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Table 1 Cluster-sparse compressed sensing

From: 60 GHz ultra-wideband channel estimation based on a cluster sparsity compressed sensing

Step

Description/instruction

A

Cluster identification

B

Cluster-based classification

C

If sparsity of primary cluster is greater than threshold, go to step E, otherwise go to step D

D

Extract the primary cluster as the first classification and the rest as the second part, go to F

E

Extract the primary cluster and the second cluster as the first classification and the rest as the second part, go to F

F

Reconstruction

Input measurement vector h N; sparsity K

Initialize index set Λ = ; and the residual error r = h. Repeat the following steps by K times or until |Λ| ≥ 2K

Select the maximum K nonzero values from measurement matrix u = Φr and insert into index set j

Regularization: let all subset j 0 j for all k, l j 0 satisfy u(k)| ≤ 2|u(l)|. Then select the index set with a maximum energy as j0

Update: add subset j 0 to index set: ΛΛ j 0 ,update the residual error r:

y= arg min z R I h Φz 2 , r = hΦy

If the iteration number is greater than K or the number of indexes is greater than 2 K, stop the iteration, otherwise continue the iteration

Index set: Λ {1, … d}, then reconstruct the signal estimate as v ^ = y

G

Signal synthesis