Asymptotic Analysis of Full-Duplex Bidirectional MIMO Link with Transmitter Noise

Transcription

1 Asymptotic Analysis of Full-Duplex Bidirectional MIMO Link with Transmitter Noise Mikko Vehkaperä, Taneli Riihonen, and Risto Wichman Aalto University School of Electrical Engineering, Finland Session PHY42: Single- and Multi-User MIMO II, September 11, th Annual IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC)

2 Introduction Taneli Riihonen Full-Duplex Bidirectional MIMO 2 / 24

3 Full-Duplex Wireless Communication Systems Advanced radio transceivers which are able to simultaneously transmit and receive (STAR) on a single frequency band Potential applications of full-duplex operation are many This work concentrates on bidirectional links Full duplex renders up to double spectral efficiency at link level!... but there is still a significant technical challenge: the mitigation of unavoidable self-interference Two main digital techniques: time-domain cancellation spatial-domain suppression Taneli Riihonen Full-Duplex Bidirectional MIMO 3 / 24

4 Asymptotic Analysis of Bidirectional Links Terminal 1 Terminal 2 Bidirectional full-duplex multiantenna (MIMO) link large number of antennas symmetric configuration in numerical results Achievable rates, i.e., (generalized) mutual information The replica method, originally developed in the field of statistical physics and recently applied to communication theory problems necessitates the assumption of the large-system limit where the degrees of freedom in the system grow without bound However, simulated (Monte Carlo) results for small-scale systems agree well with the corresponding asymptotic results Taneli Riihonen Full-Duplex Bidirectional MIMO 4 / 24

5 Transmitter Noise and M(ism)atched Decoding distortion Unknown transmit-side noise due to analog imperfections nonlinear distortion, e.g., power amplifier (PA) measured with EVM Feedback transmit-side noise may be on a par with the far-end signal due to the high gain of the near-end interference channel Feedforward transmit-side noise can be neglected since it is typically below receive-side noise after channel attenuation Mitigation transparently around the actual multiplexing protocol which can operate without being aware of self-interference Mismatched detection and decoding due to unexpected noise Taneli Riihonen Full-Duplex Bidirectional MIMO 5 / 24

6 Self-interference Mitigation with Transmitter Noise Spatial-domain suppression: enc. noise Time-domain cancellation: enc. noise filter dec. filter dec. The link needs efficient self-interference mitigation at both ends Suppression: receiving only in the null space of interference Cancellation: subtracting the interfering signal before decoder Both can eliminate the data-dependent part of self-interference Suppression eliminates also the self-induced transmit-side noise, at the cost of consuming some spatial degrees of freedom Taneli Riihonen Full-Duplex Bidirectional MIMO 6 / 24

7 System Model Taneli Riihonen Full-Duplex Bidirectional MIMO 7 / 24

8 Signal Model (Fig. 1) m 1 n 2 x 1 H 12 G 2 y 2 n 1 H 11 H 22 m 2 y 1 G 1 H 21 x 2 Terminal 1 Terminal 2 Terminal i {1,2} has M i transmit and N i receive antennas In communication direction ij {12, 21}: y j = G j H ij (x i +m i )+G j H jj (x j +m j )+G j n j noise terms m i and m j due to transmitter imperfections ˆNj receive streams remain after self-interference mitigation Terminal i does not know H ij but Terminal j knows H ij and H jj Taneli Riihonen Full-Duplex Bidirectional MIMO 8 / 24

9 Spatial-Domain Suppression n 2 x 1 H 12 G 2 y 2 n 1 y 1 G 1 H 21 x 2 Terminal 1 Terminal 2 In Terminal j {1,2} after suppression using G j of rank ˆN j : y j = G j (H ij x i +H ij m i )+G j H jj (x j +m j ) +G j n j }{{}}{{} 0 eliminated when G j H jj =0 ˆNj = N j M j if H jj has full rank, thus requiring N j > M j When enclosing any conventional (e.g., half-duplex) transceiver by transparent suppression, it still performs matched decoding Taneli Riihonen Full-Duplex Bidirectional MIMO 9 / 24

10 Time-Domain Cancellation n 2 x 1 m 1 y 1 n 1 H 12 H 11 H 22 H 21 y 2 m 2 x 2 Terminal 1 Terminal 2 In Terminal j {1,2} after cancellation presuming G j = I: y j = H ij x i +H ij m i +H jj x j +H jj m j +n j }{{}}{{}}{{} 0 eliminated unknown! ˆNj = N j, i.e., all degrees of freedom are saved for data reception Conventional receivers may adapt imperfectly to the presence of unexpected transmitter noise, leading to mismatched decoding Taneli Riihonen Full-Duplex Bidirectional MIMO 10 / 24

11 Analytical Results Taneli Riihonen Full-Duplex Bidirectional MIMO 11 / 24

12 Problem Statement Unified signal model: y j G j H ij x i +w j where w j = G j H jj m j +G j n j with R wj = σ2 j M j G j H jj H H jj GH j +I 1. Matched decoding uses the true density p(y j x i,h ij ) 2. Mismatched decoding estimates R wj as R wj and uses a postulated density q(y j x i,h ij ) Generalized mutual information (GMI) is defined as ( ) I gmi (y j ; x i ) = supi (s) gmi (y j; x i ) = sup Elnq(y j x i,h ij ) s Elnq (s) (y j H ij ) s>0 s>0 where q (s) (y j H ij ) = E xi q(y j x i,h ij ) s The first term is easy to calculate, yielding I (s) gmi (y j; x i ) = ( c setr( ) 1 R w j R wj ) Elnq (s) (y j H ij ), while the second term needs special tricks as follows Taneli Riihonen Full-Duplex Bidirectional MIMO 12 / 24

13 Replica Analysis Instead of trying direct calculation, let us take a different route and start by reformulating the difficult term as Elnq (s) (y j H ij ) = c+ lim u 0 u lnez(y j,h ij ;s) u where Z(y j,h ij ;s) = E xi e (y j G j H ij x i ) H s To circumvent the problem of u being real-valued, the replica trick then postulates Z(x 0,w j,h ij ;s) u = E {xa } u a=1 u a=1 e [w j+g j H ij (x 0 x a )] H s R 1 w j (y j G j H ij x i ) R 1 w j [w j +G j H ij (x 0 x a )] where x 0 and {x a } u a=1 denote the original and replicated vectors If we manage to assess the above expectation as a function of u when matrix dimensions in H ij grow without bound with fixed ratios, analytically continuing u 0 recovers the per-stream GMI as 1 M I(s) gmi (y j; x i ) = s M Etr( R 1 w j R wj ) lim M 1 M lim u 0 u lnez(x 0,w j,h ij ;s) u Taneli Riihonen Full-Duplex Bidirectional MIMO 13 / 24

14 Matched Decoding: Per-stream Achievable Rate When H ij and H jj are i.i.d. Gaussian with gains γ ij and γ jj and the receiver adapts perfectly to residual self-interference: R ij M i = ln(1 + η ij ) η ij + 1 [ ( I α jj, γ jj σ 2 j 1 + η ij α ; 1 + ij γ ij 1 + η ij ) I(α jj, γ jj σ 2j ; 1) ] for which the fixed-point η ij is found numerically by iterating η ij = γ [ ij α ij γ ij 1+η ij α ii 4 γ jj σ 2 j ( γjj σj 2 F α ii and the auxiliary functions are given by F(x,β) = I(β,σ 2 ; t) = lnt + β ln [1 + σ2 tβ 1 ( σ 2 )] 4 F tβ,β γ ij 1+η ij,α ii ( x(1 + β) x(1 ) 2 β) )] + ln [1 + σ2 t 1 ( σ 2 )] 4 F tβ,β tβ ( σ 2 ) 4σ 2 F tβ,β N.B.: This result is for cancellation only while the counterpart with suppression is already analyzed in our CISS 13-paper (ref. [12]) Taneli Riihonen Full-Duplex Bidirectional MIMO 14 / 24

15 Mismatched Decoding: Per-stream Achievable Rate When H ij and H jj are i.i.d. Gaussian with gains γ ij and γ jj and the receiver postulates imperfectly R wj = (1+ γ jj σ 2 j )I N: R ij s(1 + γ jj σj 2 = ) M i α ij (1 + γ jj σ j 2 + sẽij) sẽij 1 + γ jj σ 2 j + ln ( 1 + s γ ij α ij (1 + γ jj σ 2 j + sẽij) ) + 1 ( ln 1 + α ij sẽij 1 + γ jj σ 2 j ) where Ẽij is directly given as Ẽ ij = s γ ij (1 + γ jj σ 2 j ) 2s γ ij 2α ij + (1 + γ jj σ j 2) γ ij s ( s γij (1 + γ jj σ j 2 + ) 2s γ ) 2 ij 2α ij the case of σ j 2 = 0 is illustrated in the numerical examples asymptotic result at large-system limit: M i and N j while M i N j α ij for all i,j {1,2} (like in the previous slide) Optimization is required for the parameter s though, in order to find more tight lower bounds for the maximum achievable rate Taneli Riihonen Full-Duplex Bidirectional MIMO 15 / 24

16 Numerical Examples Taneli Riihonen Full-Duplex Bidirectional MIMO 16 / 24

17 Example Setups The numerical results concentrate on symmetric systems where M = M 1 = M 2 N = N 1 = N 2 γ = γ 12 = γ 21 γ I = γ 11 = γ 22 σ 2 = σ 2 1 = σ2 2 There may be transmit/receive antenna imbalance (M/N) Yet M and N grow asymptotically at the large-system limit Choice σ 2 = corresponds to transmitter EVM of 30 db (or equivalently 3.2%) which is a practical but slightly optimistic value In summary, there are three key parameters to explore: γ γ I M/N Taneli Riihonen Full-Duplex Bidirectional MIMO 17 / 24

18 Achievable Rates vs. SNR (Fig. 2) cancellation without transmit-side noise cancellation and matched decoding suppression and matched decoding cancellation and mismatched decoding cancellation without transmit-side noise cancellation and matched decoding suppression and matched decoding cancellation and mismatched decoding Rij/ ln 2 [bit/s/hz] Fig. 3 Rij/ ln 2 [bit/s/hz] Fig γ [db] (a) M = 4, N = 8, γ I = 33 db γ [db] (b) M = 4, N = 6, γ I = 39 db Simulations (markers) corroborate analytical results (solid lines) (a) when M/N 1/2, suppression reduces receive array gain (b) when M/N > 1/2, suppression reduces multiplexing order Taneli Riihonen Full-Duplex Bidirectional MIMO 18 / 24

19 Matched Decoding: Suppression vs. Cancellation [%] γi [db] cancellation preferred γ [db] (a) M/N = 1/2 as in Fig. 2(a) γi [db] γ [db] cancellation preferred (b) M/N = 2/3 as in Fig. 2(b) 60 Suppression is worse than cancellation if matched decoding is still feasible under residual self-interference, since such receivers already comprise ideal interference and noise control Taneli Riihonen Full-Duplex Bidirectional MIMO 19 / 24

20 Mismatched Decoding: Suppression vs. Cancellation [%] γi [db] suppression preferred Fig. 2(a) 100 γi [db] suppression preferred Fig. 2(b) γ [db] 83 cancellation preferred (a) M/N = 1/2 as in Fig. 2(a) cancellation preferred γ [db] (b) M/N = 2/3 as in Fig. 2(b) 50 Transmitter noise and mismatched decoding cause an intricate interplay between the parameters corresponding to the channel gains of the data and self-interference links and the antenna ratio Taneli Riihonen Full-Duplex Bidirectional MIMO 20 / 24

21 Mismatched Decoding: Switching Boundaries (Fig. 3) suppression preferred 5/6 4/5 3/4 Fig. 2(b) 3/5 γi [db] /5 3/4 2/3 2/3 3/5 Fig. 2(a) 3/5 1/2 1/2 2/5 1/3 1/4 1/2 2/5 1/3 1/ γ [db] 2/5 1/3 1/4 cancellation preferred Suppression becomes preferred in wide SNR range when the number of receive antennas vs. transmit antennas is large The level of self-interference is a significant factor at low SNR Taneli Riihonen Full-Duplex Bidirectional MIMO 21 / 24

22 Conclusion Taneli Riihonen Full-Duplex Bidirectional MIMO 22 / 24

23 Conclusion Wireless full-duplex communication becomes a hot research topic A progressive frequency-reuse concept: significantly improved spectral efficiency at the cost of self-interference Achievable rates in bidirectional full-duplex link Mismatched decoding due to transmitter imperfections Analysis at the large-system limit based on the replica method Monte Carlo simulations with small number of antennas match well with the corresponding asymptotic results Comparison of spatial suppression and subtractive cancellation for characterizing the cost and benefit of allocating a part of spatial degrees of freedom for self-interference mitigation The study reveals a trade-off between reduced multiplexing order or array gain and residual self-interference Taneli Riihonen Full-Duplex Bidirectional MIMO 23 / 24

24 Taneli Riihonen Full-Duplex Bidirectional MIMO 24 / 24