MIMO detector algorithms and their implementations for LTE/LTE-A

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MIMO detector algorithms and their implementations for LTE/LTE-A

Markus Myllylä and Johanna Ketonen

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© Centre for Wireless Communications, University of Oulu

Outline

• Introduction

• System model

• Detection in a MIMO-OFDM system

• SIC and K-best LSD implementation

• MMF – LSD Implementation

• Summary and Conclusions

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Introduction

•

Orthogonal frequency division multiplexing (OFDM), which simplifies the receiver design, has become a widely used technique for broadband wireless systems

• Multiple-input multiple-output (MIMO) channels offer improved capacity and potential for improved reliability compared to single- input single-output (SISO) channels

• MIMO technique in combination with OFDM (MIMO-OFDM) has been identified as a promising approach for high spectral

efficiency wideband systems

• 3GPP LTE, WiMax

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A MIMO-OFDM system

 OFDM based multiple antenna system with N_T transmit and N_R receive antennas

 Received signal y=Hx+h

where H is the channel matrix,

x is the transmitted symbol vector, h is a noise vector.

Figure: A MIMO-OFDM system model

Encoder QAM Int

S/P Mod IFFT

FFT SISO

detector DeInt SISO

decoder Channel

x

y LD1 LA2 LD2

+LE1

-

Int +

LA1 LE2

b

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Detection for MIMO-OFDM

CWC | Centre For Wireless Communications 5

 Detection means that the detector calculates an estimate of the transmitted signal vector x as an output of the detector

 Transmitted signal vector x includes N_T different symbols

 The OFDM technique simplifies the receiver structure by decoupling

frequency selective MIMO channel into a set of parallel flat fading channels

 Different data is sent in different subcarriers

 However, the reception of the signal has to be done seperately for each subcarrier

 E.g. in 3GPP LTE standard 512 subcarriers (300 used) with 5MHz bandwidth (BW) and the the interval of OFDM symbol is 71s

 Thus, detector must calculate an estimate of 300 x N_T symbols in 71s

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 The use of maximum a posteriori (MAP) detector is the optimal solution for soft output detection

 In practice coded systems are used, i.e., soft output detection is applied

 The calculation of maximum likelihood (ML) and MAP solutions with conventional exhaustive search algorithms is not feasible with large constellation and high number of transmit antennas

 Suboptimal linear minimum mean square error (LMMSE) and zero forcing (ZF) criterion based detectors feasible with reduced

performance

 The LMMSE performance can be improved by performing successive interference cancellation (SIC) between the MIMO streams, i.e., detecting the strongest signal first and cancelling its interference from each received signal.

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 Sphere detectors (SD) calculate ML solution with reduced complexity

 List sphere detector (LSD) is an enhancement of SD that can be used to approximate the MAP detector

 Sphere detectors more complex compared to linear detectors

 Linear detectors calculate a weight matrix W which can be possibly be used for multiple subcarriers and OFDM symbols

 Depending on the channel coherence time and frequency

 SD and LSD execute a tree search always separately for each subcarrier and OFDM symbol

 List sphere detector executes a tree search

 Gives a list L of candidate symbol vectors as an output, which is used to approximate the soft output information L_D(b_k)

 The list size |L| affects the quality of the approximation and depending on the list size, the LSD provides a tradeoff between the performance and the computational complexity

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Tree search algorithms

• The tree search algorithms are often divided according to their search strategy into different categories:

– Breadth first (BF)

• Fixed complexity can be easily determined – Depth search (DF)

• More efficient than BF in terms of visited nodes and variable complexity – Metric-first (MF)

• Optimal in the sense of visited search tree nodes and variable complexity

• Visited nodes should be maintained in metric order to ensure the optimality -> requires the nodes to be stored in memory

LSD algorithm

LLR calculation

H

Q, R

y

L_D1(b_k)

Preprocessing L

~

Figure: A high level architecture of LSD

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9

The K-best LSD algorithm

Root layer

layer 4

layer 3

• The K-best LSD is a breadth-first search algorithm

2

1 2 transmit antennas, 4 quadrature amplitude modulation (QAM), real valued

1 -1

1 -1 1 -1

2

4 4 , 4

4

r x

y -

2

3 3 , 3

3

r x r x

y -

^3,4 ⁴

-

2

4 4 , 1 3

, 2

,

1

r x r x r x r x

y -

^1,1 ¹

-

¹ ²

-

¹ ³

-

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Soft successive interference cancellation (SIC)

10

H 1 2

H

)

( H H I H

W   

_M ^

} 7 , 5 , 3 , 1 {

|, ) tanh(log

| ) sgn(log

ˆ  P S P

^ ²

S 

x

^re ⁱ ⁱ

P log

1. stream 2. stream

xˆ

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• The LSD receiver outperforms the SIC receiver and LMMSE receivers.

• In an uncorrelated channel, the SIC receiver performs better.

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Implementation results

– Mentor Graphics Catapult C tool used for RTL generation

• VHDL generated from C code

– A field programmable gate array (FPGA) implementation

• Xilinx Virtex-4 chip

• Synthesis with Precision RTL

– An application specific intrated circuit (ASIC) implementation

• 0.18um CMOS technology

• Synthesis with Design Compiler

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Complexity comparison in a 2x2 system

• 2x2 16-QAM results for complexity in equivalent gates, power consumption and maximum decoding rate

• 140 Mb/s is the required decoding rate of coded bits in LTE for a 20 MHz bandwidth for 2x2 16-QAM.

• The goodput is the detection rate times (1-FER) at the given SNR.

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Receiver Complexity Power Decoding rate

Goodput 16 dB

LMMSE 66 k ge 59 mW 140 Mb/s 0 Mb/s 45 Mb/s

SIC 85 k ge 83 mW 140 Mb/s 5.3 Mb/s 84 Mb/s

8-best LSD 197 k ge 175 mW 140 Mb/s 21.4 Mb/s 128 Mb/s 8-best, 2 it. 236 k ge 251 mW 140 Mb/s 63.3 Mb/s 139.6 Mb/s

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Complexity comparison in a 4x4 system

• 4x4 16-QAM

• Decoding rate was set to meet the LTE requirements for a 20 MHz bandwidth

• The iterative K-best gives the highest goodput at low SNRs

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Receiver Complexity Power Decoding rate

LMMSE 480 k ge 376 mW 280 Mb/s 0 Mb/s 101 Mb/s

SIC 540 k ge 449 mW 280 Mb/s 0 Mb/s 246 Mb/s

8-best LSD 582 k ge 568 mW 280 Mb/s 14 Mb/s 280 Mb/s 8-best, 2 it. 634 k ge 700 mW 280 Mb/s 68 Mb/s 280 Mb/s

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• Modified metric first (MMF) - LSD

• The architecture includes four different units

• Tree pruning unit

• Final candidate memory

• Partial candidate memory

• Control logic unit

• Architecture operates in a sequential fashion

• Two tree nodes calculated in one iteration

MMF-LSD architecture design

Figure: The MMF-LSD algorithm architecture

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Implementation trade-offs

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

10^-2 10^-1 10⁰

SNR (dB)

FER

4x4 MIMO, LSD with list 15, Winner B1, 60kmph

MMF,logMAP,D_max= MMF,maxlog,D_max= MMF,maxlog,D_max=120/300it MMF,maxlog,D_max=100/150it MMF,maxlog,D_max=80/100it maxlog, ML

LMMSE

DF,maxlog,D_max=750it 16-QAM

64-QAM

Figure: FER vs. SNR: Performance of the real LSD based receivers in a 4x4 antenna system

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• MMF-LSD synthesis results

– Architecture units

• SEE-LSD synthesis results

– Depth first comparison

• LLR calculation

– Max-log-MAP solution

• 4x4 system with 16-QAM

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Summary

Successive interference cancellation (SIC)

– Improves the LMMSE performance with cancellation step – Simple implementation

K-best List Sphere Detector (LSD) – Parallel tree search algorithm

– Implementation can be parallel and easy to pipeline Modified Metric First (MMF) – LSD

– Dijkstra’s algorithm – Metric first search

– Modified to be feasible for implementation

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Conclusions

In a 2x2 system

– SIC performs well with low complexity

– For high data rates at low SNRs, a more complex LSD receiver can be used

In a 4x4 system

– The K-best LSD gives goodput at low SNRs

– In better channel conditions, SIC also performs well

Implementation of MMF-LSD presented

– 4x4 MIMO system with 16-QAM – FPGA synthesis results

– ASIC synthesis results

 LSD feasible for practical systems

 Design comparable to the state-of-the-art