June 15, 2014 / Vol. 39, No. 12 / OPTICS LETTERS

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Real-time validation of receiver state information in optical space–time block code systems John Alamia* and Timothy Kurzweg Department of Electrical and Computer Engineering, Drexel University, 3141 Chestnut St., Philadelphia, Pennsylvania 19104, USA *Corresponding author: [email protected] Received March 14, 2014; revised May 8, 2014; accepted May 8, 2014; posted May 9, 2014 (Doc. ID 208186); published June 10, 2014 Free space optical interconnect (FSOI) systems are a promising solution to interconnect bottlenecks in high-speed systems. To overcome some sources of diminished FSOI performance caused by close proximity of multiple optical channels, multiple-input multiple-output (MIMO) systems implementing encoding schemes such as space–time block coding (STBC) have been developed. These schemes utilize information pertaining to the optical channel to reconstruct transmitted data. The STBC system is dependent on accurate channel state information (CSI) for optimal system performance. As a result of dynamic changes in optical channels, a system in operation will need to have updated CSI. Therefore, validation of the CSI during operation is a necessary tool to ensure FSOI systems operate efficiently. In this Letter, we demonstrate a method of validating CSI, in real time, through the use of moving averages of the maximum likelihood decoder data, and its capacity to predict the bit error rate (BER) of the system. © 2014 Optical Society of America OCIS codes: (060.4510) Optical communications; (200.2605) Free-space optical communication; (200.4650) Optical interconnects. http://dx.doi.org/10.1364/OL.39.003559

Optical interconnects have been proposed as a solution to bandwidth limitations, expected to occur as semiconductors continue to operate at increasingly higher speeds [1,2]. One optical interconnect architecture proposed to address this issue is the free-space optical interconnect (FSOI), utilizing laser and photodiode arrays [3]. This architecture promises to deliver the bandwidth density required of next generation interconnects without 3D waveguide structures being fabricated on board, or associated large form factor components [2,3]. FSOIs are susceptible to diminished performance as a result of optical crosstalk from static and dynamic optical misalignment, beam expansion, turbulent atmospheres, and atmospheric scattering [4–9]. To mitigate the effect of optical crosstalk, various methods have been proposed including beam steering through microelectromechanical systems (MEMS), focusing through lensing systems, and multiple hardware links in a multiple-input multipleoutput (MIMO) configuration [10–14]. The carefully designed geometries of passive lensing system, and the reconfigurable geometries of MEMS are both means to optimize power transfer in the optical channel, but fail to correct dynamic thermal effects [8,9]. MIMO systems, which are not exclusive of beam steering or passive lensing systems, improve BER by utilizing optical crosstalk and CSI obtained during training, in a space–time block coding (STBC) encoding scheme [14–16]. The data received in the STBC system is reconstructed through a maximum-likelihood (ML) detection which utilizes CSI. [14–16]. Data reconstruction becomes more error-prone when CSI inaccurately describes the actual channel. Therefore, in these systems, a training sequence is used to measure the CSI. Dynamic changes that occur in optical channels dictate that systems must be capable of retraining the CSI to ensure BER targets are met, while maximizing throughput. Direct measurement of BER requires independent verification of data received, and large amounts of data, constraining such measurements to laboratory settings. To identify dynamic changes, and 0146-9592/14/123559-04$15.00/0

the need to retrain, we investigate a means of determining the accuracy of the CSI in a STBC MIMO system in real-time through ML values. STBC systems utilize multiple transmitter-receiver pairs and multiple transmit time slots, using N transmitters and M receivers over N transmit time slots, as described by Eq. (1) ~ Y  XH  N;

(1)

where Y is a matrix of the received signals, X is a matrix of the transmitted signals, H is the channel matrix, and N~ is Gaussian white noise, which is used to model electrical noise and random optical noise. In the case of optical signals, the received signal must be a real positive intensity, differing from RF applications that contain complex signals [14,15]. The received signal matrix, detailed in Eq. (2), is comprised of signals received at different receiver elements (RX) as well as in different time slots (T). TX N 12 0 TX 1 h11 … x1N x 11 T1 B .. C6 .. . . . . Y @ . . A4 . . TN x hN1    x N1 NN

… .. . …

3 h1N .. 7: . 5 hNN

(2)

Similarly, the transmitted signal occurs over multiple transmitters (TX) and time slots (T), and the channel matrix elements hmn , in Eq. (2) and depicted in Fig. 1, refer to the power transfer from transmitter n to receiver m. The estimation or measurement of H, the channel matrix, is the CSI used in MIMO systems, and can be obtained in multiple fashions using so-called blind, semi-blind, or trained techniques [17–19]. These methods provide different means of determining CSI, but do not offer a means to verify accuracy. In orthogonal frequency division multiplexing (OFDM) MIMO systems, cyclical data used in OFDM encoding is used in place of a training sequence. As a result no new communications overhead is added. © 2014 Optical Society of America

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Fig. 2. Schematic of optical system.

Fig. 1. Schematic of H elements in a 2 × 2 FSOI system.

In on-off keying (OOK), training involves halting transmission to send a predetermined sequence. As a result, each new training session reduces throughput. The transmitted elements, X, in Eq. (2) are shown in Eq. (3) for the 2 × 2 STBC OOK case. TX TX 2  1  X1 X2 X : T2 X2 X1 T1

(3)

The received signals are used to construct the estima~ which is used to reconstruct the transmitted tor X, symbol by comparing X~ with the possible OOK symbols ˆ through the ML metric shown in Eq. (4) [14] X, ~ X ˆ  X~ − X ˆ 2 mX;

X

 h2ij − 1 Xˆ 2 :

(4)

This metric is used to determine the ML values for both OOK symbols Sˆ1 and Sˆ0 . The symbol S n is chosen as the decoded OOK symbol by using the ML values from ~ Sˆn  < mX; ~ Sˆi , where n ≠ i. Eq. (4) and comparing mX; The performance of the system is dependent on accurately trained CSI. If H is no longer accurately reflected by the CSI, system performance will suffer as BER increases. This occurs during operation as the transmitter and receiver planes begin to shift as a result of thermal expansion of printed circuit boards or atmospheric turbulence [8,9]. These two events occur as a result of dynamic effects during operation, and, as such, cannot be corrected in advance. These events cause significant changes in the channel, where optical misalignment on the order of 20 μm has been measured in blade servers during operation [10]. These dynamic changes due to thermal effects are expected to be system dependent. As a result of dynamic changes in H, FSOI performance is expected to change during operation. The measurement of BER requires a large number of transmissions, as well as direct comparison of the transmitted and received data. To facilitate system evaluation during operation we have developed a metric to indicate the accuracy of the receiver CSI. In this Letter, a method is proposed to provide near real-time verification of CSI accuracy, through tracking the moving average of the value pro~ X. ˆ duced by the ML decoder, mX; To demonstrate the proposed method, a 2 × 2 STBC system was modeled, as depicted in Fig. 2, with two pairs

of transmitter and receiver elements. The transmitterreceiver channels are spaced by Δ  250 μm, and the distance between the receiver and transmitter planes is z  5 mm. The VCSEL beam is modeled as a Gaussian beam with a half-width initial beam of w0  0.5 μm and a wavelength λ  850 nm. The radius of the photodetector is r  P 50 μm, and the channel SNR  13, defined as SNR  hij ∕σ 20 . Training is achieved by simulating one laser and calculating the power received by each photodiode. The process is repeated for each laser in the system. The measured power has Gaussian white noise added with a variance σ train  1∕40σ 20 to the channel matrix H as indicated in Table 1. The channel matrices and CSI used throughout the simulation are defined in Table 1. Each successive row in Table 1 indicates a new H matrix with an additional 10 μm linear misalignment of the optical axis starting with H 1 being perfectly aligned or ϵ  0, H2 being misaligned by ϵ  10 μm, H 3 being misaligned by ϵ  20 μm, H 4 , H5 , and H6 being misaligned by ϵ  30 μm, ϵ  40 μm, and ϵ  50 μm, respectively. Here we have chosen to simulate only a linear misalignment to represent dynamic changes in the channel, but tilt misalignment is also expected to occur. Here we use linear misalignment to serve as a first approximation of effects due to tilt misalignment and the resulting shifted centroid of an optical beam. The first simulation demonstrates the effect of accurate training on BER. The BER of the 2 × 2 system, shown in red in Fig. 3, is determined for the receiver that has trained the CSI when H  H1 . The channel matrix is then changed to H2 , then H 3 , H4 , H5 , and H6 , while the CSI remains unchanged. It is seen that with each new H, representing an increase in misalignment, the BER increases. The green line demonstrates the BER in this case that begins as with the previous case, then the system retrains the CSI when H  H4 ; the CSI remains unchanged from these values for the remaining channel matrices. In this case the BER is seen to increase over the first three values of H, as in the red case, then sharply Table 1. Table of H Matrices Used for Simulations H1 H2 H3 H4 H5 H6

h11

h12

h21

h22

ϵ (μm)

16.46E−3 16.45E−3 16.41E−3 16.36E−3 16.28E−3 16.18E−3

10.82E−3 11.18E−3 11.54E−3 11.88E−3 12.24E−3 12.58E−3

10.82E−3 10.45E−3 10.09E−3 9.720E−3 9.355E−3 8.991E−3

16.46E−3 16.45E−3 16.41E−3 16.36E−3 16.28E−3 16.18E−3

0 10 20 30 40 50

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Fig. 3. BER with constant CSI (green) and retrained CSI at H  H 4 (red).

decrease on H4 when the CSI is changed to H4 . The increases in BER seen in the red line, and at times in green as CSI deviates from H, demonstrate the increased BER of a poorly trained system over a well-trained system. To develop a method of real time CSI validation, we start by demonstrating the stability of the moving average of mX~1 ; Sˆ1 . The moving averages of mX~1 ; Sˆ1  values, shown in red in Fig. 4, are calculated with CSI  H1 and the channel H is varied from H1 to H6 over 107 STBCs for each channel matrix. The mean ML value readily settles to one level for each H matrix, and changes abruptly when H is changed, correlating with the change in BER seen in Fig. 3. The same correlation of mean ML values to BER can be seen for the case in green, where CSI is retrained to H4 when H  H4 ; a sharp decrease occurs in mean ML corresponding to a decrease in BER seen in Fig. 4. A significant feature of this method is that the data received need not be independently verified with the transmitted data; only the ML values are needed. This demonstrates the usefulness of the mean ML as a means to verify the accuracy of the CSI in real time. To show the mean ML, as H changes during operation, we simulate a system that maintains the initial training at H1 , and sweep the channel matrix from H1 to H 6 over 5 · 107 STBCs. The mean, shown in red in Fig. 5, increases in value as H begins to differ from the receiver CSI, which corresponds with an increase in BER. Since the BER cannot be measured directly we utilize the moving average of the ML. If a threshold of approximately 5.5% change in ML is selected, it is seen that the system is

Fig. 4. Moving average maximum likelihood of last 104 STBCs for 107 transmissions.

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Fig. 5. Moving average maximum likelihood of last 106 STBCs as H varies from H 1 to H 6 with constant CSI.

identified as stale after 3 · 107 bits when the moving average reaches this threshold, indicating the system should be retrained. The mean ML is shown in green in Fig. 5, when the system retrains according to the threshold. This sequence, and its effect on the mean ML value in Fig. 5, corresponds with the change in BER seen in Fig. 3. Figure 6 demonstrates the curve fitted relationship between the percent change of mean ML, and percent change of BER, allowing prediction of BER based on mean ML value. It can be seen that for small changes in mean ML the BER may change only negligibly, but as the percent difference in mean ML continues to rise, the percent difference in BER rises parabolically in this region of interest. It is expected to saturate at some point outside the region shown here. In the simulations presented, a change of approximately 60% in BER is selected as the BER threshold, and the corresponding 5.5% change in mean ML is used as the threshold for retraining, as shown in the scenarios depicted in green in Fig. 5 and Fig. 4. The negative impact that a disparity between H and CSI has on BER has been shown. Determining a system’s BER directly requires comparison of predetermined transmitted and received data streams, limiting the use of this method of determining system performance to lab testing. The dynamic nature of H, and impracticality of directly measuring BER, motivates the need for a real-time measurement to validate the receiver CSI. This Letter demonstrates a method of determining the validity of CSI as an accurate representation of H. The increase in BER for inaccurate CSI mirrors the increased mean ML of a poorly trained system. The method proposed

Fig. 6. Relationship between mean maximum likelihood and BER.

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relies only on the ability to accurately train H once it has been identified that retraining is needed, which is required of all MIMO systems. This demonstrates the proposed method can be used to predict BER after observing only 104 STBCs, providing a useful near realtime diagnostic of CSI accuracy and system performance in MIMO FSOI systems. References 1. J. W. Goodman, F. J. Leonberger, S.-Y. Kung, and R. A. Athale, Proc. IEEE 72, 850 (1984). 2. D. Miller, Proc. IEEE 88, 728 (2000). 3. M. W. Haney, M. P. Christensen, P. Milojkovic, G. J. Fokken, M. Vickberg, B. K. Gilbert, J. Rieve, J. Ekman, P. Chandramani, and F. Kiamilev, Proc. IEEE 88, 819 (2000). 4. W. Hu, X. Li, J. Yang, and D. Kong, J. Opt. Soc. Am. A 27, 200 (2010). 5. R. Wang, A. D. Raki, and M. L. Majewski, Appl. Opt. 41, 3469 (2002). 6. S. K. Patra, J. Ma, V. H. Ozguz, and S. H. Lee, Opt. Eng. 33, 1561 (1994). 7. B. E. Yoxall, R. Walmsley, H.-P. Kuo, S.-Y. Wang, M. Tan, and D. A. Horsley, IEEE J. Sel. Top. Quantum Electron. 17, 559 (2011). 8. R. Rachmani, A. Zilberman, and S. Arnon, J. Lightwave Technol. 30, 156 (2012).

9. K. Wang, A. Nirmalathas, C. Lim, E. Skafidas, and K. Alameh, in Photonics Global Conference (PGC) (IEEE, 2012), pp. 1–5. 10. H. P. Kuo, P. Rosenberg, R. Walmsley, S. Mathai, L. Kiyama, J. Straznicky, M. Mclaren, M. Tan, and S.-Y. Wang, Appl. Phys. A 95, 955 (2009). 11. J. B. Chou, K. Yu, and M. C. Wu, J. Microelectromech. Syst. 21, 1107 (2012). 12. A. Tuantranont, V. Bright, J. Zhang, W. Zhang, J. Neff, and Y. Lee, Sens. Actuators A 91, 363 (2001). 13. K. Hirabayashi, T. Yamamoto, S. Hino, Y. Kohama, and K. Tateno, J. Lightwave Technol. 15, 874 (1997). 14. M. K. Simon and V. A. Vilnrotter, IEEE Trans. Wireless Commun. 4, 35 (2005). 15. S. M. Alamouti, IEEE J. Sel. Areas Commun. 16, 1451 (1998). 16. S. V. Chinta, T. P. Kurzweg, D. S. Pfeil, and K. R. Dandekar, in SPIE OPTO: Integrated Optoelectronic Devices (International Society for Optics and Photonics, 2009), p. 722116. 17. P. Stoica and G. Ganesan, Digital Signal Process. 13, 93 (2003). 18. C. Komninakis, C. Fragouli, A. Sayed, and R. Wesel, in Communications, 2000. ICC 2000. 2000 IEEE International Conference on, Vol. 3 (IEEE, 2000), pp. 1655–1659. 19. J. Pang, J. Li, L. Zhao, and Z. Lu, in Vehicular Technology Conference, 2007. VTC-2007 Fall. 2007 IEEE 66th (IEEE, 2007), pp. 651–655.

Real-time validation of receiver state information in optical space-time block code systems.

Free space optical interconnect (FSOI) systems are a promising solution to interconnect bottlenecks in high-speed systems. To overcome some sources of...
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