Mohammad, Fayazur Rahaman and Khan, Mohammed Zafar Ali
(2018)
Low Complexity Optimal Hard Decision
Fusion under Neyman-Pearson Criterion.
PhD thesis, Indian institute of technology Hyderabad.
Abstract
Decision fusion is a fundamental operation in many signal processing systems where
multiple sensors collaborate to improve the accuracy and robustness of the decision
being made. The decision of each individual binary decision maker (or sensor) is often
error-prone due to various environment challenges. These challenges are mitigated
to certain extent using the spatial diversity obtained by deploying the sensors over
a geographically distributed area. Subsequently, the decisions from the individual
sensors are collected and fused at a fusion center to obtain a global decision.
One such recent application of decision fusion is cooperative spectrum sensing in
cognitive radio networks (CRN). The secondary users (SUs) of the CRN are tasked
to garner the much needed unutilized spectrum allocated to the primary users (PUs).
It is important for the SUs to precisely detect the spectrum usage opportunities
inorder to improve the spectral efficiency and also to restrict the interference caused
to PUs in this process. However, these are two conflicting objectives. Tuning the
system to low levels of interference to the primary network will result in higher missed
spectrum utilization oppurtunities. Similarly, increasing the detection of spectral
usage opportunities will lead to increased interference to the primary users.
The fusion centers require optimal fusion rules that improve the spectral efficiency
of the CRN and minimize the interference caused to the primary network. The spectrum sensing in this case is generally modeled as a binary hypothesis problem: ‘PU
signal present’ and ‘PU signal absent’. The fusion rules are broadly classified into
two categories, namely (i) non-randomized (ii) randomized. In a ‘non-randomized’
rule, the global decision generated is deterministic for all the combinations of the
local observations received. And in a ‘randomized’ rule the global decision generated
is random (0 or 1) with a certain probability distribution for some local observations.
The design of the optimal randomized decision fusion is generally simple, however introduce randomness in the decision equations and are difficult to implement. Whereas
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the design of the optimal non-randomized hard decision fusion rule is difficult, and
under the Neyman-Pearson (NP) criterion is known to be exponential in complexity.
In this thesis, we develop low-complexity (i) optimal and (ii) near-optimal algorithms for two variants of non-randomized hard decision fusion problems under NP
crierion (i) clairvoyant1 decision fusion and (ii) novel (semi-)blind decision fusion. In
all the sub-categories considered therein, we present low-complexity algorithms and
obtain receiver operating characteristics (ROCs) for different number of participating
sensors (N) which was intractable with the existing approaches.
We formulate a more generalized version of this problem called “Generalized Decision Fusion Problem (GDFP)” and relate it to the classical 0−1 Knapsack problem.
Consequently we show that the GDFP has a worst case pseudo-polynomial time solution using dynamic programming approach. Additionaly, we show that the decision
fusion problem exhibits semi-monotonic property in most practical cases. We propose to exploit this property to reduce the dimension of the feasible solution space.
Subsequently, we apply dynamic programming to efficiently solve the problem with
further reduction in complexity.
Further, we show that though the non-randomized single-threshold likelihood ratio
based test (non-rand-st LRT) is sub-optimal, its performance approaches the upper
bound obtained by randomized LRT (rand LRT) with increase in N. This alleviates
the need for employing the exponentially complex non-randomized optimal solution
for N larger than a specific value.
As a variant of GDFP, we propose novel (semi-)blind hard decision fusion rules
that use the mean of the secondary user characteristics instead of their actual values.
We show that these rules with slight (or no) additional system knowledge achieve
better ROC than existing (semi-)blind alternatives.
Finally, we present a branch and bound algorithm with novel termination to obtain
1A rule that has complete knowledge of the system
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a near-optimal solution as the proposed dynamic programming approach exhibits
limitations for the GDFP that require high-precision computations. We validate the
performance of the proposed branch and bound algorithm for a wide range of {high,
low} precision and {monotonic, semi, non-monotonic} GDFPs.
All the algorithms have been rigorously verified by simulations in Matlab
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