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Decentralized Power Control for Random Access with Multi-User Detection

Decentralized Power Control for Random Access with Multi-User Detection. Chongbin Xu, Peng Wang, Sammy Chan, and Li Ping. Department of Electronic Engineering City University of Hong Kong December 27, 2012. Reference:

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Decentralized Power Control for Random Access with Multi-User Detection

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  1. Decentralized Power Control for Random Access with Multi-User Detection Chongbin Xu, Peng Wang, Sammy Chan, and Li Ping Department of Electronic Engineering City University of Hong Kong December 27, 2012

  2. Reference: • C. Xu, Li Ping, P. Wang, S. Chan, and X. Lin, “Decentralized Power Control for Random Access with Successive Interference Cancellation” to appear in IEEE JSAC.

  3. Overview Background and Motivation Decentralized Power Control Two-User AWGN Channel K-User AWGN Channel K-User Fading Channel Conclusions and Future Work 3

  4. Overview Background and Motivation Decentralized Power Control Two-User AWGN Channel K-User AWGN Channel K-User Fading Channel Conclusions and Future Work 4

  5. Cognitive Radio with Multiple Primary Users secondary user 1 secondary user 2 AP primary user 1 primary user 2 Consider a cognitive radio with multiple users. The secondary users can transmit only when the primary users are silent. The secondary users access the channel opportunistically whenever a spectrum hole is detected. 5

  6. System Characteristics • There is usually no time to establish centralized control such as TDMA. • Thus random access is necessary. • If the spectrum holes are scarce, the secondary users may accumulate many un-transmitted packets. Thus is highly probable that each user has a packet to transmit whenever a spectrum hole is detected. • This is equivalent to the system with packet arrival rate l1. 6

  7. Collision and Throughput In random-access systems, a collision will occur if k users transmit their packets simultaneously. Conventionally, the packets involved in a collision are assumed to be unrecoverable. The system throughout is limited by collision probability. When kl ≥1and k∞, the maximum throughput is 36.8% due to high collision probability Performance of conventional slotted ALOHA 7

  8. How to improve the random access performance? 8

  9. Multi-Packet Reception (MPR) In many situations, it is possible to recover some or all packets from a collision. This phenomenon is captured by the multi-packet reception (MPR) model. Early work on MPR model is focused on low-rate CDMA-type applications [1][2]. Both [1] and [2] allow multi-user detection (MUD). However, they are based on the traditional ALOHA with only one non-zero transmission power level. The work in [3] allows multi-level transmission power but it is limited to single user detection (SUD) only. [1] S. Ghez, S. Verdu, and S. Schwartz, “Stability properties of slotted ALOHA with multipacket reception capability,” IEEE Trans. Autom. Control, vol. 33, no. 7, pp. 640-649, Jul. 1988. [2] L. Tong and V. Naware, “Signal processing in random access,” IEEE Signal Process. Mag., vol. 21, no.5, pp. 29-39. Sep. 2004. [3] Y. Leung, “Mean power consumption of artificial power capture in wireless networks,” IEEE Trans. Commun., vol. 45, no. 8, pp. 957-964, Aug. 1997. 9

  10. Performance of MPR in Fading Channel channel multi-level aware [a] SUD [b] The channel aware technique assume only a single non-zero transmission power level. The multi-level SUD technique is limited to SUD only. standard slotted ALOHA R = 1 bit/symbol [a] M. H. Ngo, V. Krishnamurthy, and L. Tong, “Optimal channel-aware ALOHA protocol for random access in WLANs with multi-packet reception and decentralized channel state information,” IEEE Trans. Signal Process., vol. 56, no. 6, pp. 2575-2588, Jun. 2008. [b] Y. Leung, “Mean power consumption of artificial power capture in wireless networks,” IEEE Trans. Commun., vol. 45, no. 8, pp. 957-964, Aug. 1997. 10

  11. Serial Interference Cancellation Multi-user detection (MUD) has the potential to solve the problem by serial interference cancellation (SIC) [4][5]. In this case, the signals of the users that have been correctly detected are subtracted from the received signal, and there is no interference to the others. Assume that the signals of users 1, 2, …, k-1 have been correctly detected and subtracted from the received signal. Then the SINR of user k is given by from remaining interfering users. [4] T. M. Cover and J. A. Thomas, Elements of Information Theory, New York: Wiley, 2006. [5] D. Tse and P. Viswanath, Fundamentals of Wireless Communications, Cambridge: Cambridge University Press, 2005. 11

  12. Power Requirement for SIC The following is an illustration of the power requirement for a two-user SIC system. We can recover both packets during an collision. transmission power user 1 decoded first: user 2 decoded second: user 1 user 2 12

  13. Power Control and Feasible Region Power control is crucial for MUD. We refer to the closure of power profiles that can support reliable transmissions of all users as feasible power region. The following is an example of the feasible region for a two-user system with R ≥ 1 bit/symbol, ideal coding and SIC. e1=e2 is the worst-case situation. E1 = (2R – 1)N0 E2 = (2R – 1)∙(E1 + N0) 13

  14. Feasible Region E1 = (2R – 1)N0 E2 = (2R – 1)∙(E1 + N0) When R>1, equal power line is not in the feasible region. If centralized power control is possible, we can allocate the two users with power inside the feasible region. In particular, the power pair (E1, E2) or (E2, E1) leads to the minimum information theoretic sum-power. However, how to allocate powers without centralized control? 14

  15. Objectives We aim to improve the throughput of random-access systems by allowing MUD at the receiver and decentralize power control at the transmitters. We will limit our discussions to the simple slotted ALOHA systems. It is expected that the results can be extended to systems with more sophisticated random access protocols such as CSMA. We will discuss the decentralized power control problems in two-user AWGN channel, K-User AWGN channel, and K-User fading Channel. 15

  16. Overview Background and Motivation Decentralized Power Control Two-User AWGN Channel K-User AWGN Channel K-User Fading Channel Conclusions and Future Work 16

  17. Problem Formulation e2 e1 f(e) f(e) e e To improve the performance by optimizing the power distribution f(e). 17

  18. Discrete Power Levels We define a discrete set {En} with 0 = E0 < E1 < … En < …, where En is the minimum power level that guarantees successful decoding of one user when the interference power level from the other user is En–1. 18

  19. Theorem 1 The support of the optimal distribution is a subset of the discrete set {En}. This theorem greatly simplifies the optimization problem. 19

  20. Optimization Problem Based on Theorem 1, the design problem can be formulated as follows. pn 2 p0 Notes: (1) p0 is the probability that a user does not transmit. (2) pn2 is the probability that both users using the same powers, and so transmission will fail. 20

  21. Proof of Theorem 1 Any transmit power E'  (E0, E1) is unnecessary since E1 is the minimum power for reliable transmission without interference. 21

  22. Proof of Theorem 1 (Continued) Provided that the probability of (E0, E1) is zero, any E' (E1, E2) is also unnecessary since E2 is the minimum power for reliable transmission when the interfering packet has power E1. 22

  23. Proof of Theorem 1 (Continued) The above reasoning is generalized to show that E' (En, En+1) is unnecessary for any n. 23

  24. Example: Packet Throughput Comparison Packet throughput T of a 2-user AWGN channel with ideal coding. R = 1 bit/symbol 24

  25. Overview Background and Motivation Decentralized Power Control Two-User AWGN Channel K-User AWGN Channel K-User Fading Channel Conclusions and Future Work 25

  26. K-User Systems To optimize the power distribution in a K-user system, we need to analyze the general K-user feasible region, which is a tedious issue and we will not pursuit it further. Instead, we will discuss a simple and sub-optimal solution. We refer to a collision involving k (2 ≤ k ≤ K) users as a type-k collision. For the sub-optimal solution, we will only consider type-2 collisions. In this sub-optimal solution, the system throughput is given by T = T1 + T2, where T1 is the throughput related to transmissions without collisions and T2 the throughout related to type-2 collisions. 26

  27. Throughput Calculation Denote by pn the probability of transmission power taking value En. We calculated T1 and T2 as follows. For convenience, we assume full load for all users. The discussions can be extended to the general loading case. T1 is the throughput related to transmissions without collisions, calculated by T2 the throughout related to type-2 collisions, calculated by Thus, we have 27

  28. Throughput Optimization Repeat: To optimize the throughput of the proposed scheme, we discretize the value of p0, and solve the following optimization problem for each discretized p0. 28

  29. Example: Performance Comparison Performance in a 3-user system with ideal coding. R = 1 bit/symbol. 29

  30. Example: Performance Comparison Performance comparison among various schemes in AWGN channels with ideal coding and different K. R = 1 bit/symbol. 30

  31. Overview Background and Motivation Decentralized Power Control Two-User AWGN Channel K-User AWGN Channel K-User Fading Channel Conclusions and Future Work 31

  32. Fading Channels Consider a K-user system with fading. The received signal is given by where the channel gains of all users, {gk}, are assumed to be independent and identically distributed. Assume that each user k knows its instantaneous channel gain gk. Our aim is to optimize the conditional distributions {fT(eT|g)}, with eT the transmit power, such that the system throughput is maximized. The basic assumption above is that each user knows its own channel gain. This can be accomplished in different ways. A possible general solution is that the receiver will transmit a beacon signal, which will be used by the transmitters for channel estimation. 32

  33. Channel-Aware ALOHA As a reference, a channel-aware ALOHA scheme is proposed in [6] based on the following special form of fT(eT|g), where ET is a predetermined power value and p(g) the transmission probability when the channel gain is g. In the following, we will show that the system throughput can be significantly enhanced by jointly optimizing the transmission power levels and the related transmission probabilities. [6] M. H. Ngo, V. Krishnamurthy, and L. Tong, “Optimal channel-aware ALOHA protocol for random access in WLANs with multi-packet reception and decentralized channel state information,” IEEE Trans. Signal Process., vol. 56, no. 6, pp. 2575-2588, Jun. 2008. 33

  34. Support in Fading Channels Given g, the support of the optimal conditional transmit power distribution fT(eT|g) is a subset of {E0/g, E1/g, E2/g, …..}. Let y(g) be the PDF of g. The received power distribution fR(eR) is given by With {pn} available, the throughput can be calculated similarly as in AWGN channels. We next discuss the optimization of {pn(g)} based on the discretization of g. 34

  35. Throughput Optimization in Fading Channels We discretize the value of g according to M+1thresholds {g(m)|m = 1,…, M+1} and assume that the received power distributions when g [g(m), g(m+1)) are the same, i.e., pn(g) = pn(m) for g(m)≤ g < g(m+1). We optimize {pn(m)} to maximize the system throughput. 35

  36. Example: Performance Comparison Performance comparison among various schemes in fading channels with ideal coding and different K. R = 1 bit/symbol. 36

  37. MUD for Practically Coded Systems We have focused on ideal coding and assume successive interference cancellation (SIC) for MUD in the previous discussions. We now consider practically coded systems, where IDMA is a simple scheme for MUD with relatively low receiver complexity. . . . . . . user-1 x1 p1 p1 ENC DEC p1-1 h1 user-k pk hk xk chip-by-chip Processing pk DEC ENC pk-1 h pK hK user-K xK DEC pK pK-1 ENC 37

  38. MUD Feasible Region with LDPC Coding 8 feasible 7 6 5 unfeasible power of user 2 4 3 feasible 2 1 unfeasible 0 0 1 2 3 4 5 6 7 8 power of user 1 The following is the feasible region of a (3, 6) regular LDPC coded systems with iterative receiver for BER ≤ 10-5. Please note the followings. 1) When powers for both users are low, near equal powers are not feasible. 2) When powers for both users are high, equal powers are feasible. 38

  39. Analysis of the Optimal Support In this case, the support of the optimal power distribution f(∙) is a subset of {E0, E1, …, En, …,EQ} (for a feasible region with monotonically increasing boundary function). 39

  40. Example: LDPC Coding Performance comparison among various schemes in fading channels with LDPC coding and different K. R = 1 bit/symbol 40

  41. Overview Background and Motivation Decentralized Power Control Two-User AWGN Channel K-User AWGN Channel K-User Fading Channel Conclusions and Future Work 41

  42. Conclusions We have developed a decentralized power control scheme for random access systems with MUD. We proved that the support of the optimal power distribution f is discrete. Based on this finding, we designed f. Numerical results demonstrate that significant performance gain can be obtained by the proposed scheme. We have limited our focus to slotted ALOHA-type random access schemes. It is expected that the results can be extended to systems with more sophisticated random access protocols such as CSMA. 42

  43. Q & A Thank you! 43

  44. Introduction: Decentralized Power Control We study the decentralized power control for ALOHA-type random access scheme with MUD. d(∙) is the Dirac delta function Example: f1(2) = f2(2) = f (2) = 0.5d (e) + 0.5d (e – E1) 44

  45. Merging of Probabilities For given f, we define a new distribution f[n] constructed as follows. 45

  46. Proof of Theorem 1 The distribution pair (f[n+1], f[n]) has a better performance than (f[n], f[n]), n. a sample of f[n+1] can be equivalently obtained through the following steps: Step 1: Draw a power value e1 according to f[n]; Step 2: If En < e1 < En+1, reduce e1 to En; otherwise, keep e1 unchanged. Denote by white circles {Ai} power pairs drawn from (f[n], f[n]) while black circles {Ai'} represent those after the power change in Step 2, which are also samples drawn from (f [n+1], f[n]). 46

  47. Example: SUD based Optimization We also consider optimizing the power distribution for systems with SUD (denoted by ML-SUD for multiple-level transmission and SUD). The conventional slotted ALOHA can be regarded as a special case of ML-SUD, where the distribution is optimized over two levels E0 = 0 and E1 only. 47

  48. Optimization Problem Based on Theorem 1, the design problem can be formulated as follows. pn 2 p0 Notes: (1) p0 is the probability that a user does not transmit. (2) pn2 is the probability that both users using the same powers, and so transmission will fail. 48

  49. Proof of Theorem 1 The power change leads to the following three possibilities. a) A1 fails while A1' succeeds. Such events result in increased throughput; b) A2 succeeds while A2' fails. Such events cannot happen as f[n](e2) = 0,e2(En–1, En); c) In all other situations, both power pairs fail or succeed simultaneously. 49

  50. Example: Power Constraint System throughput of a four-user Rayleigh fading channel with ideal coding under different power constraints. R = 1 bit/symbol. 50

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