）在不同的信噪比下分别独立进行500次仿真。图1 不同算法对QPSK信号的估计均值和标准误差（L=500）图2为新算法对BPSK、QPSK和8PSK信号在不同数据样本长度下的估计标准误差。由图可以看出，对各种PSK信号，随着样本长度的增加，估计的标准误差均不断减小，特别是低信噪比时性能的改善更为明显。图2 新算法对不同调制信号的信噪比估计的标准误差算法的时间复杂度关系到该算法能否在实时系统上实现，运算时
8、间越短，越容易在硬件上实现，并为其它功能模块节省运算时间，图3为以上各算法在CCS-Simulator（64xx）上进行测试，每一算法在每个样本上进行500次计算，然后对总时间求平均，得到每次估计的平均时间。由图3可以看出，新算法（即算法1）的时间复杂度略优于算法3和算法4，三种算法的时间复杂度处于同一量级；算法2的时间复杂度最小，但是算法2的估计性能比新算法差，尤其在低信噪比时性能很差。图3 不同算法的时间复杂度对比5 结 论在软件无线电系统中，受系统实时性和芯片处理能力的限制，先前使用高阶累量的信噪比估计算法由于需要大量复数运算很难满足实时处理要求，本文提出的基于四阶累量的信噪比估计算法巧
9、妙地避免了复数运算，具有较好的性能和较低的运算复杂度。该算法可以用于BPSK、QPSK和8PSK信号的信噪比估计，且不需要预先对PSK信号的调制阶数进行识别，节省了运算时间。当系统传输的PSK信号的调制阶数改变时，算法仍然可以进行信噪比估计，具有自适应特性。参考文献1 Dong-Joon Shin. Wonjin Sung, In-Kyung Kim, Simple SNR estimation methods for QPSK modulated short bursts. Proc IEEE GLOBECOM, 2001C, 2001.36443647.2 David R.Pauluzzi
10、. Norman C.Beaulieu, a comparison of SNR estimation techniques for the AWGN channel. IEEE communication letters, 2000;2(2)3 许华、樊龙飞、郑辉. 一种精确的QPSK信号信噪比估计算法. 通信学报，2004;25(2):55604 Matzner R, Enlberger F. An SNR Estimation Algorithm Using Fourth-Order Moments. Proceedings of ICFS 2002C.Tokyo: Waseda Uni
11、versity, 20025 张贤达.现代信号处理. 北京：清华大学出版社，1995Editors note: Judson Jones is a meteorologist, journalist and photographer. He has freelanced with CNN for four years, covering severe weather from tornadoes to typhoons. Follow him on Twitter: jnjonesjr (CNN) - I will always wonder what it was like to huddl
12、e 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 Neil 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 fa
13、scinated 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 childhood dreams to reach for the stars.As a meteorologist, Ive still seen many important weather and space events, but right now, if you were s
14、itting 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.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 uni
15、maginable 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 the Red Bull Stratos Mission. I watched the balloons positioned at different altitudes in the sky to test the winds, knowing that if they wo
16、uld 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, 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 t
17、his, 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 wind 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
18、, 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, you could see the wrinkles of disappointment on the face of the current record holder and capcom (capsule communications), Col. Joe Kittinger.
19、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.The 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
20、precipitation or humidity and limited cloud cover. The balloon, with capsule attached, will move through the lower level of the atmosphere (the troposphere) where 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 t
21、he cruising altitude of commercial airliners (5.6 miles/9.17 kilometers) and into the stratosphere. As he crosses the boundary layer (called the tropopause), he 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, Fear
22、less 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, the 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
23、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 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
24、 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 control, 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 2
25、70-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 to 172 mph (277 kph). He will have a reserve parachute that will open automatically if he loses consciousness at mach speeds.Even if everyth
26、ing 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 higher 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.