Two-Way MIMO Decode-and-Forward Relaying Systems with Tensor Space-Time Coding
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This document presents a new closed-form semiblind receiver for two-way MIMO decode-and-forward (DF) relaying systems using tensor space-time coding. The proposed receiver avoids error propagation at the relay by decoding and re-encoding the signals before forwarding to the sources. Simulation results show the DF receiver outperforms amplify-and-forward receivers in terms of symbol error rate due to less noise sensitivity. The cross-coding scheme employed at the relay also simplifies the receiver design and eliminates interference between sources.
![Simulation Results
SER comparison between DF and AF receivers.
• DF receiver outperforms AF due to less sensitivity to noise amplification
0 2 4 6 8 10 12 14 16 18
Es/N0 [dB]
10-8
10-6
10
-4
10
-2
10
0
SER
AF w/ reciprocity
AF w/out reciprocity
DF
14/17](https://image.slidesharecdn.com/eusipco2019v6-200407234558/85/Two-Way-MIMO-Decode-and-Forward-Relaying-Systems-with-Tensor-Space-Time-Coding-14-320.jpg)
![Simulation Results
NMSE of estimated channels and with/without reciprocity
• NMSE performance is impacted by the reciprocity assumption
0 2 4 6 8 10 12 14 16 18
Es/N0 [dB]
10-5
10-4
10-3
10-2
10-1
NMSE
15/17](https://image.slidesharecdn.com/eusipco2019v6-200407234558/85/Two-Way-MIMO-Decode-and-Forward-Relaying-Systems-with-Tensor-Space-Time-Coding-15-320.jpg)
![Simulation Results
SER comparison between DF, EF and ZF receivers
• EF Ideal - has no error propagation at the relay
• DF ZF - LS Kronecker factorization in Eq. (8) with one factor known
0 1 2 3 4 5 6 7 8 9 10
Es/N0 [dB]
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100
SER
DF
EF Ideal
DF ZF
• EF Ideal - relay re-encodes
the exact symbol matrices
• DF ZF - full knowledge of
the channel phases
16/17](https://image.slidesharecdn.com/eusipco2019v6-200407234558/85/Two-Way-MIMO-Decode-and-Forward-Relaying-Systems-with-Tensor-Space-Time-Coding-16-320.jpg)
Two-Way MIMO Decode-and-Forward Relaying Systems with Tensor Space-Time Coding
- 1. Two-Way MIMO Decode-and-Forward Relaying Systems with Tensor Space-Time Coding W. C. Freitas(1) , G. Favier(2) , A. L. F. de Almeida(1) , and Martin Haardt(3) September 4, 2019 (1) Wireless Telecom Research Group Federal University of Cear´a Fortaleza, Brazil http://www.gtel.ufc.br (2) Laboratoire I3S Universit´e Cˆote d’Azur Nice, France http://www.i3s.unice.fr (3) Comm. Research Lab. Ilmenau University of Technology Ilmenau, Germany http://tu-ilmenau.de/crl 1/17
- 2. Agenda • Introduction • System model • Decode-and-Forward (DF) closed-form semiblind receiver • Simulation results • Conclusions 2/17
- 3. Introduction • Tensor-based receivers have been successfully used for joint symbol and channel estimation in cooperative MIMO communications • Previous works derived two-way cooperative MIMO receivers, most assuming amplify-and-forward (AF) relays • Proposal: a new closed-form semiblind receiver for a two-way DF relaying system that: 1. avoids error propagation problems; 2. exploits a cross-coding structure that suppresses interference between sources and simplifies the receiver. 3/17
- 4. System Model Two-way MIMO Relaying System Source i . . . Ms Relay . . . Mr Source j . . . Ms H(sir) H(rsi) H(sj r) H(rsj ) • Two-way MIMO: each source aims to estimate the signals sent by the other • Uplink phase: sources transmit to the relay • Downlink phase: relay transmits re-encoded data to the sources • Ms and Mr denote the number of antennas at sources and relay • H(sir) ∈ Mr×Ms and H(rsi) ∈ Ms×Mr , denote the channels during the uplink and downlink phases, respectively 4/17
- 5. Tensor of Signals Received at the Relay Uplink Transmission Source i . . . Ms Relay . . . Mr Source j . . . Ms H(sir) H(sj r) • Symbol matrix transmitted by source i: S(i) ∈ N×R containing N data symbols in R data-streams • Tensor space-time code (TSTC) at source i: C(i) ∈ R×Ms×P , P the time spreading length of the codes at the sources • The signals received at the relay form a tensor X ∈ N×Mr×P X = C(i) ×1 S(i) ×2 H(sir) + C(j) ×1 S(j) ×2 H(sj r) (1) ⇓ Block Tucker-2 model5/17
- 6. Relay Processing Downlink Transmission Source i . . . Msi Relay . . . Mr Source j . . . Msj H(rsi) H(rsj ) • Assuming a DF protocol, the relay estimates and decodes the symbol matrices ˆS(i) and ˆS(j) • A cross-coding scheme is proposed at the relay to suppresses interference between sources, using C(j) to encode ˆS(i) , while C(i) is used to encode ˆS(j) 6/17
- 7. Relay Processing Symbols Estimation and Projection on the Alphabet • From the flat 3-mode unfolding of X (disregarding the noise) XP ×NMr = C (i) 3 S(i) ⊗ H(sir) T + C (j) 3 S(j) ⊗ H(sj r) T . (2) • C (i) 3 , C (j) 3 ∈ P ×RMs are chosen as two blocks extracted from a P × 2RMs DFT matrix, i.e., C (i)H 3 C (i) 3 = IRMs and C (i)H 3 C (j) 3 = 0RMs • Least-square (LS) estimation of the Kronecker products from Eq. (2) given by Z (i) RMs×NMr ∼= C (i)H 3 XP ×NMr = S(i) ⊗ H(sir) T Z (j) RMs×NMr ∼= C (j)H 3 XP ×NMr = S(j) ⊗ H(sj r) T . (3) 7/17
- 8. Identifiability Ambiguity Suppression and Complexity • Kronecker product factorization algorithm can be used to estimate S(i) and H(sir) for the source i from Z (i) RMs×NMr • Uniqueness of Kronecker factors and S(i) and H(sir) estimated at source i up to scalar ambiguity • Element s (i) 1,1 is known and equal to 1. Final estimates of the channels and symbol matrices is (λS(i) = 1/ˆs (i) 1,1) ˆS(i) ← ˆS(i) λS(i) , ˆH (sir) Mr×Ms ← ˆH (sir) Mr×Ms λ−1 S(i) , • Complexity associated with the SVD calculation of matrix J × K ⇒ Ç(min(J, K)JK) • Relay complexity: Ç(min(NMr, RMs)NMrRMs) 8/17
- 9. Cross-Coding at the Relay Relay Processing • Relay re-encodes the estimated signals to be transmitted using tensor space-time codes C(i) and C(j) ∈ R×Ms×P • Relay re-encodes the estimated signals using cross-coding: ˆS(i) using C(j) , and ˆS(j) using C(i) • 3-mode unfoldings C (i) 3 , C (j) 3 ∈ P ×RMs are chosen as two blocks extracted from a P × 2RMs DFT matrix as C (j)H 3 C (i) 3 = 0RMs (4) C (j)H 3 C (j) 3 = IRMs (5) • Such orthogonal design allows to derive the closed-form semiblind receiver 9/17
- 10. Tensor of Signals Received at the Receiver Downlink Transmission Source i . . . Msi Relay . . . Mr Source j . . . Msj H(rsi) H(rsj ) • Tensor of signals received at source i: Y(i) ∈ N×Ms×P (Mr = Ms) Y(i) = C(i) ×1 ˆS(j) ×2 H(rsi) + C(j) ×1 ˆS(i) ×2 H(rsi) (6) ⇓ Block Tucker-2 model 10/17
- 11. Proposed Closed-Form Semiblind Receiver Source i Processing • The flat 3-mode unfolding of the received signals tensor Y(i) Y (i) P ×NMs = C (i) 3 ˆS(j) ⊗ H(rsi) T + C (j) 3 ˆS(i) ⊗ H(rsi) T . (7) • LS estimate of the Kronecker product is given by R (i) RMr×NMs ∼= C (i)H 3 Y (i) P ×NMs = ˆS(j) ⊗ H(rsi) T . (8) • Kronecker product factorization algorithm can be used to estimate S(j) for the source i from R(i) • Source complexity: Ç(min(NMs, RMr)NMsRMr). • The same approach can be followed by source j to estimate S(i) from R(j) 11/17
- 12. Closed-form DF Semiblind Receiver Inputs: X , Y(i) , C(i) and C(j) . • Relay Processing 1. Compute the LS estimate of Z (i) RMs×NMr = S(i) ⊗ H(sir) T using Eq. (3). 2. Use the Kronecker factorization algorithm to estimate S(i) and H(sir) . 3. Remove the scaling ambiguities of ˆS(i) and ˆH(sir) . 4. Project the estimated symbols onto the alphabet. 5. Re-encode ˆS(i) using C(j) , and ˆS(j) using C(i) . • Source i Processing 1. Compute the LS estimate of R (i) RMr×NMs = S(j) ⊗ H(rsi) T using Eq. (8). 2. Use the Kronecker factorization algorithm to estimate S(j) and H(rsi) . 3. Remove the scaling ambiguities of ˆS(j) and ˆH(rsi) , and project the estimated symbols onto the alphabet. 12/17
- 13. Simulation Assumptions • Performance criteria - SER and NMSE of estimated channels averaged over 4 × 104 Monte Carlo runs. • Each run corresponds to a realization of all channel and symbol matrices, and noise tensors • Transmitted symbols are randomly drawn from a unit energy m-QAM symbol alphabet • Number of data symbols N = 4, of data-streams R = 2 and of antennas Ms = Mr = 2 • Modulation order m and spreading length P are adjusted to ensure the same transmission rate, equal to 4/5 bit per channel use 13/17
- 14. Simulation Results SER comparison between DF and AF receivers. • DF receiver outperforms AF due to less sensitivity to noise amplification 0 2 4 6 8 10 12 14 16 18 Es/N0 [dB] 10-8 10-6 10 -4 10 -2 10 0 SER AF w/ reciprocity AF w/out reciprocity DF 14/17
- 15. Simulation Results NMSE of estimated channels and with/without reciprocity • NMSE performance is impacted by the reciprocity assumption 0 2 4 6 8 10 12 14 16 18 Es/N0 [dB] 10-5 10-4 10-3 10-2 10-1 NMSE 15/17
- 16. Simulation Results SER comparison between DF, EF and ZF receivers • EF Ideal - has no error propagation at the relay • DF ZF - LS Kronecker factorization in Eq. (8) with one factor known 0 1 2 3 4 5 6 7 8 9 10 Es/N0 [dB] 10-7 10-6 10-5 10-4 10-3 10-2 10-1 100 SER DF EF Ideal DF ZF • EF Ideal - relay re-encodes the exact symbol matrices • DF ZF - full knowledge of the channel phases 16/17
- 17. Conclusions • New closed-form semiblind receiver for two-way MIMO DF relaying systems • Advantages of DF receiver compared with AF receivers: • Orthogonal cross-coding to eliminate sources interference • Better SER due to the smaller propagation error, at the price of an additional decoding at the relay • Channel reciprocity is not needed • Compared with ALS-based receivers, closed-form is simpler 17/17
- 18. Thank you for your attention. 17/17