Multiple input multiple output techniques
- 1. 03/05/2016 DOT Shivaji University Kolhapur 1 Narrowband MIMO Model, parallel decomposition of MIMO channel, MIMO channel capacity, MIMO diversity gain, Space-time modulation and coding. MIMO Systems
- 2. SISO 03/05/2016 DOT Shivaji University Kolhapur 2 Tx Antenna Rx Antenna 1) It suffers from fading 2) Diversity gain can’t be achieved 3)Data rate is limited to Shanoon’s Channel capacity theorem 4)C= Blog2(1+SNR)
- 3. ◼ IEEE 802.11g uses SISO system with BW =20 MHz and SNR =25 dB. and uses 64 QAM modulation calculate the data rate or throughput of the system ◼ 03/05/2016 DOT Shivaji University Kolhapur 3
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- 6. MISO System 03/05/2016 DOT Shivaji University Kolhapur 6 Tx Antennas Rx Antenna 1) It doesn’t suffer from fading 2) Diversity gain can be achieved 3)Data rate is limited to Shanoon’s Channel capacity theorem C= Blog2(1+SNR)
- 7. SIMO System 03/05/2016 DOT Shivaji University Kolhapur 7 Tx Antenna Rx Antennas 1) It doesn’t suffer from fading 2) Diversity gain can be achieved 3)Data rate is limited to Shanoon’s Channel capacity theorem C= Blog2(1+SNR)
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- 9. MIMO System 03/05/2016 DOT Shivaji University Kolhapur 9 Tx Antenna Rx Antennas 1) It doesn’t suffer from fading 2) Diversity gain can be achieved 3)Data rate is not limited to Shanoon’s Channel capacity theorem C= Blog2(1+SNR) but = C=NBLog2(1+SNR) 1 2 t 1 2 r
- 10. MISO System ◼ Find The max data rate which we get in 3X4 MIMO system? 03/05/2016 DOT Shivaji University Kolhapur 10 https://www.google.com/search?q=fexplanation+of+fading+video&rlz=1C1GCEU_e nIN869IN869&oq=fexplanation+of+fading+video&gs_lcrp=EgZjaHJvbWUyBggAEEUY OdIBCTIxMDUyajBqN6gCALACAA&sourceid=chrome&ie=UTF- 8#fpstate=ive&vld=cid:08d2d152,vid:nIata4K7egE,st:0
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- 12. Narrowband MIMO Model 03/05/2016 DOT Shivaji University Kolhapur 12 h21 h12 h22 h1Mt h2Mt
- 13. Narrowband MIMO Model 03/05/2016 DOT Shivaji University Kolhapur 13 Y = Hx + n
- 14. Parallel Decomposition of the MIMO Channel ◼ From matrix theory, for any matrix H we can obtain its singular value decomposition (SVD) as ◼ ◼ H = UΣVH ◼ where the Mr×Mr matrix U and the Mt×Mt matrix V are unitary matrices and Σ is an Mr×Mt diagonal matrix of singular values {σi} of H. 03/05/2016 DOT Shivaji University Kolhapur 14
- 15. ◼ The parallel decomposition of the channel is obtained by defining a transformation on the channel input and output x and y through transmit precoding and receiver shaping. In transmit precoding the input to the antennas x is generated through a linear transformation on input vector x˜ as x = VHx˜. Receiver shaping performs a similar operation at the receiver by multiplying the channel output y with UH , as shown in Figure 10.2. 03/05/2016 DOT Shivaji University Kolhapur 15
- 16. ◼ The transmit precoding and receiver shaping transform the MIMO channel into RH parallel single- input single-output (SISO) channels with input x˜ and output y˜, since from the SVD, we have that ◼ y˜ = U H (Hx + n) ◼ = U H (UΣVx + n) ◼ = U H (UΣVV H x˜ + n) ◼ = U H UΣVV H x˜ + U H n ◼ = Σx˜ + n˜, ◼ where n˜ = U H n and Σ is the diagonal matrix of singular values of H with σi on the ith diagonal. 03/05/2016 DOT Shivaji University Kolhapur 16
- 17. Parallel Decomposition of the MIMO Channel ◼ https://www.google.com/search?q=parallel+decomp osition+of+mimo+channel&rlz=1C1JZAP_enIN1025I N1025&oq=parallel+decomposition+of+MIMO+chan nel&gs_lcrp=EgZjaHJvbWUqBwgAEAAYgAQyBwgAEA AYgATSAQkyODgwOWowajeoAgCwAgA&sourceid=ch rome&ie=UTF- 8#fpstate=ive&vld=cid:67fbcbae,vid:dAvbXONxWSk, st:0 03/05/2016 DOT Shivaji University Kolhapur 17
- 19. ◼ 17. Consider a 2x2 MIMO system with channel gain matrix H given by ◼ H = .3 .5 ◼ .7 .2 ◼ Assume H is known at both the transmitter and receiver, and that there is a total transmit power of P = 10 mW across the two transmit antennas, AWGN with power No = 10−9 W/Hz at each receive antenna, and bandwidth B = 100 KHz. ◼ 03/05/2016 DOT Shivaji University Kolhapur 19
- 20. ◼ (a) Find the SVD for H. ◼ (b) Find the capacity of this channel. ◼ (c) Assuming transmit precoding and receiver shaping is used to transform this channel into two parallel independent channels with a total power constraint P . Find the maximum data rate that can be transmit- ted over this parallel set assuming MQAM modulation on each channel with optimal power adaptation across the channels subject to power constraint P . Assume a target BER of 10−3 on each channel, the BER is bounded by ≤ .2e−1.5γ/(M−1), and the constellation size of the MQAM is unrestricted. ◼ (d) Suppose now that the antennas at the 03/05/2016 DOT Shivaji University Kolhapur 20
- 21. ◼ (d) Suppose now that the antennas at the transmitter and receiver are all used for diversity with optimal weighting at the transmitter and receiver to maximize the SNR of the combiner output. Find the SNR of the combiner output, and the BER of a BPSK modulated signal transmitted over this diversity system. Compare the data rate and BER of this BPSK signaling with diversity (assuming B = 1/Tb) to the rate and BER from part (b). ◼ (e) Comment on the diversity/multiplexing tradeoffs between the systems in parts (b) and (c). 03/05/2016 DOT Shivaji University Kolhapur 21
- 22. MIMO Diversity Gain: Beamforming 03/05/2016 DOT Shivaji University Kolhapur 22
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