Capacity scaling laws in MIMO relay networks


Helmut Bölcskei, Rohit U. Nabar, Özgür Oyman, and Arogyaswami J. Paulraj


IEEE Transactions on Wireless Communications, Vol. 5, No. 6, pp. 1433-1444, June 2006.

DOI: 10.1109/TWC.2006.1638664

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The use of multiple antennas at both ends of a wireless link, popularly known as multiple-input multiple-output (MIMO) wireless, has been shown to offer significant improvements in spectral efficiency and link reliability through spatial multiplexing and space-time coding, respectively. This paper demonstrates that similar performance gains can be obtained in wireless relay networks employing terminals with MIMO capability. We consider a setup where a designated source terminal communicates with a designated destination terminal, both equipped with M antennas, assisted by K single-antenna or multiple-antenna relay terminals using a half-duplex protocol. Assuming perfect channel state information (CSI) at the destination and the relay terminals and no CSI at the source, we show that the corresponding network capacity scales as C = (M/2)log(K) + O(1) for fixed M, arbitrary (but fixed) number of (transmit and receive) antennas N at each of the relay terminals, and K going to infinity. We propose a protocol that assigns each relay terminal to one of the multiplexed data streams forwarded in a "doubly coherent'' fashion (through matched filtering) to the destination terminal. It is shown that this protocol achieves the cut-set upper bound on network capacity for fixed M and K going to infinity (up to an O(1)-term) by employing independent stream decoding at the destination terminal. Our protocol performs inter-stream interference cancellation in a completely decentralized fashion, thereby orthogonalizing the effective MIMO channel between source and destination terminals. Finally, we discuss the case where the relay terminals do not have CSI and show that simple amplify-and-forward relaying, asymptotically in K, for fixed M and fixed N >= 1, turns the relay network into a point-to-point MIMO link with high-SNR capacity C =(M/2)log(SNR)+O(1), demonstrating that the use of relays as active scatterers can recover spatial multiplexing gain in poor scattering environments.


Relay channel, adhoc network, distributed orthogonalization, MIMO, fading channels


Correction: The argument right after Eq. (4) stating "... where conditioning on the t_k in the first term can be dropped since neither s nor the r_k depend on the t_k." is misleading. It should be replaced by "The first term on the RHS of Eq. (4) is upper-bounded by I(s;r_1,...,r_K) as s-{r_i}-{t_i} forms a Markov chain." Furthermore in the fifth line of the proof of Theorem 1 "C_u=" should be removed and the sentence "We can therefore ..." starting in line 6 after Eq. (4) should be "We can therefore summarize our result as the capacity of the MIMO relay network being upper bounded by ...".

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