IMPLEMENTATION OF COMPLEX ENUMERATION FOR

MULTIUSER MIMOVECTOR PRECODING

Signal Theory and Communications AreaDepartment of Electronics and Computer Science,

University of Mondragon

Maitane Barrenechea, Mikel Mendicute, Idoia Jiménez and Egoitz Arruti

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Outline

Introduction

Complex enumeration

The puzzle enumerator

Implementation of Complex Enumeration Techniques

Conclusions

Introduction

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Vector Precoding

The set of equations that describe the MMSE solution for VP are:

Use a distributed distance computation model

It is a common practice to limit the cardinality of the search set Specially if there is no sphere constraint Select the lattice points closest to the origin

Tree search features N users N levels child nodes stem from each parent node

Introduction

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Tree search techniques

Introduction

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Tree search techniques: The sphere encoder

The search is constrained to the perturbation vectors belonging to a hypersphere around a reference signal. Achieves the optimum solution.

Introduction

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Tree search techniques: The K-Best

Fixed-complexity algorithm Performance-complexity trade-off given by the design parameter K

Selects the K most promising branches at each level K elements need to be sorted at each level Bottleneck

Introduction

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Tree search techniques: The fixed sphere encoder (FSE) Fixed-complexity algorithm

Performance-complexity trade-off given by the design parameter

At each level expand the most promising nodes No sorting stages

Complex Enumeration

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Schnorr-Euchner Enumeration

The S-E enumeration is necessary in all tree-search techniques: Sphere Encoder:

Improve the pruning efficiency and run-time of the algorithm.

K-Best: The bottleneck produced by the sorting stages can be alleviated by using distributed sorting schemes that takes advantage of the S-E ordered sequence of nodes.

FSE: The sort-free node selection is performed based on the S-E enumeration.

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Outline

Introduction

Complex enumeration

The puzzle enumerator

Implementation of Complex Enumeration Techniques

Conclusions

Complex Enumeration

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Schnorr-Euchner (S-E) Enumeration Visit the nodes according to their distance increment

Order the nodes - in increasing distance to Real vs. Complex-plane enumeration

Real Simple, zig-zag pattern

Complex Complicated pattern

Complex Enumeration

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Methods for Complex EnumerationFull Sort

Computationally expensive Need to compute distance increments.

Sorting A lot of data movement Power consumption

Identification of the admissible set Presented in [Hochwald2003] .

Identify the admissible set of candidates given a certain sphere constraint by means of trigonometric calculations.

Unsuitable for HW implementation.

[Hochwald2003] Hochwald, B. and ten Brink, S. , “Achieving near-capacityon a multiple antenna channels,” IEEE Transactions on Communications,vol. 51, pp. 389–399, 2003.

Complex Enumeration

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Methods for Complex EnumerationCircular set enumeration

Implementation-friendly version of the ideas in [Hochwald2003].

Initial point and direction of the local enumeration determined by boundaries.

Neighbour Expansion Locally enumerate in the real and imaginary axis.

Compose a candidate list based on the locally enumerated neighbouring nodes .

Variable length candidate list.

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Outline

Introduction

Complex enumeration

The puzzle enumerator

Implementation of Complex Enumeration Techniques

Conclusions

The Puzzle Enumerator

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Step 1: Setting the size of the complex grid

A.- Define from the distribution of

B.- Compute the minimum cardinality of the set

Rz

The Puzzle Enumerator

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Step 2: Local Enumeration

Enumeration index Values Locally Enumerated

2-3 2

4-7 3

8-11 4

Step 3: Compute Boundary Lines

The Puzzle Enumerator

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Step 4: Identify the corresponding region=2 =3 =4 =5

=6 =7 =8

The Unordered Puzzle Enumerator

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For the FSE, it is sufficient to merely identify the set of most favourable nodes, regardless of their order.

If the union of the puzzle pieces for a certain symbol spans over the whole puzzle area That symbol is unequivocally part of the most favourable nodes.

Otherwise, another puzzle must be solved.

Example:

Set of most preferable nodes

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Outline

Introduction

Complex enumeration

The puzzle enumerator

Implementation of Complex Enumeration Techniques

Conclusions

Implementation of Complex Enumeration

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Fully-pipelined architectures of the aforementioned enumerators have been implemented on a Virtex-5 XC5Vlx30-3 FPGA.

Each enumerator provides the optimum S-E sequence of 8 nodes.

Puzzle enumerator No distance computation Rest of enumerators Computed distances can be later reused in the tree traversal

Fair comparison

8 MCUs added to the puzzle

enumerator design

Implementation of Complex Enumeration

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ArchitecturesFull Sort

Circular Subsets & Neighbour expansion

Implementation of Complex Enumeration

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ArchitecturesPuzzle Enumerator

Implementation Results

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Latency Required amount of clock cycles ( ) to output the th enumerated value and its distance increment.

Implementation Results

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Device Occupation

No distance computations required

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Outline

Introduction

Complex enumeration

The puzzle enumerator

Implementation of Complex Enumeration Techniques

Conclusions

Conclusions

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Benefits of the Puzzle enumerator:

Independent symbol selection

No distance computations required

No sorting or minimum searches required

Constant and reduced latency

Minimum area occupation

The puzzle enumerator is specially suitable for fixed-complexity approaches, but it can also be used along with the sphere encoder if a certain limit is set on the eligible child nodes.

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Thanks for your attentionMaitane Barrenechea

mbarrenetxea@eps.mondragon.edu