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1、Interference: An Information Theoretic View David Tse Wireless Foundations U.C. BerkeleyISIT 2009 Tutorial June 28TexPoint fonts used in EMF: AAAAAAAAAAAAAAThanks: Changho Suh.Context Two central phenomena in wireless communications: Fading Interference Much progress on information theory of fading
2、channels in the past 15 years Led to important communication techniques: MIMO Opportunistic communication Already implemented in many wireless systems.Interference These techniques improve point-to-point and single cell (AP) performance. But performance in wireless systems are often limited by inter
3、ference between multiple links. Two basic approaches: orthogonalize into different bands full sharing of spectrum but treating interference as noise What does information theory have to say about the optimal thing to do?State-of-the-Art The capacity of even the simplest two-user interference channel
4、 (IC) is open for 30 years. But significant progress has been made in the past few years through approximation results. Some new ideas: generalized degrees of freedom deterministic modeling interference alignment. Goal of the tutorial is to explain these ideas.Outline Part 1: two-user Gaussian IC. P
5、art 2: Resource-sharing view and role of feedback and cooperation. Part 3: Multiple interferers and interference alignment.Part I: 2-User Gaussian ICTwo-User Gaussian Interference Channel Characterized by 4 parameters: Signal-to-noise ratios SNR1, SNR2 at Rx 1 and 2. Interference-to-noise ratios INR
6、2-1, INR1-2 at Rx 1 and 2.message m1message m2want m1want m2Related Results If receivers can cooperate, this is a multiple access channel. Capacity is known. (Ahlswede 71, Liao 72) If transmitters can cooperate , this is a MIMO broadcast channel. Capacity recently found. (Weingarten et al 05) When t
7、here is no cooperation of all, its the interference channel. Open problem for 30 years.State-of-the-Art in 2006 If INR1-2 SNR1 and INR2-1 SNR2, then capacity region Cint is known (strong interference, Han- Kobayashi 1981, Sato 81) Capacity is unknown for any other parameter ranges. Best known achiev
8、able region is due to Han- Kobayashi (1981). Hard to compute explicitly. Unclear if it is optimal or even how far from capacity. Some outer bounds exist but unclear how tight (Sato 78, Costa 85, Kramer 04).Review: Strong Interference Capacity INR1-2 SNR1, INR2-1 SNR2 Key idea: in any achievable sche
9、me, each user must be able to decode the other users message. Information sent from each transmitter must be common information, decodable by all. The interference channel capacity region is the intersection of the two MAC regions, one at each receiver.Han-Kobayashi Achievable Scheme Problems of com
10、puting the HK region: - optimal auxillary r.v.s unknown - time-sharing over many choices of auxillary r.v,s may be monprivatecommon privatedecodedecodeInterference-Limited Regime At low SNR, links are noise-limited and interference plays little role. At high SNR and high INR, links are interference-
11、 limited and interference plays a central role. Classical measure of performance in the high SNR regime is the degree of freedom.Baselines (Symmetric Channel) Point-to-point capacity: Achievable rate by orthogonalizing: Achievable rate by treating interference as noise:Generalized Degrees of Freedom
12、 Let both SNR and INR to grow, but fixing the ratio: Treating interference as noise:Dof plotOptimal Gaussian HKDof-Optimal Han-Kobayashi Only a single split: no time-sharing. Private power set so that interference is received at noise level at the other receiver.Why set INRp = 0 dB? This is a sweet
13、spot where the damage to the other link is small but can get a high rate in own link since SNR INR.Can we do Better? We identified the Gaussian HK scheme that achieves optimal gdof. But can one do better by using non-Gaussian inputs or a scheme other than HK? Answer turns out to be no. The gdof achi
14、eved by the simple HK scheme is the gdof of the interference channel. To prove this, we need outer bounds.Upper Bound: Z-Channel Equivalently, x1 given to Rx 2 as side information.How Good is this Bound?Whats going on?Scheme has 2 distinct regimes of operation:Z-channel bound is tight.Z-channel boun
15、d is not tight.New Upper Bound Genie only allows to give away the common information of user i to receiver i. Results in a new interference channel. Capacity of this channel can be explicitly computed!New Upper Bound + Z-Channel Bound is TightBack from InfinityIn fact, the simple HK scheme can achie
16、ve within 1 bit/s/Hz of capacity for all values of channel parameters:For any in Cint, this scheme can achieve rates(Etkin, T. & Wang 06)Symmetric Weak Interference The scheme achieves a symmetric rate per user:The symmetric capacity is upper bounded by:The gap is at most one bit for all values of SN
