Fixed point Software Implementation of a

Low-Complexity Soft Demapper

Presented By : Adeel Akhtar Supervised By : Imran AliPresented To : Prof. Norbert Wehn

Microelectronics Seminar

Outline Introduction

Goals

Work Description

Simulation Results

Conclusion

2

Channel Encoder

Channel

Mapper

Demapper

Channel Decoder

The received symbols are mapped to soft values:0.7,-1.3,-0.1,1.4; 3.1, -0.7, -1.1, 2.3

Error correction data is added to the message:01100110

The soft values are used to recover the original message: 1011

Message to be sent: 1011

The message is mapped to symbolsdescribing the signal.

(-1+2i, -1+2i)

Sending the signal through the channel distorts it.

(-0.76+1.3i; -1.1+2.15i)

Wireless Communication

3

Channel Encoder

Channel

Mapper

Demapper

Channel Decoder

Im

Re

0111 0110

01000101

0010 0011

00010000

1000 1001

10111010

1101 1100

11101111

Due to interference the sent signal isdeformed.

Wireless Channel

4

1.Optimal Soft DemapperChannel Encoder

Channel

Mapper

Demapper

Channel Decoder

0

2

1

00

2

||exp

||exp

log

Nxy

Nxy

LLR

i

i

Sx

Sx

i

Im

Re

0111 0110

01000101

0010 0011

00010000

1000 1001

10111010

1101 1100

11101111

Demapper Algorithms

5

Channel Encoder

Channel

Mapper

Demapper

Channel Decoder

Im

Re

0111 0110

01000101

0010 0011

00010000

1000 1001

10111010

1101 1100

11101111

2.Sub-optimal Demapper

0

2

0

2

1||min||min

N

xyxyLLR ii SxSx

i

6

Channel Encoder

Channel

Mapper

Demapper

Channel Decoder

0

20min

21min ||||

N

xyxyLLR ii

i

3.Less Complex Sub-Optimal Soft Demapper [1]

Im

Re

0111 0110

01000101

0010 0011

00010000

1000 1001

10111010

1101 1100

11101111

7

Fixed point software implementation of the algorithm in C++.

Simulation of the demapper with Duo binary Turbo Decoder.

Communication performance analysis with different bit widths and comparison with Optimal technique.

8

Goals of Seminar

Block Diagram of Algorithm

9

Received Symbol Real Img

Rounding

Distance Calculation

Magnitude to Gray Code

Closest flipped bit constellation point

Gray Code to Magnitude

Calculation of Log Likelihood Ratio (LLRs)

(-2.7,1.4)

(-3,1)

(1001)

10010011100111011001101110011000

0011( 1, 1)1101(-3,-1)1011(-1, 1)1000(-3, 3)

llro = -72.3llr1 = 29.9llr2 = 15.9llr3 = -10.4

Closest flipped bit constellation points

Flipping the bit at needed position.

…xxxxxxxxx… ...x’x1x0x0x0… The next less significant bit is set. All lesser significant bits are reset. Real and imaginary numbers are interleaved.

10

Example: symbol with four bits (1001)

Flip bit 0: xxxx → x’x1x (10010011)

Flip bit 1: xxxx → xx’x1 (10011101)

Flip bit 2: xxxx → xxx’x (10011011)

Flip bit 3: xxxx → xxxx’ (10011000)

Fixed-Point Low-Complexity Soft Demapper

11

Received Symbol Real Img

Rounding

Distance Calculation

Magnitude to Gray Code

Closest flipped bit constellation point

Gray Code to Magnitude

Calculation of Log Likelihood Ratio (LLRs)

(-906,485)

(-971,323)

(1001)

10010011100111011001101110011000

0011( 323, 323)1101(-971,-323)1011(-971, 323)1000(-971, 971)

llro = -13llr1 = 30llr2 = 16llr3 = -10

Fixed point number Q.10,8

Simulation Setup

12

Source

Statistics

Turbo encoder 16 QAM Mapper

16 QAMDe-Mapper

Turbo Decoder

Transmitter (Tx)

Receiver(Rx)

Channel

Simulation Results

13

6 6.2 6.4 6.6 6.8 7 7.210

-5

10-4

10-3

10-2

10-1

100

SNR Eb/N0 dB

FE

R

Info bits1552 total bits1864-16QAM R0.833 Turbo Decoder

Optimal Demapper

Simulation Results

14

6 6.2 6.4 6.6 6.8 7 7.210

-5

10-4

10-3

10-2

10-1

100

SNR Eb/N0 dB

FE

R

Info bits1552 total bits1864-16QAM R0.833 Turbo Decoder

Optimal Demapper

Proposed. Q10,8

Simulation Results

15

6 6.2 6.4 6.6 6.8 7 7.210

-5

10-4

10-3

10-2

10-1

100

SNR Eb/N0 dB

FE

R

Info bits1552 total bits1864-16QAM R0.833 Turbo Decoder

Optimal Demapper

Proposed. Q10,8

Proposed. Q8,6

Conclusions

1. Understanding of a less complexity sub-optimal demapper.

2. Fixed point software implementation of the proposed algorithm.

3. The performance of the algorithm is exactly similar to the optimal algorithm for 16 QAM.

4. Less number of distances computation, consequently less computation complexity in hardware.

16

17

Thank You