Approximation IV of the proposed iterative MMSE detector

Compare to the first term of inverse of

( ) ^g

^{apIIp H,}

^{h h}

^p

( )

^{p H, the term}σn²INRis very small at high SNR. Therefore, we can ignore the term

R

2 n N

σ I at high SNR or no information about SNR in the receiver.

Then,

( ) ( )

^{gapIVp H}

⁼

^{hp H}

^⎡ _{⎢ ⎣}

^{h hp}

( )

^{p H}

^⎤ _{⎥ ⎦}

^-1

^=pinv ( )

^{hp (4.62)}

where

^pinv ( ) • is a pseudo inverse function

It is similar as to Maximum Ration Combining (MRC) with normalization.

The computation of

( ) ^g

^{apIVp His}

N . We need to compute

^T

( ) ^g

^{apIVp H}per transmitter antenna at the first iteration. The

( ) ^g

^{apIVp H}is the same value over all the time and at any iteration. And this approximation is suitable to no information about SNR or at high SNR condition.

4.3 Simulation Results

Our simulation platform is based on the proposal of TGn Sync. The signal bandwidth (BW) is 20MHz. The transmitter and receiver use 128-points IFFT and FFT, respectively. The antenna spacing in the transmitter and receiver are equal to 0.5 wavelength. The decoder uses MAP algorithm (BCJR) to decide information bits with trace back length of 42. Assume there are perfect synchronization in the receiver, i.e.

without frequency offset, clock offset, and phase rotation. The channel is well-kwon

in the receiver. And the channel model is IEEE802.11n Channel Model B. There are at least 200 packet errors down to 1% packet error rate (PER) or a total of 3,000 packets in our simulation. The iterative detector design in this section is based on the MMSE criterion. Compare the performance of iterative MMSE detector with proposed algorithm and four approximations. The SNR is defined in chapter 2.

Case1: Observe the performance of proposed iterative MMSE detector

( ) g

^{ˆt,mp H=E}

{ ^s

^tp

( ) ^s

^{tp *}

} ^{( )} h

^{tp H⎡}⎢⎣

h

^tpE

{ ^s

^tp

^{( ) s}

^{tp *}

} ^{( )} h

^{tp H+}

H V H

^{tp tp}

^{( )}

^{tp H+}

^σ

ⁿ²

I

^NR⎤⎥⎦^-1 From the simulation result Fig. 4-11, we find that there is 1dB enhancement at first iteration and about 2dB enhancement at more iteration.

23 26 29 32 35

10^-1 10⁰

proposed iterative MMSE detector (64-QAM,R

c=3/4, 2x2)

SNR_dB

PER

iter 1 iter 2 iter 3 iter 4 iter 5 iter 6

Fig. 4-10: Performance of the proposed iterative MMSE detector (64QAM, Rc=3/4, 2x2)

Case2: Observe the performance of proposed iterative MMSE detector with

approximation I, shown in Fig. 4-11, Fig. 4-12, and Fig. 4-13.

( ) ( )

^{apI H}

⁼

^H

( )

^H

⁺ ( )

^H

⁺

² R ^-1

p p p p p p p

t

^⎡ _⎢

t t t t t σn N

^⎤ _⎥

⎣ ⎦

g h h h H V H I

From the simulation results Fig. 4-10 and Fig. 4-12, the performance of the proposed iterative MMSE detector with approximation I is very close to the performance of the proposed iterative MMSE detector.

3 5 7 9

10^-1 10⁰

proposed iterative MMSE detector with approx. I (BPSK,R

c=1/2, 2x2)

SNR_dB

PER

iter 1 iter 2 iter 3 iter 4 iter 5 iter 6

Fig. 4-11: Performance of proposed iterative MMSE detector with approximation I (BPSK, Rc=1/2, 2x2)

23 26 29 32 35 10^-1

10⁰

proposed iterative MMSE detector with approx. I (64-QAM,R

c=3/4, 2x2)

SNR_dB

PER

iter 1 iter 2 iter 3 iter 4 iter 5 iter 6

Fig. 4-12: Performance of proposed iterative MMSE detector with approximation I (64-QAM, Rc=3/4, 2x2)

28 31 34 37 40 10^-1

10⁰

proposed iterative MMSE detector with approx. I (64-QAM,R

c=3/4, 3x3)

SNR_dB

PER

iter 1 iter 2 iter 3 iter 4 iter 5 iter 6

Fig. 4-13: Performance of proposed iterative MMSE detector with approximation I (64-QAM, Rc=3/4, 3x3)

Case3: Observe the performance of the proposed iterative MMSE detector with

approximation II compared to the proposed iterative MMSE detector.

( ) ( )

^{apII H}

⁼

^H

( )

^H

⁺ ( )

^H

⁺

² R ^-1

p p p p p p p

n N

⎡

σ

⎤

⎢ ⎥

⎣ ⎦

g h h h H V H I

From the simulation result Fig. 4-14, we can find that the performance of the proposed iterative MMSE detector with approximation II is very close to the performance of the proposed iterative MMSE detector.

23 26 29 32 10^-1

10⁰

proposed iterative MMSE detector with approx. II (64-QAM,R

c=3/4, 2x2)

SNR_dB

PER

iter 1 iter 2 iter 3 iter 4 iter 5 iter 6

Fig. 4-14: Compare the performance of the proposed iterative MMSE detector with approximation II to the proposed iterative MMSE detector (64-QAM, Rc=3/4, 2x2)

Proposed iterative detector Proposed with Approx.II

Case4: Observe the performance of the proposed iterative MMSE detector with

approximation III compared to the proposed iterative MMSE detector.

( ) ( )

^{apIII H}

⁼

^H

( )

^H

⁺

² R ^-1

p p p p

n N

⎡

σ

⎤

⎢ ⎥

⎣ ⎦

g h h h I

From simulation result Fig. 4-15, we can find that the performance of the proposed iterative MMSE detector with approximation III by ignoring interference term is very close to the performance of the proposed iterative MMSE detector.

23 26 29 32 10^-1

10⁰

proposed iterative MMSE detector with approx. III (64-QAM,R

c=3/4, 2x2)

SNR_dB

PER

iter 1 iter 2 iter 3 iter 4 iter 5 iter 6

Fig. 4-15: Compare the performance of the proposed iterative MMSE detector with approximation III to the proposed iterative MMSE detector (64-QAM, Rc=3/4, 2x2)

Proposed iterative detector Proposed with Approx.III

Case5: Observe the performance of the proposed iterative MMSE detector with

approximation IV compared to the proposed iterative MMSE detector.

( ) ( )

^{gapIVp H}

⁼

^{hp H}

^⎡ _{⎢ ⎣}

^{h hp}

( )

^{p H}

^⎤ _{⎥ ⎦}

^-1

^=pinv ( )

^hp

From simulation result Fig. 4-16, we can find that the performance of the proposed iterative MMSE detector with approximation IV by ignoring interference and noise terms is very close to the performance of the proposed iterative MMSE detector.

23 26 29 32 10^-1

10⁰

proposed iterative MMSE detector with approx. IV (64-QAM,R_c=3/4, 2x2)

SNR_dB

PER

iter 1 iter 2 iter 3 iter 4 iter 5 iter 6

Fig. 4-16: Compare the performance of the proposed iterative MMSE detector with approximation IV to the proposed iterative MMSE detector (64-QAM, Rc=3/4, 2x2)

Proposed iterative detector Proposed with Approx.IV

4.4 Conclusions

There is 1dB enhancement at first iteration and about 2dB enhancement at more iteration in iterative MMSE detector. The performances of three methods of approximation are similar to the performance of iterative MMSE detector without approximation. That is because that in the inverse of the equation (4.47), the interference and noise term are very small compared to the first term

^{h h}

^tp

( )

^{tp H.}

However, if we use those methods of approximation, we can reduce the times of inverse computation from

N

_T⋅ ⋅

L N

_{s iteration}⋅

log M

₂ to

N without degrading the

_T performance.

Chapter 5:

Conclusions and Future Works

5.1 Conclusions

In this thesis, at first, we introduce to the system architectures of 802.11n proposal of TGn Sync and the channel models. Then, we derive the weight of bit metrics for MIMO BICM systems in the MMSE detector and the ZF detector. We analyze the performance of bit metric calculation with weighted gain and equal gain.

If we can present exactly the pdf of the interference and noise, there is about 3~4dB enhancement of performance. At lower modulation scheme, there is only about 1dB enhancement with pdf of the interference and noise by Gaussian approximation. By the way, the ZF detector has noise enhancement so the performance of MMSE detector is better than those of ZF detector about 1~4dB, especially at lower SNR.

At high SNR, the MMSE detector is similar as the ZF detector and makes more effort on interference suppression.

Besides, we design low complexity iterative MMSE detector with turbo principle and propose some methods of approximation to reduce computation complexity. From the simulation results, it proves that using weighted bit metrics can improve the performance. There is 1dB enhancement at first iteration and about 2dB enhancement at more iteration in iterative MMSE detector. Employing approximation of iterative MMSE detector can reduce the computation complexity without performance deterioration. That is because that in the inverse of the equation(4.47), the interference and noise term are very small compared to the first

term

^{h h}

^tp

( )

^{tp H}. However, if we use those methods of approximation, we can reduce the times of inverse computation from

N

_T⋅ ⋅

L N

_{s iteration}⋅

log M

₂ to

N without

_T degrading the performance.

5.2 Future Works

We combine detection and decoding to design a lower-complexity and higher-performance iterative signal detector based on MMSE criterion and turbo principle for MIMO BICM systems. We may consider advanced codes, such as turbo code and LDPC, to improve performance. We may design a iterative signal detector based on LDPC principle. We can joint channel estimation and decoding or detection to improve the ability of estimating channels. We can use geometrical approaches, such as sphere decoding and lattice decoding, to approximate ML detection.

Appendix A:

Multistage Detection for A Linear MMSE Receiver

To calculate the coefficients of adaptive linear detector based on MMSE Criterion,

G

^{MMSEk =arg min E}G_k

{ y

^.k－

s

^{.k 2}

}

^{=arg min E}G_k

{ G r

^{k .k}－

s

^{.k 2}

}

(A.1)

Find the minimum value of J, Assume the energy of signal is equal to 1.

{

^.

( )

^{. *}

}

²

E

s

^p_k

s

^p_k =

σ

_s=1 Then, the coefficient of linear MMSE detector is

^MMSEk

⁼ ( )

k ^H

^⎡ _⎢

k

( )

k ^H

⁺

σn² NR

^⎤ _⎥

^-1

⎣ ⎦

G H H H I (A.8)

Appendix B:

Multistage Detection for Iterative MMSE Receiver

To calculate the coefficients of adaptive linear iterative detector based on MMSE Criterion,

Find the minimum value of J,

^{p =}

( )

^{tp H E}

{ (

^{t tp tp(i)}

)(

^{t tp tp(i)}

)

^H

}

^E

{

^tp

⁽

^{t tp tp(i)}

⁾

^H

}

⁼⁰

( )( )

Appendix C:

Modulation-Coding Scheme (MCS)

The TGn Sync proposal augments the 802.11a MCS set through the use of multiple spatial streams and bandwidth extension. The MCS filed defines the modulation and coding scheme, as indicated in Table C-1. The proposal recommends a mandatory data of 243Mbps using two spatial streams in regulatory domains that permit 40MHz operation. In the future, their proposal supports scalability to 4 spatial streams, offering data rates in excess of 600Mbps.

GI = 800ns GI = 400ns

17 3 QPSK 1/2 36 81 40 90 18 3 QPSK 3/4 54 121.5 60 135 19 3 16-QAM 1/2 72 162 80 180 20 3 16-QAM 3/4 108 243 120 270 21 3 64-QAM 2/3 144 324 160 360 22 3 64-QAM 3/4 162 364.5 180 405 23 3 64-QAM 7/8 189 425.25 210 472.5 24 4 BPSK 1/2 24 54 26.67 60 25 4 QPSK 1/2 48 108 53.33 120 26 4 QPSK 3/4 72 162 80 180 27 4 16-QAM 1/2 96 216 106.67 240 28 4 16-QAM 3/4 144 324 160 360 29 4 64-QAM 2/3 192 432 213.33 480 30 4 64-QAM 3/4 216 486 240 540 31 4 64-QAM 7/8 252 567 280 630

32 1 BPSK 1/2 6 6.67

Table C-1: Modulation-coding scheme

Appendix D:

IEEE 802.11n Channel Model B

Tap index 1 2 3 4 5 6 7 8 9

Excess delay

[ns] 0 10 20 30 40 50 60 70 80

Cluster 1 Power [dB] ^{0 -5.4 -10.8 -16.2 -21.7}

AoA AoA [°] ^{4.3 4.3 4.3 4.3 4.3}

AS

(receiver) AS [°] ^{14.4 14.4 14.4 14.4 14.4}

AoD AoD [°] ^{225.1 225.1 225.1 225.1 225.1}

AS

(transmitter) AS [°] ^{14.4 14.4 14.4 14.4 14.4} Cluster 2 Power [dB] ^{-3.2 -6.3 -9.4 -12.5 -15.6 -18.7 -21.8}

AoA AoA [°] ^{118.4 118.4 118.4 118.4 118.4 118.4 118.4}

AS AS [°] ^{25.2 25.2 25.2 25.2 25.2 25.2 25.2}

AoD AoD [°] ^{106.5 106.5 106.5 106.5 106.5 106.5 106.5}

AS AS [°] ^{25.4 25.4 25.4 25.4 25.4 25.4 25.4}

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