On Distributed Space-Time Coding Techniques for Cooperative Wireless Networks and their Sensitivity to Frequency Offsets
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1 On Distributed Space-Time Coding Techniques for Cooperative Wireless Networks and their Sensitivity to Frequency Offsets Jan Mietzner, Jan Eick, and Peter A. Hoeher (ICT) University of Kiel, Germany ITG Workshop on Smart Antennas Munich, March 18, 2004
2 Distributed Space-Time Coding Techniques 1 Space-time coding (STC) techniques for multiple-antenna wireless communication systems Performance of wireless systems often limited by fading due to multipath signal propagation. System performance may be significantly improved by exploiting some sort of diversity.
3 Distributed Space-Time Coding Techniques 1 Space-time coding (STC) techniques for multiple-antenna wireless communication systems Performance of wireless systems often limited by fading due to multipath signal propagation. System performance may be significantly improved by exploiting some sort of diversity. = Employ STC techniques to exploit spatial diversity.
4 Distributed Space-Time Coding Techniques 1 Space-time coding (STC) techniques for multiple-antenna wireless communication systems Performance of wireless systems often limited by fading due to multipath signal propagation. System performance may be significantly improved by exploiting some sort of diversity. = Employ STC techniques to exploit spatial diversity. Concept of multiple antennas may be transferred to cooperative wireless networks. Multiple (single-antenna) nodes cooperate in order to perform a joint transmission strategy.
5 Distributed Space-Time Coding Techniques 1 Space-time coding (STC) techniques for multiple-antenna wireless communication systems Performance of wireless systems often limited by fading due to multipath signal propagation. System performance may be significantly improved by exploiting some sort of diversity. = Employ STC techniques to exploit spatial diversity. Concept of multiple antennas may be transferred to cooperative wireless networks. Multiple (single-antenna) nodes cooperate in order to perform a joint transmission strategy. = Nodes share their antennas by using a distributed STC scheme.
6 Examples for Cooperative Wireless Networks 2 Simulcast networks for broadcasting or paging applications: Conventionally, all nodes simultaneously transmit the same signal using the same carrier frequency.
7 Examples for Cooperative Wireless Networks 2 Simulcast networks for broadcasting or paging applications: Conventionally, all nodes simultaneously transmit the same signal using the same carrier frequency. Relay-assisted communication, e.g., in cellular systems, sensor networks, ad-hoc networks: Signal transmitted by a given source node is received by several relay nodes and forwarded to a destination node. Relay nodes may either be fixed stations or other mobile stations ( user cooperation diversity ). A relay-assisted network may be viewed as a type of simulcast network (only few errors between source node and relay nodes).
8 Examples for Cooperative Wireless Networks 2 Simulcast networks for broadcasting or paging applications: Conventionally, all nodes simultaneously transmit the same signal using the same carrier frequency. Relay-assisted communication, e.g., in cellular systems, sensor networks, ad-hoc networks: Signal transmitted by a given source node is received by several relay nodes and forwarded to a destination node. Relay nodes may either be fixed stations or other mobile stations ( user cooperation diversity ). A relay-assisted network may be viewed as a type of simulcast network (only few errors between source node and relay nodes). = Distributed STC techniques suitable for both simulcast and relay-assisted networks.
9 Simulcast Network 3 N transmitting nodes (Tx 1,...,Tx N ), one receiving node (Rx) Tx 1 s1(t) s N (t) Tx N Rx s 2 (t) Tx 2
10 Simulcast Network 3 N transmitting nodes (Tx 1,...,Tx N ), one receiving node (Rx) Tx 1 s1(t) s N (t) Tx N Distributed STC scheme such that Diversity degree N accomplished in case of no shadowing. s 2 (t) Rx Diversity degree (N n) accomplished if any subset of n Tx nodes is obstructed. Tx 2
11 Simulcast Network 3 N transmitting nodes (Tx 1,...,Tx N ), one receiving node (Rx) Tx 1 s1(t) s N (t) Tx N Distributed STC scheme such that Diversity degree N accomplished in case of no shadowing. s 2 (t) Rx Diversity degree (N n) accomplished if any subset of n Tx nodes is obstructed. Example: Tx 2 Space-time block codes (STBCs) from orthogonal designs (Tarokh et al. 99)
12 Key Problem 4 Key problem specific to cooperative wireless networks: Transmitters introduce independent frequency offsets f t1,..., f tn with respect to the nominal carrier frequency.
13 Key Problem 4 Key problem specific to cooperative wireless networks: Transmitters introduce independent frequency offsets f t1,..., f tn with respect to the nominal carrier frequency. = May cause severe performance degradations, diversity advantage may be lost.
14 Key Problem 4 Key problem specific to cooperative wireless networks: Transmitters introduce independent frequency offsets f t1,..., f tn with respect to the nominal carrier frequency. = May cause severe performance degradations, diversity advantage may be lost. Scenarios: (i) Frequency offsets perfectly known at the receiver. (ii) Non-perfect estimates of the frequency offsets available at the receiver. (iii) Frequency offsets completely unknown at the receiver.
15 Key Problem 4 Key problem specific to cooperative wireless networks: Transmitters introduce independent frequency offsets f t1,..., f tn with respect to the nominal carrier frequency. = May cause severe performance degradations, diversity advantage may be lost. Scenarios: (i) Frequency offsets perfectly known at the receiver. (ii) Non-perfect estimates of the frequency offsets available at the receiver. (iii) Frequency offsets completely unknown at the receiver. Focus on the Alamouti scheme (orthogonal STBC for N = 2 transmitters).
16 Outline 5 Influence of the Frequency Offsets Conventional Alamouti Detection Zero-Forcing Detection and Maximum-Likelihood Detection Bit Error Probability Simulation Results Frequency-Offset Estimation Conclusions
17 Influence of the Frequency Offsets 6 Overall frequency offset for transmitted signal s ν (t): f ν = f tν f r. Tx 1 f t1 s1(t) s N (t) Tx N f tn Rx f r s 2 (t) Tx 2 f t2
18 Influence of the Frequency Offsets 6 Overall frequency offset for transmitted signal s ν (t): f ν = f tν f r. Normalized frequency offset: Tx 1 f t1 s1(t) Rx s N (t) Tx N f tn ζ ν. = fν T ζ ν 0.04 assumed for all ν = 1,..., N. f r s 2 (t) Tx 2 f t2
19 Influence of the Frequency Offsets 6 Overall frequency offset for transmitted signal s ν (t): f ν = f tν f r. Normalized frequency offset: Tx 1 f t1 s1(t) Rx s N (t) Tx N f tn ζ ν. = fν T ζ ν 0.04 assumed for all ν = 1,..., N. s 2 (t) f r Quasi-static frequency-flat fading: Complex channel coefficients h 1,..., h N. Tx 2 f t2 = Frequency offsets cause time-varying phase: h ν [k]. = h ν e j2πζ νk
20 Ideal Local Oscillators Alamouti-Detection 7 Distributed Alamouti scheme (N = 2 Tx nodes); ideal local oscillators (LOs), ζ 1 = ζ 2 = 0 = y[k] = H eq x[k] + n[k] (1)
21 Ideal Local Oscillators Alamouti-Detection 7 Distributed Alamouti scheme (N = 2 Tx nodes); ideal local oscillators (LOs), ζ 1 = ζ 2 = 0 = y[k] = H eq x[k] + n[k] (1) y[k]: Received samples, x[k]: Transmitted symbols, n[k]: Noise samples, [ ] h1 h H eq = 2 h 2 h : Equivalent orthogonal (2x2)-channel matrix. 1
22 Ideal Local Oscillators Alamouti-Detection 7 Distributed Alamouti scheme (N = 2 Tx nodes); ideal local oscillators (LOs), ζ 1 = ζ 2 = 0 = y[k] = H eq x[k] + n[k] (1) y[k]: Received samples, x[k]: Transmitted symbols, n[k]: Noise samples, [ ] h1 h H eq = 2 h 2 h : Equivalent orthogonal (2x2)-channel matrix. 1 = Alamouti detection: z[k]. = H H eq y[k] = HH eq H eq x[k] + H H eq n[k] ( = h h 2 2) x[k] + H H eq n[k] (2)
23 Non-Ideal Local Oscillators Alamouti-Detection 8 Channel matrix H eq becomes H eq [k] = [ h 1 [k] h 2 [k+1] h 2 [k] h 1 [k+1] ]. (3) Assumption: Receiver has perfect knowledge of h 1 and h 2 at the beginning of each block.
24 Non-Ideal Local Oscillators Alamouti-Detection 8 Channel matrix H eq becomes H eq [k] = [ h 1 [k] h 2 [k+1] h 2 [k] h 1 [k+1] ]. (3) Assumption: Receiver has perfect knowledge of h 1 and h 2 at the beginning of each block. (i) Frequency offsets perfectly known at the receiver = Receiver uses H H eq [k] for detection. Product matrix H H eq [k] H eq[k] is close to diagonal matrix (for practical values of ζ 1, ζ 2 ).
25 Non-Ideal Local Oscillators Alamouti-Detection 8 Channel matrix H eq becomes H eq [k] = [ h 1 [k] h 2 [k+1] h 2 [k] h 1 [k+1] ]. (3) Assumption: Receiver has perfect knowledge of h 1 and h 2 at the beginning of each block. (i) Frequency offsets perfectly known at the receiver = Receiver uses H H eq [k] for detection. Product matrix H H eq [k] H eq[k] is close to diagonal matrix (for practical values of ζ 1, ζ 2 ). (ii) Non-perfect estimates ˆζ. ν = ζν +ɛ ν of the frequency offsets available at the receiver [ ] = Receiver uses H H eq,ɛ [k] = h 1 e j2π ˆζ 1 k h 2 e j2π ˆζ 2 (k+1) h 2 e j2π ˆζ 2 k h 1 e j2π ˆζ for detection. 1 (k+1) Depending on the quality of the estimates ˆζ ν, more or less severe orthogonality loss.
26 Non-Ideal Local Oscillators 9 (iii) Frequency offsets completely unknown at the receiver = Receiver uses H H eq for detection. Depending on k, the product matrix H H eq H eq[k] can even be an anti-diagonal matrix = Severe performance degradations.
27 Non-Ideal Local Oscillators 9 (iii) Frequency offsets completely unknown at the receiver = Receiver uses H H eq for detection. Depending on k, the product matrix H H eq H eq[k] can even be an anti-diagonal matrix = Severe performance degradations. Alternatives to Alamouti detection (a) Zero-forcing (ZF) detection: Use inverse matrix for detection instead of hermitian conjugate. (b) Maximum-likelihood (ML) detection.
28 Non-Ideal Local Oscillators 9 (iii) Frequency offsets completely unknown at the receiver = Receiver uses H H eq for detection. Depending on k, the product matrix H H eq H eq[k] can even be an anti-diagonal matrix = Severe performance degradations. Alternatives to Alamouti detection (a) Zero-forcing (ZF) detection: Use inverse matrix for detection instead of hermitian conjugate. (b) Maximum-likelihood (ML) detection. Performance of ZF detection is virtually the same as that of ML detection in all cases. Given ideal LOs Alamouti detection, ZF detection, and ML detection are equivalent.
29 Bit Error Probability 10 Non-ideal LOs, Alamouti detection or ZF detection Quasi-static frequency-flat fading QPSK symbols x[k] with Gray mapping [b 1k b 2k ] x[k]: [00] exp[j π/4] [01] exp[j 3π/4] [11] exp[j 5π/4] [10] exp[j 7π/4].
30 Bit Error Probability 10 Non-ideal LOs, Alamouti detection or ZF detection Quasi-static frequency-flat fading QPSK symbols x[k] with Gray mapping [b 1k b 2k ] x[k]: z[k] corresponding symbol after Alamouti detection/ ZF detection [00] exp[j π/4] [01] exp[j 3π/4] [11] exp[j 5π/4] [10] exp[j 7π/4]. Let d Re [k], d Im [k] denote real and imaginary part of z[k] for high SNRs (E s /N 0 ); may be determined analytically.
31 Bit Error Probability 11 = BEP for bit b 1k : P b1 [k] = Q ( P b1 [k] = 1 Q 2 d 2 Im [k] ( h h 2 2 ) E s No ( 2 ) d 2 Im [k] ( h h 2 2 ) E s No ) if Im{x[k]} and Im{z[k]} have equal signs else Similarly for bit b 2k (using d Re [k]) = P b2 [k]
32 Bit Error Probability 11 = BEP for bit b 1k : P b1 [k] = Q ( P b1 [k] = 1 Q 2 d 2 Im [k] ( h h 2 2 ) E s No ( 2 ) d 2 Im [k] ( h h 2 2 ) E s No ) if Im{x[k]} and Im{z[k]} have equal signs else Similarly for bit b 2k (using d Re [k]) = P b2 [k] = Overall average BEP given blocks of L B QPSK symbols: P b = 1 2L B L B 1 k=0 E {P b1 [k]} + E {P b2 [k]} (4) (Expectation is with respect to the channel coefficients h 1 and h 2.)
33 Outline 12 Influence of the Frequency Offsets Simulation Results Alamouti Detection and ZF/ ML detection Perfect and Non-Perfect Frequency-Offset Estimates Frequency-Offset Estimation Conclusions
34 Simulation Results 13 Uncoded transmission, Tx power normalized w.r.t. number of Tx nodes QPSK symbols, Gray mapping Quasi-static frequency-flat fading, Rice factor K = 0 db Channel coefficients perfectly known at the beginning of each block
35 Simulation Results 13 Uncoded transmission, Tx power normalized w.r.t. number of Tx nodes QPSK symbols, Gray mapping Quasi-static frequency-flat fading, Rice factor K = 0 db Channel coefficients perfectly known at the beginning of each block Alamouti detection Frequency offsets ζ 1 = +0.03, ζ 2 = Frequency offsets perfectly known/ completely unknown
36 Simulation Results 13 Uncoded transmission, Tx power normalized w.r.t. number of Tx nodes QPSK symbols, Gray mapping Quasi-static frequency-flat fading, Rice factor K = 0 db Channel coefficients perfectly known at the beginning of each block Alamouti detection Frequency offsets ζ 1 = +0.03, ζ 2 = Frequency offsets perfectly known/ completely unknown BER (1x1) System (2x1) Alamouti, ideal LOs (2x1) Alamouti, freq. offsets unknown (2x1) Alamouti, freq. offsets unknown (analyt.) (2x1) Alamouti, freq. offsets perf. known (2x1) Alamouti, freq. offsets perf. known (analyt.) E s /N 0 (db)
37 Simulation Results 14 Alamouti detection (solid lines) vs. ZF/ ML detection (dashed lines) Frequency offsets ζ 1 = +0.03, ζ 2 = Frequency-offset estimates: Absolute errors of 2%... 5%
38 Simulation Results 14 Alamouti detection (solid lines) vs. ZF/ ML detection (dashed lines) (1x1) System (2x1) Alamouti, ideal LOs (2x1) Alamouti, both frequency offsets +5% (2x1) Alamouti, both frequency offsets +4% (2x1) Alamouti, both frequency offsets +3% (2x1) Alamouti, both frequency offsets +2% Frequency offsets ζ 1 = +0.03, ζ 2 = Frequency-offset estimates: Absolute errors of 2%... 5% BER E s /N 0 (db)
39 Simulation Results 15 ML detection E s /N 0 = 10 db Frequency offsets ζ 1, ζ Frequency-offset estimates: Absolute errors of 3%
40 Simulation Results 15 ML detection E s /N 0 = 10 db 0.05 Both frequency offsets +3% Frequency offsets ζ 1, ζ BER BER (1x1) System Frequency offsets perfectly known Frequency-offset estimates: Absolute errors of 3% ζ ζ 2
41 Outline 16 Influence of the Frequency Offsets Simulation Results Frequency-Offset Estimation Training-Based Estimation Method Blind Estimation Method Conclusions
42 Frequency-Offset Estimation 17 Training-Based Estimation Method Estimating channel coefficients given known data symbols is dual to estimating data symbols given known channel coefficients = Principle of Alamouti detection can be applied. Average over the phase differences of several subsequent channel-coefficient estimates = Explicit estimates for the frequency-offsets.
43 Frequency-Offset Estimation 17 Training-Based Estimation Method Estimating channel coefficients given known data symbols is dual to estimating data symbols given known channel coefficients = Principle of Alamouti detection can be applied. Average over the phase differences of several subsequent channel-coefficient estimates = Explicit estimates for the frequency-offsets. Blind Estimation Method QPSK symbols: Raise the received samples to the power of four and perform an FFT = Spectral lines at 4ζ 1 and 4ζ 2 plus noise. Average over several FFTs to eliminate the influence of noise.
44 Frequency-Offset Estimation 17 Training-Based Estimation Method Estimating channel coefficients given known data symbols is dual to estimating data symbols given known channel coefficients = Principle of Alamouti detection can be applied. Average over the phase differences of several subsequent channel-coefficient estimates = Explicit estimates for the frequency-offsets. Blind Estimation Method QPSK symbols: Raise the received samples to the power of four and perform an FFT = Spectral lines at 4ζ 1 and 4ζ 2 plus noise. Average over several FFTs to eliminate the influence of noise. Frequency-offset estimation in cooperating wireless networks is more difficult than in (1x1)-systems.
45 Conclusions 18 Influence of frequency offsets on the performance of a distributed Alamouti scheme Different receiver concepts (Alamouti detection, ZF detection, ML detection) Bit error probability given non-ideal local oscillators The performance of a distributed Alamouti scheme is very sensitive to frequency offsets. Frequency-offset estimates Accurate frequency-offset estimates are required at the receiver (e.g. error of less than 3%) Two different methods for frequency-offset estimation Frequency-offset estimation is more difficult than in (1x1)-systems.
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