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... as m increases. A. Proof of Theorem 2 From (3), we have Csum ≤ RMIMO ≤ 2log(1+2PK) (5) where the second inequality follows from Jensen’s inequality and the fact that log det(·) is a concave function =-=[16]-=-. Also, RIN (a) =2E{θ1,··· ,θK} ( (b) ≥ 2log 1+ − 2δK ( ⎡ ⎛ ⎢ ⎜ ⎣log ⎝1+ 16 π2 P 2K 2 1+P (2K +2) P 2 ( ∑K √ k=1 2 − 2cosθk ) P 2 4 , , 2 1+P (2K +2) π ) , 1+P (2K +2) ) 2 ⎞⎤ ⎟⎥ ⎠⎦ where θk = θ2k−1,1 ...

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...nt years, there has been significant progress towards understanding fundamentals of multi-source single-hop networks. Approximate capacity results have been proved for the 2-user interference channel =-=[1]-=-, many-to-one or one-tomany interference channel [2], and two-way channel [3], which characterize the capacity within a constant number of bits/sec/Hz independent of signal-to-noise ratio (SNR) and ch...

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...nel [2], and two-way channel [3], which characterize the capacity within a constant number of bits/sec/Hz independent of signal-to-noise ratio (SNR) and channel parameters. It has also been proved in =-=[4]-=- that interference alignment can achieve the optimal degrees of freedom (DoF) of the time-varying K-user interference channel. The recently proposed ergodic interference aliment in [5] makes interfere...

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...ultiple paths through the network, a technique termed as interference neutralization. Proper use of such interference neutralization is the key for an approximate capacity [6] or DoF characterization =-=[7]-=-–[11] of multi-source multi-hop networks. In spite of recent progress in this area, the best known capacity characterization for fully connected 2-user 2-hop networks is within o(log(SNR)) bits/sec/Hz...

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...s understanding fundamentals of multi-source single-hop networks. Approximate capacity results have been proved for the 2-user interference channel [1], many-to-one or one-tomany interference channel =-=[2]-=-, and two-way channel [3], which characterize the capacity within a constant number of bits/sec/Hz independent of signal-to-noise ratio (SNR) and channel parameters. It has also been proved in [4] tha...

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...als of multi-source single-hop networks. Approximate capacity results have been proved for the 2-user interference channel [1], many-to-one or one-tomany interference channel [2], and two-way channel =-=[3]-=-, which characterize the capacity within a constant number of bits/sec/Hz independent of signal-to-noise ratio (SNR) and channel parameters. It has also been proved in [4] that interference alignment ...

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... been proved in [4] that interference alignment can achieve the optimal degrees of freedom (DoF) of the time-varying K-user interference channel. The recently proposed ergodic interference aliment in =-=[5]-=- makes interference aligned at finite SNR. For multi-source multi-hop networks, interference can be cancelled by aligning multiple paths through the network, a technique termed as interference neutral...

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...[11] of multi-source multi-hop networks. In spite of recent progress in this area, the best known capacity characterization for fully connected 2-user 2-hop networks is within o(log(SNR)) bits/sec/Hz =-=[8]-=-, which can be arbitrarily large as SNR increases. The aim of this paper is to close the capacity gap of the 2user 2-hop networks within a constant number of bits/sec/Hz, independent of SNR and the nu...

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...ple paths through the network, a technique termed as interference neutralization. Proper use of such interference neutralization is the key for an approximate capacity [6] or DoF characterization [7]–=-=[11]-=- of multi-source multi-hop networks. In spite of recent progress in this area, the best known capacity characterization for fully connected 2-user 2-hop networks is within o(log(SNR)) bits/sec/Hz [8],...

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...se the capacity gap of the 2user 2-hop networks within a constant number of bits/sec/Hz, independent of SNR and the number of relays. Our achievability is based on ergodic interference neutralization =-=[9]-=-, [12], † He is also with the Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, CA, USA. W1 W2 S1 S2 x1[t] x2[t] H[t] zR,1[t] zR,2[t] yR,1[t] yR,2[t] R1 R...

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...n be cancelled by aligning multiple paths through the network, a technique termed as interference neutralization. Proper use of such interference neutralization is the key for an approximate capacity =-=[6]-=- or DoF characterization [7]–[11] of multi-source multi-hop networks. In spite of recent progress in this area, the best known capacity characterization for fully connected 2-user 2-hop networks is wi...

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...with L ≥ 3 interference neutralization can be achieved without channel pairing. However, maximizing the achievable sum rate exploiting interference neutralization without channel pairing presented in =-=[15]-=- is non-convex and, as a result, it is unclear how to determine the sum rate gap from the cut-set upper bound. By contrast, we now show that our achievable rate expression from Theorem 1 permits to de...

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...e capacity gap of the 2user 2-hop networks within a constant number of bits/sec/Hz, independent of SNR and the number of relays. Our achievability is based on ergodic interference neutralization [9], =-=[12]-=-, † He is also with the Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, CA, USA. W1 W2 S1 S2 x1[t] x2[t] H[t] zR,1[t] zR,2[t] yR,1[t] yR,2[t] R1 R2 xR,1...