## 1 Introduction
The proposed scheme is a simple non-cooperative space-time technique for single-radio frequency(RF)-switched antenna systems. It significantly reduces both the transmission and the circuit energy consumption. In [22], the combination of MIMO systems with nonlinear detection has been proposed to achieve low power consumption, due to nonlinear modulation and detection, and higher rates, due to spatial multiplexing with multiple antennas. Although previous works provide efficient ways to exploit MIMO in WSNs, they have not considered the mobility of sensor nodes and, consequently, are effective only in fixed WSNs. In mobile WMSNs, the spatial correlation of a wireless channel between mobile sensor nodes can vary frequently, and thus, the gain of a given MIMO scheme can be degraded. To overcome this problem, we propose an adaptive multi-node MIMO transmission scheme for mobile WMSNs. In an adaptive MIMO transmission, various MIMO schemes are dynamically exploited based on the correlation of the given channels. In cellular systems, a number of adaptive MIMO transmission techniques have been proposed [29, 30, 31, 32, 33, 34, 35]. The concept of switching between diversity and multiplexing modes was first proposed in [29] and [30] to improve the bit error rate for a fixed rate transmission based on instantaneous channel state information. A general approach for switching between diversity and multiplexing modes for higher spectral efficiency in broadband channels has been described in [31], where time-frequency selectivity indicators are used to maximize spectral efficiencies for a predetermined target error rate and, yet, reduce overhead. The research in [29, 30] and [32] performs spatial mode adaptation using feedback from the receiver derived from the instantaneous channel state. In spatially-correlated channels, however, the spatial modes may be largely determined by the correlation in the channel. Consequently, other research has focused on spatial adaptation based only on the spatial correlation matrices. An advantage of these approaches is that the spatial correlation matrix varies on a slower time scale than the instantaneous channel realizations [33]. Therefore, correlation-based adaptive approaches require much less feedback overhead and incur a small performance penalty relative to instantaneous adaptation. Along these lines, [34] proposes to switch between statistical beamforming, double space-time transmit diversity and spatial multiplexing with linear receivers and a four-antenna system based on ergodic link capacity (the ergodic mutual information assuming a certain transmit configuration). [PERSON] _et al_. [35] propose to switch between orthogonal space-time block coding, double space-time transmit diversity and spatial multiplexing with linear receivers for a four-antenna system based on ergodic link capacity, as well as coded bit error rate for bit-interleaved coded modulation. Unfortunately, there are limitations with regards to applying these works directly to mobile WMSNs. Most of all, they have been designed for cellular systems and considered only single-node (SN) MIMO systems, where all the signals for a target mobile station come from its associated base station. However,the signals for a mobile sink node come from its associated multiple sensor nodes in mobile WMSNs. Thus, conventional SN MIMO switching schemes cannot avoid performance degradation when there is spatial correlation among a mobile sink node and associated sensor nodes. To tackle this problem, we propose an adaptive multi-node (MN) MIMO transmission scheme for mobile WMSNs, which performs spatial MIMO mode adaptation and antenna set switching with associated multiple sensor nodes. The following are the principal contributions of this paper. First, we propose a suitable model for multi-node, spatially-correlated channels that includes the different path gains from each sensor node. This allows us to include the difference between the average received signal-to-noise ratio for each sensor and the mobile sink link.