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- W2950290599 abstract "We study the problem of recovering an $n$-dimensional vector of ${pm1}^n$ (BPSK) signals from $m$ noise corrupted measurements $mathbf{y}=mathbf{A}mathbf{x}_0+mathbf{z}$. In particular, we consider the box relaxation method which relaxes the discrete set ${pm1}^n$ to the convex set $[-1,1]^n$ to obtain a convex optimization algorithm followed by hard thresholding. When the noise $mathbf{z}$ and measurement matrix $mathbf{A}$ have iid standard normal entries, we obtain an exact expression for the bit-wise probability of error $P_e$ in the limit of $n$ and $m$ growing and $frac{m}{n}$ fixed. At high SNR our result shows that the $P_e$ of box relaxation is within 3dB of the matched filter bound MFB for square systems, and that it approaches MFB as $m $ grows large compared to $n$. Our results also indicates that as $m,nrightarrowinfty$, for any fixed set of size $k$, the error events of the corresponding $k$ bits in the box relaxation method are independent." @default.
- W2950290599 created "2019-06-27" @default.
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- W2950290599 date "2015-10-06" @default.
- W2950290599 modified "2023-09-26" @default.
- W2950290599 title "BER Analysis of the box relaxation for BPSK Signal Recovery" @default.
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