SNR penalty from the path-loss disparity in virtual multiple-input-single-output (VMISO) link

Cooperative transmission (CT), in which spatially separated wireless nodes collaborate to form a virtual antenna array or virtual multiple-input-multiple-output (VMISO) link, is an effective technique to mitigate multi-path fading by spatial diversity. In this paper, we study the disparities in path losses between the randomly placed relay nodes in a transmit cluster and the destination nodes. Many authors assume that the elements in a virtual antenna array are co-located, even though they are spread out. In this paper, we show that a signal-to-noise-ratio (SNR) penalty of up to 3dB should be included when making this assumption. By the high-SNR approximation of the outage rates, we show that the performance degradation caused by the path-loss disparity can be characterized equivalently by log-normal shadowing. Moreover, we derive the upper and lower bounds of the real outage probabilities in closed forms based on the log-normal shadowing model, by which we can estimate the SNR penalty of the co-located assumption.