## 2 Summary of the Paper
### Significance and Related Work  
For wideband (GHz) spectrum sensing, there is no practical way to locate all receivers of communications from the transmitter [43]. One challenge is wideband RF front-end capable of simultaneous sensing of several GHz wide spectrum [11; 17; 18; 41; 44; 45].  
ADC implementations--trade sampling frequency against dynamic range--are the bottleneck of some emerging applications such as wideband cognitive radios and cognitive radar. Emerging applications require conversion of instantaneous bandwidth in the gigahertz range with dynamic range of up to 16 bits. This translates to ADC sampling rates of multiple gigasamples per second (GS/s) with a sample aperture jitter held to one-tenth of a picosecond. Current capabilities fall well short of needs and are advancing at a rather slow rate--improving about 1.5 bits in eight years. For example, UWB is allowed to operate from 3.1 to 10.6 GHz (a bandwidth of 7.5 GHz). ADC speed is far behind the need for digital receivers.  
Compressed sensing principles enable the design of flexible imaging devices and techniques [32]. By time multiplexing a single detector, they can employ a less expensive and yet more sensitive photo sensor. Their new camera architecture that employs a digital micromirror array to perform optical calculations of linear projections of an image onto pseudo-random binary patterns. Its hallmark includes the ability to obtain an image with a single detector element, while sampling the image fewer times than the number of pixels. The idea is to off-load processing from data collection into data reconstruction. Not only will this lower the complexity and power consumption of the device, but it will enable adaptive new measurements schemes. The most intriguing feature of their system is that, since it relies on a single photo detector, it can be adapted to _image at wavelengths that are currently impossible with conventional imagers_.  
This surprising feat of the single-detector camera has inspired this research. A natural question arises from this observation. Can one use the same principle for wideband (multi-GHz) communication and radar? The UWB signal at the receiver consists of short, transient pulses with huge bandwidth that is impossible for the current semiconductor industry to handle. The UWB signal, however, is _sparse_ in time domain (like Dirac pulses). Can this signal sparsity be exploited in a novel UWB system design? This idea appears very promising, according to preliminary investigations. For example, a system bandwidth of 5 GHz has been achieved over the wireless channel, by using an A/D converter of 125 MHz (asdescribed above). As in the case of the one-detector camera, the most important advantage is to adapt this system architecture to work at bandwidths that are currently impossible with conventional designs (based on Shannon/Nyquest sampling). For example, the most advanced A/D can sample at 10 GS/s with 8 bits (www.Maxtek.com), and D/A (model DX-10G) can reach a clock rate of 10 GS/s with 10 bits. Assuming analog processing is available at the transmitter, the system bandwidth can go much higher. This implies digital signal processing will, thus, be feasible at the receiver.  
On the other hand, there is some sparsity in spectrum that can be exploited in the framework of CS [46]. This potential is not as large as the signal domain since we can pre-code the transmitted waveform in a way suitable for CS.