Study Of Compressive Sensing Based Ultra-wideband Communication

Shannon / Nyquist sampling theorem provides for the reduction of the original signal without distortion if the sampling frequency is at least twice of the signal bandwidth. According to the criteria order to obtain broadband signal and high-resolution images requires very high sampling rate or resolution for expressing, which store down the data with very large number. After sampling the original sample data have to be compressed, otherwise it will spend a great storage space and transmission bandwidth, causing great waste of resources. D. Donoho proposed compressed sampling theory based on the sparse property of natural signals in 2004, which provides a solid theoretical basis to overcome this problem. In recent years, ultra-wideband technology comes to alive. It has aroused keen concern from all aspects because of its great advantages relative to the traditional transmission technology. However, this technology requires the high performance of the DAC and the existed technology restricts its development greatly. The appearance of CS theory provides a theoretical basis for sampling with low rate, and gives a good solution for the technical bottleneck of the ultra-wideband high-frequency band and high-bandwidth digital-analog conversion.The compression process of the CS theory is very different from that of the conventional sampling method and it combines the sampling and compression processes, which compresses the signal during the sampling process, thus directly obtains the compressed data. On the other hand, compressed sensing firstly compresses the signal, and then uses the appropriate observation matrix to make it uniformly dispersed so that non-adaptive sampling with low rate is possible. All of these result in the highly and efficiently using of the transmission channel. CS theory is to express a n-dimensional signal f by m number of measurement units whose dimension is much less than that of the former one, and then rebuild the original signal by convex optimization method. UWB is a wireless communication technology developed in recent years. Signal whose any relative bandwidth with 20% higher than the common one or absolute bandwidth with more than 0.5GHz bandwidth can be called ultra-wideband signals. UWB communication means the transmission signal bandwidth is greater than the respective center frequency, which differs from the traditional ratio signal. UWB was first proposed by the U.S. Military in 90 years during the 20th century, which has been widely used in many civilian aspects with the development of the technology. Because of its large bandwidth, UWB can be applied in many fields, such as ultra-wideband communications, data communications, wireless sensor networks, wireless location, imaging applications and so on.Sampling is the bottleneck of UWB communications. CS theory was presented here based on the framework of UWB implementation. We also confirmed that it still have to take a long time to complete the hardware for the 3.1 ~ 10.6GHz or 60GHz bandwidth of UWB system with low cost by traditional sampling techniques. According to the previous CS theory, we propose a UWB system, which can reduce the sampling rate below the 10% of Nyquist rate.Here we consider the simplest situation, UWB communication process is performed at a fixed location in the room. We assume that the channel estimation process and communication process are time-invariant. To simplify testing, we do not consider the channel at first, Because the computing can be achieved by adding additional step when joining the channel. Now we will focus on the condition, which utilized A/D converter with 5% Nyquist frequency or even lower and reduction of more than half of the observation matrix, whether can reconstruct the original signal well or not. Simulation confirmed that: 1) Application of compressed sensing theory in ultra-wideband communication, breaking the Nyquist sampling law is indeed feasible; 2) Using a random filter means to achieve the compression sensing is feasible and can greatly accelerate the computation rate; 3) The selection of random filter is very important, and different random distribution has a great effect on the probability of reconstructing the original signal; 4) Sampling rate increasement pays a important role in increasing the probability of reconstructing the original signal; 5) The length of the filter also influences on increasing the probability of reconstructing sigal but not obviously relative to sampling rate. We use 1GHz low sampling rate to reconstruct the original signal with high probability, which reduces the Nyquist sampling rate from more than 2 times to around 10%.This thesis reduces the sampling rate of traditional sampling methods to 10% of the Nyquist sampling rate based on combining the CS theory and UWB communication, and the results are obvious. But also there are much work remaining done: 1) The simulation process did not introduce channel, so it needs to adopt ideal state which means very little movement in the room and this channel is determined. We still have to further study the UWB indoor channel, according to its multi-path fading for finding great new models to achieve large bandwidth of UWB indoor communications; 2) The UWB simulating signal used in this thesis is baseband signal, although part of UWB communication directly use the baseband signals, a direct baseband signal may significantly interfere other frequency signals and it is not convenient to use. We have worded out that the frequency shift can result in the decreasement of reconstructing effect, so it is necessary to find other methods to effectively solve such problems.