As shown in Figure 4-1, normal network re-entry is performed when an MS in the Idle State transitions to the Connected State (through Access State) as a result of paging or availability of scheduled uplink data or messages for transmission. The Initialization State procedures may be skipped, depending on whether system information at the MS is up-to-date and downlink synchronization with the cell has been maintained during idle period. Also during handover, the MS must perform a successful network re-entry with the target BS to establish data-plane and start or resume data transmission with the new BS.

In general any quadrilateral can form a periodic tiling of the plane. This is true for convex as well as concave quadrilaterals. Tilings can also be generated in an iterative process from fractals. These tilings are referred to as fractiles. A well-known example is the fudgeflake fractile [27]. Individual tilings are generated in an iterative process starting with a regular hexagon. The first six steps of the iteration process are shown in Fig. 1-13. At any iteration level, the resulting fractile can be used to periodically tile the plane. An example of tiling the plane with the sixth iteration of the fudgeflake fractile is shown in Fig. 1-14 [39]. Antenna array design approaches that employ fractals have been considered in [40]-[45]. Tilings can also be applied to curved surfaces. Figure 1-15 shows three different aperiodic tilings of a sphere using various sets of prototiles.

For an aperiodic tiling, the basis vectors u1 , u2 ,…, ud that will satisfy the above periodicity condition do not exist. Figure 1-16 shows the pattern of an aperiodic tiling known as the Amman tiling, discovered by Robert Amman in 1977 [39]. Over the past 50 years, several sets of aperiodic tilings have been discovered. Probably the best known aperiodic tiling is the Penrose tiling discovered by Sir Roger Penrose in 1974 [46], [47] (Fig. 1-17). The tiling is built from only two prototiles. Once the prototiles are known, there are several ways to generate the tiling. Perhaps the most intuitive way is placing tiles next to each other according to specific matching rules, which are meant to preserve the aperiodicity of the tiling. The shortfall of this method is the fact that the tiling might be generated to a point at which no additional tiles can be added via matching rules.

A more systematic approach, which lends itself better to programming, is the use of an iterative inflation process [39], [48], [49]. This process is also known as stone inflation. Stone inflation specifies how each tile is first expanded by a given factor and then subdivided into smaller tiles. Figure 1-18 shows the two prototiles of the Penrose tiling. Figure 1-19 shows an illustration of the iterative inflation process. It is interesting to note that the number of tiles grows according to the Fibonacci sequence.

Penrose tilings are not the only known aperiodic tilings of the plane. Some of the more well-known aperiodic tilings include chair, pinwheel, sphinx, and Danzer tilings [38], [39]. Danzer tilings in particular are of interest for antenna array applications. The Danzer tiling is comprised of three prototiles. Similar to a Penrose tiling, starting with the prototiles, the tiling can be generated by either placing the prototiles next to each other according to matching rules or by stone inflation. The prototiles of the Danzer aperiodic set are shown in Fig. 1-20. Figure 1-21 shows the iterative process applied to the third Danzer prototile in Fig. 1-20.

A mobile terminal PHY’s real value is largely tied to its ability to be a power miser. In the case of the M-PHY minimizing power is accomplished by:

The M-PHY makes efficient use of many different modes of operations: unpowered, disable, hibernate (Hibern8), low-speed mode and high-speed mode. The state machine is shown in Figure 6 below. Disable mode is the lowest power mode entered into once the power supply is turned on. Hibern8 is an ultra low power state, which can be used without configuration loss. It enables online wake up capability without any side band signals (in Type-I). The transition to another M-PHY state takes hundreds to thousands of microseconds. That recovery time is programmable to fit the application requirements.