precoder detection for cooperative decode-and-forward relaying … · 2016. 6. 11. ·...

1

Precoder Detection for Cooperative

Decode-and-Forward Relaying in OFDMA

Systems

Abhijit Kiran Valluri, Richard J. La, Mark A. Shayman

2 2

Problem Description

A cooperative relay scenario in LTE

3 3

Problem Description


Primary Mobile User

Cooperative Mobile Relay

• Secondary user acts as a Cooperative Mobile Relay (CMR)

• Uses decode-and-forward relaying

mechanism with Primary User (PU)

• CMR needs to detect unknown Precoder

CLSM

eNodeB

4 4

Problem Description


Primary Mobile User






CLSM

eNodeB

𝒙 →

𝑎11 ⋯ 𝑎1𝑛

⋮ ⋱ ⋮𝑎𝑚1 ⋯ 𝑎𝑚𝑛

→ 𝒙

5 5

Problem Description


Primary Mobile User






CLSM

eNodeB

A simple transmission model

𝑷 𝑯 𝒙 𝒙

𝒏

𝒚

6 6

Motivation

• In Closed-Loop Spatial Multiplexing (CLSM), downlink

transmission uses antenna ports {0, 1, 2, 3}

– Use Cell-specific Reference Signals (CRSs)

– CRSs added after precoding

7 7

Motivation





8 8

Motivation





• PU uses CRSs and knowledge of precoder used to

demodulate received signal

• Precoder information is not always specified by eNodeB

– PU knows the precoder as it chose it

– CMR is not aware of the precoder

9 9

Precoder Detection

• Goal: Design an algorithm to detect the employed

precoder in downlink transmission from eNodeB

• Approaches

Hypothesis testing Framework

• Simplified ML algorithm

• Cluster variance algorithm

10 10

Precoder Detection

Received OFDM data symbols:

𝒚𝑖 = 𝑯𝑖𝑷𝒙𝑖 + 𝒏𝑖

𝒙𝑖 – 𝑖th transmitted OFDM data symbol

𝑯𝑖 – frequency domain channel gain matrix for 𝒙𝑖

𝑷 – a precoder matrix from set 𝑷𝑗 , 𝑗 ∈ 1, … , 𝑁

𝒏𝑖 – noise (i.i.d., zero mean Gaussian)

𝑷 𝑯𝑖 𝒙𝑖 𝒙 𝑖

𝒏𝑖

𝒚𝑖

11 11

Precoder Detection

Hypothesis testing framework:

• A naïve Maximum Likelihood (ML) hypothesis test:

ℒ 𝑷𝑗 𝑯𝑖 , 𝒚𝑖 =𝟏

𝝌 𝑓 𝒚𝑖 | 𝑯𝑖 , 𝑷𝑗 , 𝒙𝑖

𝒙𝑖∈𝝌

ℒ 𝑷𝑗 𝑯, 𝒚 = ℒ 𝑷𝑗 𝑯𝑖 , 𝒚𝑖

𝑀

𝑖=1

𝝌 – set of all possible transmit vectors; can be very large!

𝑯 ≔ 𝑯1, … , 𝑯𝑀 , 𝒚 ≔ 𝒚1, … , 𝒚𝑀


12 12

Precoder Detection – Simplified ML

• Equalize 𝒚𝑖 using an MMSE filter to get 𝒚 𝑖

• Decode 𝒙𝑖 as 𝒙 𝑖(𝑗)

assuming 𝑷𝑗 is true precoder matrix:

𝒙 𝑖(𝑗)

≔ argmin𝒙∈𝜒

𝑷𝑗+𝒚 𝑖 − 𝒙

• Derive a simplified log-likelihood function:

log ℒ 𝑷𝑗 𝑯 , 𝒚, 𝒙 (𝑗) = − 1

2𝜎 2𝒚𝑖 − 𝑯 𝑖𝑷𝑗𝒙 𝑖

𝑗 2𝑀

𝑖=1

+ const.

• Choose 𝑷𝑗 that maximizes above log-likelihood function


13 13

Precoder Detection – Simplified ML

• Equivalent to ML detector

– Optimal detection when 𝑷𝑗 ’s are equiprobable

• Computation complexity:

– Linear in 𝑀, 𝑁 (number of precoder matrices), and

𝐶 (size of symbol constellation)

• Additional step needed to handle ambiguity for 4x4 MIMO

with 4 layers

14 14

Precoder Detection

Ambiguity in 4x4 MIMO scenario, 4 layers

• 16 4x4 precoder matrices grouped into

a) Three sets of four precoders

b) Two sets of two precoders,

where 𝑷𝑖 = 𝑨𝑷𝑗, 𝑷𝑖 , 𝑷𝑗 ∈ a set, 𝑨 – permutation matrix

• Ambiguity resolved using channel coding built in LTE

– All precoders in a detected set sent to receive chain

– The precoder that passes turbo decoding and CRC

check is chosen as detected precoder

15 15

Precoder Detection – Cluster variance

• Define following objective function for each precoder 𝑷𝑗

𝑙 𝑷𝑗; 𝑯 , 𝒚, 𝒙 (𝑗) ≔ 𝒙 𝑖𝑗

− 𝑷𝑗+𝒚 𝑖

2𝑀

𝑖=1

• Choose the precoder 𝑷𝑗 that minimizes 𝑙 ∙

• Similarity with minimum distance decision rule


16 16

Precoder Detection – Cluster variance

• Not equivalent to ML detector (i.e. not optimal)

– Modified noise term, after MMSE filter, is not i.i.d.

• Computation complexity:

– Linear in 𝑀, 𝑁 (number of precoder matrices), and

𝐶 (size of symbol constellation)

– Fewer floating point operations needed compared to

Simplified ML algorithm

• Additional step needed to handle ambiguity for 4x4 MIMO

– Same as with Simplified ML

17 17

System Model

Based on a MATLAB LTE link-level simulator from the Vienna University of Technology

Overall LTE simulator structure

18 18

System Model

LTE Transmitter

19 19

System Model

LTE Receiver

20 20

Simulation Results – Simplified ML

2x2 MIMO: ETU channel at 60 km/h user speed, EPA channel at 3 km/h user speed Carrier frequency = 2110 MHz, System bandwidth = 1.4 MHz 1000 subframes, 12 RBs scheduled, MMSE channel estimator, SSD receiver

21 21

Simulation Results – Cluster variance


22 22

Conclusions

• Simplified ML within 2dB of BLER performance vs. known Precoder Matrix Index (PMI) case

• Simplified ML typically outperforms cluster variance, in 2x2 MIMO

• Performance gap reduced in 4x4 MIMO

– Additional diversity as each codeword is sent on 2 antennas

• Computational requirement less than SSD receiver (linear in 𝑀, # precoders 𝑁, constellation size 𝐶)

23 23

Future Work

• Consider more realistic simulations

– Interference from neighboring cells

– Impact of scheduling multiple users

• Conduct experiments using a test-bed

– Real data and real channels

24 24

Questions?

Primary Mobile User


CLSM

eNodeB

25 25

Simulation Results – Simplified ML


26 26

Simulation Results – Cluster variance


precoder detection for cooperative decode-and-forward relaying … · 2016. 6. 11. ·...

Documents