MMSE Criterion

In this section, use MMSE approach to detect signal. It is similar to a ZF receiver. Assume the MIMO channel is multipath quasi-static Rayleigh fading channel. The received signal vector after FFT/remove-GI is defined in (3.14) and the output signal vector

y of MMSE detector is defined as

_.k

MMSE ._k

=

_k ._k

y G r

(3.28)

Now, base on the MMSE criterion to minimize the error of the detected signal vector

y and a transmitter signal vector

_.k

s

_.k

{ } { }

See Appendix A, assume the energy of signal is equal to 1.

Then, the coefficients of an MMSE detector is

( )

^H

( )

^{H -1}

3.3.1 Approximation of Bit Metrics

Observe the

p sub-stream detected signal

^th

y

^p_.k ,

( )

^H

( )

^H

( )

^H

In [21], H.V. Poor and S.Verdu show that the MMSE estimate approximates a Gaussian distribution. Hence, the co-antenna interference and noise are considered together as complex Gaussian noise

z

^p_.k with Gaussian approximation.

( )

^H

( )

^H

.

( )

Then the detect signal is shown as

( )

^H

.

=

.

+

.

p p p p p

k k k k k

y g h s z

_(3.37)

The conditional pdf of

y

^p_.k is a complex Gaussian distribution,

( )

²

( ( ) )

By the way, the signal-to-interference-and-noise ratio of

y

^p_.k is

{ } { } _{( )} ^{( )}

So the coefficient of bit metrics

c

^p_{. ,k m} for BICM is directly proportional to the signal-to-interference-and-noise ratio of detected signaly^p_.k.

3.3.2 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 soft Viterbi algorithm to decide information bits with trace back length of 128. 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. There are 8000 information bits per packet. There are at least 500 packet errors down to 1% packet error rate (PER) or a total of 10,000 packets in our simulation. The detector design in this section is based on the MMSE criterion. Compare the performance of equal and weighted coefficients of bit metrics calculation. The SNR is defined in chapter 2.

Case1: Orthogonal AWGN channel, 2x2

The signal is transmitted through the AWGN channel with orthogonal MIMO channel. equal and weighted coefficients are almost the same. That’s because the frequency response of all subchannel are equal.

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

10^-2 10^-1

10⁰ PER vs. SNR_dB PerfectCSI (AWGN)

SNR_dB

Fig. 3-6: PER of bit metrics calculation with equal and weighted coefficients by MMSE detector in AWGN channel, 2x2

W=SINR W=1

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 10^-6

10^-5 10^-4 10^-3

10^-2 BER vs. SNR_dB PerfectCSI (AWGN)

SNR_dB

BER

BPSK,R_c=1/2 QPSK,R_c=1/2 QPSK,R_c=3/4 16-QAM,R_c=1/2 16-QAM,R_c=3/4 64-QAM,R_c=2/3 64-QAM,R_c=3/4

Fig. 3-7: BER of bit metrics calculation with equal and weighted coefficients by MMSE detector in AWGN channel, 2x2

Case2: Channel B of IEEE802.11n, 2x2

From Fig. 3-8 and Fig. 3-9, we can find that the performance of weighted gain for bit metrics computation is better than those of equal gain. There are about 1dB improvement for BPSK and QPSK, about 3dB improvement for 16-QAM and about 4dB improvement for 64-QAM under the PER=0.1. Compare to ZF detectors, the improvement of MMSE detects is smaller than those of ZF detector, especially for lower modulation. That is because we use the Gaussian approximation in MMSE detector. Then in the low modulation scheme and fewer sub-streams, the Gaussian approximation of interference is loose.

W=SINR W=1

Fig. 3-8: PER of bit metrics calculation with equal and weighted coefficients by MMSE detector for BPSK and QPSK in channel B, 2x2

15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 10^-2

10^-1

10⁰ PER vs. SNR_dB Ch-B2x2 (Perfect CSI) MMSE Detector

SNR_dB

PER

16-QAM,R_c=1/2 16-QAM,R_c=3/4 64-QAM,R_c=2/3 64-QAM,R_c=3/4

Fig. 3-9: PER of bit metrics calculation with equal and weighted coefficients by MMSE detector for 16-QAM and 64-QAM in channel B, 2x2

5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 10^-2

10^-1

10⁰ P E R vs. S N R _d B C h -B 2x2 (P erfect C S I) M MS E D etecto r

S N R _d B

PER

B P S K ,R_c=1/2 QP S K ,R_c=1/2 QP S K ,R_c=3/4

W=SINR W=1

W=SINR W=1

5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

10^-1 BER vs. SNR_dB Ch-B 2x2 (Perfect CSI) MMSE detector

SNR_dB

BER

BPSK,R_c=1/2 QPSK,R_c=1/2 QPSK,R_c=3/4

Fig. 3-10: BER of bit metrics calculation with equal and weighted coefficients by MMSE detector for BPSK and QPSK in channel B, 2x2

15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 10^-4

10^-3 10^-2 10^-1

10⁰ BER vs. SNR_dB Ch-B 2x2 (Perfect CSI) MMSE detector

SNR_dB

Fig. 3-11: BER of bit metrics calculation with equal and weighted coefficients by MMSE detector for 16-QAM and 64-QAM in channel B, 2x2

W=SINR W=1

W=SINR W=1

Case3: Channel B of IEEE802.11n, 2x3

In this case, the receiver uses three antennas to receive signal. From Fig. 3-12 and Fig. 3-13, we can find that the performance of weighted gain for bit metrics computation is better than those of equal gain. There are smaller than 0.5dB improvement for BPSK and QPSK, about 1dB improvement for 16-QAM and about 1.5dB improvement for 64-QAM under the PER=0.1. Compare to case2, the receiver in the case3 uses more receiver antenna than those in case2, and then the receiver has more diversity gain. Therefore, the weight for bit metrics is close to equal.

Fig. 3-12: PER of bit metrics calculation with equal and weighted coefficients by MMSE detector for BPSK and QPSK in channel B, 2x3

-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

10^-2 10^-1

10⁰ P E R vs. S N R _dB C h-B 2x3 (P erfect C S I) MMS E D etector

S N R _dB

PER

B P S K ,R_c=1/2 QP S K ,R_c=1/2 QP S K ,R_c=3/4 W=SINR W=1

Fig. 3-13: PER of bit metrics calculation with equal and weighted coefficients by MMSE detector for 16-QAM and 64-QAM in channel B, 2x3

-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

10⁰ BER vs. SNR_dB Ch-B 2x3 (Perfect CSI) MMSE detector

SNR_dB

BER

BPSK,R_c=1/2 QPSK,R_c=1/2 QPSK,R_c=3/4

Fig. 3-14: BER of bit metrics calculation with equal and weighted coefficients by MMSE detector for BPSK and QPSK in channel B, 2x3

5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 10^-5

10^-4 10^-3 10^-2 10^-1

10⁰ BER vs. SNR_dB Ch-B 2x3 (Perfect CSI) MMSE detector

SNR_dB

BER

16-QAM,R_c=1/2 16-QAM,R_c=3/4 64-QAM,R_c=2/3 64-QAM,R_c=3/4

Fig. 3-15: PER of bit metrics calculation with equal and weighted coefficients by MMSE detector for 16-QAM and 64-QAM in channel B, 2x3

Case4: Channel B of IEEE802.11n, 3x3

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 10^-2

10^-1

10⁰ PER vs. SNR_dB Ch-B 3x3 (PerfectCSI) MMSE Detector

SNR_dB

PER

BPSK,R_c=1/2 QPSK,R_c=1/2 QPSK,R_c=3/4

Fig. 3-16: PER of bit metrics calculation with equal and weighted coefficients by MMSE detector for BPSK and QPSK in channel B, 3x3

15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 10^-2

10^-1

10⁰ PER vs. SNR_dB Ch-B 3x3 (PerfectCSI) MMSE Detector

SNR_dB

PER

16-QAM,R_c=1/2 16-QAM,R_c=3/4 64-QAM,R_c=2/3 64-QAM,R_c=3/4

Fig. 3-17: PER of bit metrics calculation with equal and weighted coefficients by MMSE detector for 16-QAM and 64-QAM in channel B, 3x3

W=SINR W=1

W=SINR W=1

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

10⁰ BER vs. SNR_dB Ch-B 3x3 (PerfectCSI) MMSE Detector

SNR_dB

BER

BPSK,R_c=1/2 QPSK,R_c=1/2 QPSK,R_c=3/4

Fig. 3-18: BER of bit metrics calculation with equal and weighted coefficients by MMSE detector for BPSK and QPSK in channel B, 3x3

15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 10^-4

10^-3 10^-2 10^-1

10⁰ BER vs. SNR_dB Ch-B 3x3 (PerfectCSI) MMSE Detector

SNR_dB

Fig. 3-19: BER of bit metrics calculation with equal and weighted coefficients by MMSE detector for 16-QAM and 64-QAM in channel B, 3x3

W=SINR W=1

W=SINR W=1

Case5: Compare MMSE and ZF detector in channel B of IEEE802.11n, 2x2

Fig. 3-20: PER of bit metrics calculation with weighted coefficients by MMSE detector and ZF detector for BPSK and QPSK in channel B, 2x2

Fig. 3-21: PER of bit metrics calculation with weighted coefficients by MMSE detector and ZF detector for 16-QAM and 64-QAM in channel B, 2x2

5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 10^-2

10^-1

10⁰ P E R vs. S N R _dB C h -B 2x2 (perfect C S I) W =S IN R

S N R _d B

PER

B P S K ,R_c=1/2 QP S K ,R_c=1/2 QP S K ,R_c=3/4

MMSE Detector ZF Detector

15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 10^-2

10^-1

10⁰ P E R vs. S N R _d B (perfect C S I) W =S IN R

S N R _dB

PER

16-QA M,R_c=1/2 16-QA M,R_c=3/4 64-QA M,R_c=2/3 64-QA M,R_c=3/4

MMSE Detector ZF Detector

在文檔中 多傳送多接收位元交錯調變碼系統之低複雜度迭代訊號偵測設計 (頁 42-56)