Amplify-and-Forward in Wireless Relay Networks: Rate, Diversity, and Network Size

  • Authors:
  • S. . Borade;Lizhong Zheng;R. . Gallager

  • Affiliations:
  • Massachusetts Inst. of Technol., Cambridge;-;-

  • Venue:
  • IEEE Transactions on Information Theory
  • Year:
  • 2007

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Abstract

A wireless network with fading and a single source-destination pair is considered. The information reaches the destination via multiple hops through a sequence of layers of single-antenna relays. At high signal-to-noise ratio (SNR), the simple amplify-and-forward strategy is shown to be optimal in terms of degrees of freedom, because it achieves the degrees of freedom equal to a point-to-point multiple-input multiple-output (MIMO) system. Hence, the lack of coordination in relay nodes does not reduce the achievable degrees of freedom. The performance of this amplify-and-forward strategy degrades with increasing network size. This phenomenon is analyzed by finding the tradeoffs between network size, rate, and diversity. A lower bound on the diversity-multiplexing tradeoff for concatenation of multiple random Gaussian matrices is obtained. Also, it is shown that achievable network size in the outage formulation (short codes) is a lot smaller than the ergodic formulation (long codes).