CompressedSensinginWirelessCommunication Thomas Arildsen∗, Tobias Lindstrøm Jensen, Karsten Fyhn, Peng Li, Pawel Pankiewicz, Jacek Pierzchlewski, Hao Shen, Ruben Grigoryan, Søren Holdt Jensen, Torben Larsen Dept. of Electronic Systems, Aalborg University, Denmark ∗tha@es.aau.dk Abstract Compressed sensing has gained a lot of attention in recent years. While the famous Shannon-Nyquist boundary for sampling of analog signals provides a suﬃcient condition for the sampling frequency, it can be reduced substantially in situations where a signal is sparse in a given domain. This can lead to compressive sensing which can be formulated as an optimization problem where an under-determined system of linear equations is solved under the con- dition of a sparse solution. In our research group at Aalborg University we are using compressed sensing theory to address some important practical challenges in radio frequency communication and more generally in analog-to- digital conversion. Radio frequency receivers for modern telecommu- nication standards in power-constrained devices are increasingly challenged by the necessary sam- pling frequencies and hardware power consump- tion. Compressed sensing techniques may help ad- dress some of these challenges, for example by re- ducing the necessary sampling rate. This is a move towards the original, but hardware-wise unrealistic, ideas of software deﬁned radios. In order to utilise compressed sensing, we must be able to represent the relevant signals sparsely – or, alternatively, ﬁnd new signal structures that allow compressed sensing. In practice, various hardware imperfections as well as noise and interference limit the applicability of compressed sensing. These issues must be ad- dressed to make compressed sensing practicable. Multi-Coset Sampling Scheme ▶The multi-coset sampling scheme is one of sev- eral possible sub-Nyquist sampling schemes. ▶The multi-coset sampling scheme can be used to sample and reconstruct frequency sparse sig- nals. Reconstruction is possible with various al- gorithms that may have diﬀerent performance. ▶We are focusing on the impact of hardware im- perfections on the reconstruction quality. Var- ious real-life restrictions such as practical sam- pling patterns are also important. ▶This research will bring multi-coset sampling schemes closer to real-life applications. ADC 1 x(t) x((m·L+c1)·T) = y1[m] ADC 2 ADC P x((m·L+c2)·T) = y2[m] x((m·L+cP)·T) = yP[m] Sparse Sampling Receivers ▶Applying multi-coset sampling on a conven- tional time-interleaved ADC may increase the input bandwidth. ▶Time-interleaved ADC traditionally uses uni- form sampling. We investigate introduction of randomized sampling. ▶We consider a sample-time error in each sub- ADC. Sample-time error is a random time delay for each sub-ADC, and it is a constant error for each sampling instance. ▶We identify these sample-time errors and ex- ploit them to introduce randomized sampling similar to multi-coset sampling. L 1c 2c 3c c1 0 0 o T 0 max s max s max s T ( 1) L T  max s max s - - - max s CS Direct Conversion Receiver ▶Increasing computational power of modern data receivers enables moving more and more pro- cessing from the analog to the digital domain. ▶In this project, compressed sensing is used to relax the analog ﬁltering requirements prior to the ADCs in a direct conversion receiver. ▶The ﬁltered down-converted radio signals are randomly sampled with an average sampling frequency below its Nyquist rate. ▶This approach exploits frequency domain spar- sity of the down-converted radio signals. ▶The approach allows identifying and remov- ing interfering signals from the sampled signal, thereby enabling reduced low-pass ﬁlter order. f f 0 Frequencies allowed by the radio band-pass filter B B f r f r f r f r Blockers Desired signal Noise s b2 s b1 s f r f r f 2f 0 Low frequency components f r f r Downconverted blockers All the high frequency components can be removed by the 1st order low- pass filters N