ENG.: Ahmed Mohamed Hamza Diversity Introduction: One of the most powerful techniques to mitigate the effects of fading is to use diversity-combining of independently fading signal paths. Diversity-combining uses the fact that independent signal paths have a low probability of experiencing deep fades simultaneously. Thus, the idea behind diversity is to send the same data over independent fading paths. These independent paths are combined in some way such that the fading of the resultant signal is reduced. For example, consider a system with two antennas at either the transmitter or receiver that experience independent fading. If the antennas are spaced sufficiently far apart, it is unlikely that they both experience deep fades at the same time. By selecting the antenna with the strongest signal, called selection combining, we obtain a much better signal than if we just had one antenna. Diversity techniques that mitigate the effect of multipath fading are called microdiversity, and that is the focus of this chapter. Diversity to mitigate the effects of shadowing from buildings and objects is called macrodiversity. Macrodiversity is generally implemented by combining signals received by several base stations or access points. This requires coordination among the different base stations or access points. Such coordination is implemented as part of the networking protocols in infrastructure-based wireless networks. Types of diversity: Space diversity: One method is to use multiple transmit or receive antennas, also called an antenna array, where the elements of the array are separated in distance. Note that with receiver space diversity, independent fading paths are realized without an increase in transmit signal power or bandwidth. Moreover, coherent combining of the diversity signals leads to an increase in SNR at the receiver over the SNR that would be obtained with just a single receive antenna, which we discuss in more detail below. Conversely, to obtain independent paths through transmitter space diversity, the transmit power must be divided among multiple antennas. Thus, with coherent combining of the transmit signals the received SNR is the same as if there were just a single transmit antenna. Space diversity also requires that the separation between antennas be such that the fading amplitudes corresponding to each antenna are approximately independent. Polarization diversity: A method of achieving diversity is by using either two transmit antennas or two receive antennas with different polarization (e.g. vertically and horizontally polarized waves). The two transmitted waves follow the same path. However, since the multiple random reflections distribute the power nearly equally relative to both polarizations, the average receive power corresponding to either polarized antenna is approximately the same. Since the scattering angle relative to each polarization is random, it is highly improbable that signals received on the two differently polarized antennas would be simultaneously in deep fades. There are two disadvantages of polarization diversity. First, you can have at most two diversity branches, corresponding to the two types of polarization. The second disadvantage is that polarization diversity loses effectively half the power (3 db) since the transmit or receive power is divided between the two differently polarized antennas. Frequency diversity: Frequency diversity is achieved by transmitting the same narrowband signal at different carrier frequencies, where the carriers are separated by the coherence bandwidth of the channel. This technique requires additional transmit power to send the signal over multiple frequency bands.
Time diversity: Time diversity is achieved by transmitting the same signal at different times, where the time difference is greater than the channel coherence time (the inverse of the channel Doppler spread). Time diversity does not require increased transmit power, but it does decrease the data rate since data is repeated in the diversity time slots rather than sending new data in these time slots. Time diversity can also be achieved through coding and interleaving. Receiver Diversity: System Model: In receiver diversity the independent fading paths associated with multiple receive antennas are combined to obtain a resultant signal that is then passed through a standard demodulator. The combining can be done in several ways which vary in complexity and overall performance. Most combining techniques are linear: the output of the combiner is just a weighted sum of the different fading paths or branches, as shown in Figure for M-branch diversity. Specifically, when all but one of the complex αis are zero, only one path is passed to the combiner output. When more than one of the αi s is nonzero, the combiner adds together multiple paths, where each path may be weighted by different value. Combining more than one branch signal requires co-phasing, where the phase θi of the ith branch is removed through the multiplication by αi = aie jθi for some real-valued ai. This phase removal requires coherent detection of each branch to determine its phase θi. Without co-phasing, the branch signals would not add up coherently in the combiner, so the resulting output could still exhibit significant fading due to constructive and destructive addition of the signals in all the branches. The multiplication by αi can be performed either before detection (predetection) or after detection (postdetection) with essentially no difference in performance. Combining is typically performed post-detection, since the branch signal power and/or phase is required to determine the appropriate αi value. Post-detection combining of multiple branches requires a dedicated receiver for each branch to determine the branch phase, which increases the hardware complexity and power consumption, particularly for a large number of branches. Type of combining: Selection Combining: In selection combining (SC), the combiner outputs the signal on the branch with the highest SNR r2 i /Ni. This is equivalent to choosing the branch with the highest r2 i + Ni if the noise power Ni = N is the same on all branches. Since only one branch is used at a time, SC often requires just one receiver that is switched into the active antenna branch. However, a dedicated receiver on each antenna branch may be needed for systems that transmit continuously in order to simultaneously and continuously monitor SNR on each branch. With SC the path output from the combiner has an SNR equal to the maximum SNR of all the branches. Moreover, since only one branch output is used, co-phasing of multiple branches is not required, so this technique can be used with either coherent or differential modulation. For M branch diversity, the CDF of γσ is given by
Threshold Combining: SC for systems that transmit continuously may require a dedicated receiver on each branch to continuously monitor branch SNR. A simpler type of combining, called threshold combining, avoids the need for a dedicated receiver on each branch by scanning each of the branches in sequential order and outputting the first signal with SNR above a given threshold γt. As in SC, since only one branch output is used at a time, co-phasing is not required. Thus, this technique can be used with either coherent or differential modulation. Once a branch is chosen, as long as the SNR on that branch remains above the desired threshold, the combiner outputs that signal. If the SNR on the selected branch falls below the threshold, the combiner switches to another branch. There are several criteria the combiner can use to decide which branch to switch. The simplest criterion is to switch randomly to another branch. With only two-branch diversity this is equivalent to switching to the other branch when the SNR on the active branch falls below γt. This method is called switch and stay combining (SSC). The switching process and SNR associated with SSC is illustrated in Figure 7.4. Since the SSC does not select the branch with the highest SNR, its performance is between that of no diversity and ideal SC.
Maximal Ratio Combining:
Equal-Gain Combining: MRC requires knowledge of the time-varying SNR on each branch, which can be very difficult to measure. A simpler technique is equal-gain combining, which co-phases the signals on each branch and then combines them with equal weighting, αi = e θi. The SNR of the combiner output, assuming equal noise PSD N0 in each branch, is then given by