Sphere Decoder Initial Radius Reduction for Lower Search Complexity
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Solution Overview
Problem
The computational complexity of sphere decoders in communication systems is high due to the large number of lattice vectors included within the hypersphere, especially when the initial radius is set too large, leading to decoding failures and increased complexity, while a radius set too small may result in missed ML estimates.
Innovation Solution
A sphere decoder with an initial radius setting unit that calculates the Euclidean distance between a lattice vector and the received signal, ensuring at least one valid lattice vector is within the hypersphere, reducing the number of included lattice vectors and overall complexity, using methods like MMSE or ZF estimates to determine the initial radius.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If the initial radius is set large to ensure at least one lattice vector is included inside the hypersphere, then the probability of decoding failure is reduced, but the number of lattice vectors included inside the hypersphere increases significantly, leading to increased computational complexity
Solution Approach 1:
The patent performs preliminary action by calculating the Euclidean distance between the ZF estimate and the received signal before setting the initial radius. This preliminary calculation allows the system to establish an informed initial radius that balances the need to include valid lattice vectors while avoiding excessive computational complexity from including too many lattice vectors.
Solution Approach 2:
The patent dynamically adjusts the initial radius parameter based on the calculated Euclidean distance. Instead of using a fixed or overly conservative large radius, the system changes the radius parameter to match the actual distance metrics, thereby reducing the number of lattice vectors that need to be searched while ensuring at least one valid lattice vector is included.
2Device complexity
If the initial radius is set using noise variances as proposed by Viterbo, then the initial radius can be chosen using fading coefficients to prevent extremely large number of lattice vectors, but valid lattice vectors may not be included inside the hypersphere with high probability, resulting in decoding failure
Solution Approach 1:
The patent introduces the ZF estimate as an intermediary element to determine the initial radius. By using the ZF estimate and calculating its Euclidean distance to the received signal, the system finds a middle ground between setting the radius too small (which would exclude valid lattice vectors) and setting it too large (which would include excessive lattice vectors).
Solution Approach 2:
The patent implements feedback by using the calculated Euclidean distance from the ZF estimate to dynamically determine the initial radius. This feedback mechanism ensures that the initial radius is adaptively set based on the actual channel conditions and signal characteristics, improving both decoding success probability and computational efficiency.
3Measurement precision
If the ZF estimate is used to determine the initial radius as proposed by Hassibi, then the exact ML performance is achieved, but the initial radius is set too large causing an extremely large number of lattice vectors to be included inside the hypersphere
Solution Approach 1:
The patent applies partial action by using only the necessary portion of the radius that is required to include valid lattice vectors. Instead of using a radius that is excessively large to guarantee inclusion of all possible lattice vectors, the system uses a radius that is just sufficient based on the Euclidean distance calculation, thereby achieving ML performance with reduced computational complexity.
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
Significantly reduces the initial radius and the number of lattice vectors inside the hypersphere, thereby decreasing the computational complexity of the sphere decoder, ensuring accurate ML estimates are obtained while minimizing operational time.
Implementation Method 1
a Euclidean distance is obtained between a lattice vector corresponding to the initial estimate and the received signal and the Euclidean distance is set as an initial radius
Data Source
AI summary
A sphere decoder sets a Euclidean distance between a lattice vector obtained by using an MMSE or ZF estimate and a received signal as an initial radius, further reduces the initial radius, and searches lattices points included inside a hypersphere with the further reduced initial radius. In addition, one lattice vector having a minimum Euclidean distance is output. One dimension is selected to reduce an initial radius, and estimates in other dimensions are kept fixed, excluding the selected dimension. Then candidate lattice points are searched in the selected dimension, excluding a current estimate, such that a minimum Euclidean distance and a lattice point estimate corresponding to the minimum Euclidean distance are obtained. The initial radius is updated by the minimum Euclidean distance, and a final lattice vector is constructed by combining a lattice point estimate corresponding to the initial radius and the lattice point estimates in other dimensions.