Lower bound on MSE of sparse vector estimation in additive white Gaussian noise

2012 ◽  
Vol 48 (25) ◽  
pp. 1593-1595
Author(s):  
L. Najjar
Keyword(s):  
Lower Bound ◽  
Gaussian Noise ◽  
Additive White Gaussian Noise ◽  
White Gaussian Noise ◽  
Sparse Vector ◽  
Vector Estimation

The Cramer–Rao lower bound in a non-AWGN model for the affine phase retrieval

2021 ◽  
pp. 2050089
Author(s):  
Zhitao Zhuang ◽  
Kaixin Wang
Keyword(s):  
Lower Bound ◽  
Mean Square Error ◽  
Gaussian Noise ◽  
Phase Retrieval ◽  
Additive White Gaussian Noise ◽  
White Gaussian Noise ◽  
Mean Square ◽  
Cramer Rao Lower Bound ◽  
The Difference

In this paper, we derive the Cramer–Rao lower bound (CRLB) in a non-additive white Gaussian noise (AWGN) model for the affine phase retrieval (APR) and simulate the difference of CRLB and mean square error produced by PhaseLift of phase retrieval and APR in AWGN and non-AWGN cases.

scholarly journals On the achievable rate of bandlimited continuous-time AWGN channels with 1-bit output quantization

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Sandra Bender ◽  
Meik Dörpinghaus ◽  
Gerhard P. Fettweis
Keyword(s):  
Lower Bound ◽  
Mutual Information ◽  
Gaussian Noise ◽  
Continuous Time ◽  
Additive White Gaussian Noise ◽  
White Gaussian Noise ◽  
Information Rate ◽  
Achievable Rate ◽  
Zero Crossing ◽  
Lower Bounding

AbstractWe consider a real continuous-time bandlimited additive white Gaussian noise channel with 1-bit output quantization. On such a channel the information is carried by the temporal distances of the zero-crossings of the transmit signal. We derive an approximate lower bound on the capacity by lower-bounding the mutual information rate for input signals with exponentially distributed zero-crossing distances, sine-shaped transition waveform, and an average power constraint. The focus is on the behavior in the mid-to-high signal-to-noise ratio (SNR) regime above 10 dB. For hard bandlimited channels, the lower bound on the mutual information rate saturates with the SNR growing to infinity. For a given SNR the loss with respect to the unquantized additive white Gaussian noise channel solely depends on the ratio of channel bandwidth and the rate parameter of the exponential distribution. We complement those findings with an approximate upper bound on the mutual information rate for the specific signaling scheme. We show that both bounds are close in the SNR domain of approximately 10–20 dB.

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