This paper considers efficient sampling of simultaneously sparse and correlated (S&C) signals for automotive radar application. We propose an implementable sampling architecture for the acquisition of S&C at a sub-Nyquist rate. We prove a sampling theorem showing exact and stable reconstruction of the acquired signals even when the sampling rate is smaller than the Nyquist rate by orders of magnitude. Quantitatively, our results state that an ensemble M signals, composed of a-priori unknown latent R signals, each bandlimited to W/2 but only S-sparse in the Fourier domain, can be reconstructed exactly from compressive sampling only at a rate RSlogα⁡W samples per second. When R≪M and S≪W, this amounts to a significant reduction in sampling rate compared to the Nyquist rate of MW samples per second. This is the first result that presents an implementable sampling architecture and a sampling theorem for the compressive acquisition of S&C signals. We resort to a two-step algorithm to recover sparse and low-rank (S&L) matrix from a near optimal number of measurements. This result then translates into a signal reconstruction algorithm from a sub-Nyquist sampling rate.

In this letter, we consider a novel problem of blind source separation from observed magnitude-only measurements of their convolutive mixture in different communication systems. The problem setups correspond to a blind receiver architecture that either does not have phase information in the measurements or has excessive phase noise that cannot be easily recovered. We have formulated the problem as a matrix recovery problem by using the lifting technique and proposed a convex programming-based solution for joint recovery of the unknown channel and source signals. We have implemented the proposed solution using the alternating direction method of multipliers (ADMM). We have plotted a phase transition diagram for random Gaussian subspaces that shows, for s source signals each of length n and channel of length k , the minimum measurements required for exact recovery are m ≥ 1.19 (sn+k) log ^2m that is in accord with our theoretical result. We have also plotted a phase transition diagram for the case where the channel delays matrix is deterministic (consisting of the first k columns of the identity matrix) that shows the minimum measurements required for exact recovery are m ≥ 2.86 (sn+k) log ^2m which are higher than random subspaces.

Future communication systems pose stringent requirements on communication latency between two nodes. One way to reduce the latency is by reducing control plane overhead by estimating the channel without training symbols. The combined process of estimating the channel and equalizing is called blind deconvolution. In this paper, our contribution is two-fold. First, we concatenate random coding (blind deconvolution using convex programming) solver with error-correcting code (ECC) decoder. Second, we propose an intelligent perturbation algorithm (IPA) that uses the ECC decoder to assist the random coding solver iteratively in solving the blind deconvolution problem. We also define the theoretical bounds for the optimal rate of the generator matrix of ECC. We have performed error-rate simulations for both Gaussian as well as Rayleigh channels. IPA provides 5 dB gain in terms of Eb/N0 over the system that uses random coding solver alone and 1 dB gain over the serial concatenation of the random coding solver and the ECC decoder, for a message length of 30 to achieve 10 -3 frame-error rate. IPA also provides 4 dB gain to achieve 10 -3 frame-error rate over the random coding solver alone, for a message length of 128.

This paper presents an algorithm to reduce the hardware complexity of the successive-cancellation decoder for polar codes. It has already been discussed in the literature that allocating 6 bits to all log-likelihood ratios instead of using floating point values, can keep performance degradation within 0.1 dB at frame-error rate of 10^-3. It has been shown in the paper that if we allocate different bits to different set of log-likelihood ratios rather than assigning the same number of bits to all log-likelihood ratios, the performance degradation is within 0.4 dB at frame-error rate of 10^-3. The results show that the proposed variable bit assignment strategy can save the processing elements in the architecture proposed by Arikan and it was observed that the bit width of N/2-1 processing elements out of total N-1 processing elements can be reduced up to 4 bits for a block length of N. In summary, this work has established a trade-off between the number of six bit processing elements and frame-error rate performance of the successive-cancellation decoder.

This paper shows that modulation protects a bandlimited signal against convolutive interference. A signal s(t), bandlimited to BHz, is modulated (pointwise multiplied) with a known random sign sequence r(t), alternating at a rate Q, and the resultant spread spectrum signal s(t) ⊙ r(t) is convolved against an M-tap channel impulse response h(t) to yield the observed signal y(t)= (s(t)⊙ r(t))⊛ h(t), where ⊙ and ⊛ denote pointwise multiplication, and circular convolution, respectively. We show that both s(t), and h(t) can be provably recovered using a simple gradient descent scheme by alternating the binary waveform r(t) at a rate Q ≳ B + M(to within log factors and a signal coherences) and sampling y(t) at a rate Q. We also present a comprehensive set of phase transitions to depict the trade-off between Q, M, and B for successful recovery. Moreover, we show stable recovery results under noise.