## 4 Analysis of Requirements and Feasibility of Assumptions for CB  
To perform CB in a WSN, we next need _Requirements (R)_:  
Figure 2: (**a**) linear array and (**b**) planar array. the exact location of the motes within the WSN
* the exact location of the receiver (or BS)
* an omnidirectional antenna in the motes
* to share beforehand the message (with the data) to be transmitted to the BS. The motes should transmit the same (identical) signal but with different phase offsets
* the necessary power transmission to reach the receiver (or BS) once the beam is created
* the ability to introduce an offset in the transmission at each mote, on the order of a fraction of the period of the carrier used for the modulation  
Without loss of generality, as the first option or starting point, we will consider the study of above requirements on TelosB motes [18]. These motes have been widely used in many real deployments [2]. Nonetheless, there are different motes with similar characteristics such as IRIS, MICAz motes from Crossbow/MEMSIC (Boston, MA, USA), Meshbean Amp and Meshbean 900 motes from Atmel Co., etc. (San Jose, CA, USA). In particular, TelosB motes are based on IEEE 802.15.4 [1] at 2.4 GHz and equipped with an omnidirectional (isotropic) antenna, radio transceiver TI CC2420 [19] and MicroController Units (MCU) TI MSP430 [20] at 8 MHz. These motes have a maximum power transmission of 0 dBm, although we can find suppliers of TelosB compatible commercial motes with RF amplifiers. TI CC2420 transceiver has a bit rate of 250 kbps using Offset-Quadrature Phase Shift Keying (O-QPSK) modulation. From previous requirements, we see that \(R\)-1 and \(R\)-2 are related to the location accuracy for both the motes and BS. Thus, for an exact location, we should take into account that, in case we use Global Positioning System (GPS) for locating of the motes, it has resolution \(\sim\)3.5 m [21], which is similar to the one we can get using other techniques based on the received strength of the signals [2]. Each 1 m error accuracy produces a time error or time delay error of 3.33 ns, assuming that electromagnetic waves travel at \(c=3\times 10^{8}\) m/s. It is important to highlight that Reference [3] proposes different techniques, which are resilient to slow mobility of the motes. Nonetheless, these are case specific and cannot be regarded for use in any scenario. Both \(R\)-3 and \(R\)-4 are feasible for most of the motes. As proof of this, TelosB motes [18] are equipped with an omnidirectional antenna (Inverted-F microstrip) and transceiver TI CC2420 [19] that transmits using Direct Sequence Spread Spectrum (DSSS). Notice that all motes should transmit identical signals simultaneously. Thus, all motes in the WSN should have the same message that is pending for transmission using CB. The message exchange should take place prior to the CB stage. In addition, IEEE 802.15.4 [1] standard is based on DSSS, and, to transmit the same signal from each mote, we need to set the same Pseudo Random Sequence to get the same exact transmission at the different motes, but applying different calculated phase offsets. Furthermore, we should disable the Media Access Control (MAC) algorithm based on CCA (Clear Channel Assessment), in order to bypass this process and to allow a direct transmission. We achieve CB once we have aligned the phases of the transmissions across the antennas (at each mote) such that, after propagation, the signals combine constructively at the destination. Fixing the power radiated by a given mote, ideal transmit beamforming with \(N\) motes results in an \(N^{2}\)-fold gain in received power [5]. As it was indicated above, TelosB motes [18] have a power transmission around 0 dBm, and we can find TelosB compatible commercial motes with Radio Frequency (RF) amplifiers. Thus, \(R\)-5 is pretty feasible and it is not an impediment. Nevertheless, increasing the number of motes (\(N\)) might incur scalability problems, affecting other issues such as synchronization.