EELE 6333: Wireless Commuications Chapter # 7 : Diversity Spring, 2012/2013 EELE 6333: Wireless Commuications - Ch.7 Dr. Musbah Shaat 1 / 19
Outline 1 Introduction 2 3 Transmitter Diversity EELE 6333: Wireless Commuications - Ch.7 Dr. Musbah Shaat 2 / 19
Introduction... 1 Diversity-combining of independently fading signal paths is one of the most powerful techniques to mitigate the effects of fading. Diversity-combining uses the fact that independent signal paths have a low probability of experiencing deep fades simultaneously. The basic idea behind diversity: 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. Initial 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. EELE 6333: Wireless Commuications - Ch.7 Dr. Musbah Shaat 3 / 19
Introduction... 2 Microdiversity Diversity techniques that mitigate the effect of multipath fading. Macrodiveristy Diversity to mitigate the effects of shadowing from buildings and objects. Macrodiversity is generally implemented by combining signals received by several base stations or access points. Frequency diversity Achieved by transmitting the same narrowband signal at different carrier frequencies, where the carriers are separated by the coherence bandwidth of the channel (require additional transmit power). Time diversity Achieved by transmitting the same signal at different times, where the time difference is greater than the channel coherence time.(does not require additional transmit power but it does decrease the data rate ). EELE 6333: Wireless Commuications - Ch.7 Dr. Musbah Shaat 4 / 19
System Model... 1 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. EELE 6333: Wireless Commuications - Ch.7 Dr. Musbah Shaat 5 / 19
System Model... 2 when all but one of the complex α i s are zero, only one path is passed to the combiner output. When more than one of the α i 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. Co-phasing: the phase θ i of the i th branch is removed through the multiplication by α i = a i e jθ i for some real-valued a i. 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 α i can be performed either before detection (predetection) or after detection (postdetection) with essentially no difference in performance. EELE 6333: Wireless Commuications - Ch.7 Dr. Musbah Shaat 6 / 19
Selection Combining... 1 There are two types of performance gain associated with receiver space diversity: array gain and diversity gain. The SNR increase in the absence of fading is referred to as the array gain. The performance advantage due to using of diversity combining is called the diversity gain The different combining techniques entail various tradeoffs between performance and complexity. In selection combining (SC), the combiner outputs the signal on the branch with the highest SNR ri 2/N i. This is equivalent to choosing the branch with the highest ri 2 + N i if the noise power N i = N is the same on all branches. SC often requires just one receiver that is switched into the active antenna branch. EELE 6333: Wireless Commuications - Ch.7 Dr. Musbah Shaat 7 / 19
Selection Combining... 2 With SC the path output from the combiner has an SNR equal to the maximum SNR of all the branches. Since only one branch output is used, co-phasing of multiple branches is not required The average SNR of the combiner output in i.i.d. Rayleigh fading is γ Σ = γ M i=1 1 i where: - γ is the average SNR per branch. - M is the number of the diversity branches and is called the diversity order. The average SNR gain increases with M, but not linearly. The biggest gain is obtained by going from no diversity to two-branch diversity. Increasing the number of diversity branches from two to three will give much less gain than going from one to two. EELE 6333: Wireless Commuications - Ch.7 Dr. Musbah Shaat 8 / 19
Selection Combining... 3 EELE 6333: Wireless Commuications - Ch.7 Dr. Musbah Shaat 9 / 19
Threshold Combining... 1 SC for systems that transmit continuously may require a dedicated receiver on each branch to continuously monitor branch SNR. Simpler type of combining, called threshold combining, avoids the need for a dedicated receiver on each branch. The way is scanning each of the branches in sequential order and outputting the first signal with SNR above a given threshold γ T. As in SC, since only one branch output is used at a time, co-phasing is not required. 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 to. EELE 6333: Wireless Commuications - Ch.7 Dr. Musbah Shaat 10 / 19
Threshold Combining... 2 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 γ T. This method is called switch and stay combining (SSC). Since the SSC does not select the branch with the highest SNR, its performance is between that of no diversity and ideal SC. EELE 6333: Wireless Commuications - Ch.7 Dr. Musbah Shaat 11 / 19
Threshold Combining... 3 When the threshold γ T is optimized, SSC has the same performance as SC. The performance with an unoptimized threshold can be much worse than SC. The performance of SSC under all three thresholds is better than the performance without diversity. EELE 6333: Wireless Commuications - Ch.7 Dr. Musbah Shaat 12 / 19
Maximal Ratio Combining... 1 In SC and SSC, the output of the combiner equals the signal on one of the branches. In maximal ratio combining (MRC) the output is a weighted sum of all branches The goal is to choose the α i s to maximize γ Σ. Branches with a high SNR should be weighted more than branches with a low SNR. The optimal weights are: a 2 i = r 2 i /N o and the resulting combiner SNR is: γ Σ = M i=1 γ i The SNR of the combiner output is the sum of SNRs on each branch. The average combiner SNR increases linearly with the number of diversity branches M. MRC has significantly better performance than SC. EELE 6333: Wireless Commuications - Ch.7 Dr. Musbah Shaat 13 / 19
Maximal Ratio Combining... 2 EELE 6333: Wireless Commuications - Ch.7 Dr. Musbah Shaat 14 / 19
Equal-Gain Combining... 1 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 (EGC), which co-phases the signals on each branch and then combines them with equal weighting α i = e jθ i. The SNR of the combiner output, assuming equal noise PSD N 0 in each branch, is then given by ( γ Σ = 1 M 2 N 0 M i=1 i) r The performance of EGC is quite close to that of MRC, typically exhibiting less than 1 db of power penalty. This is the price paid for the reduced complexity of using equal gains. EELE 6333: Wireless Commuications - Ch.7 Dr. Musbah Shaat 15 / 19
Equal-Gain Combining... 2 EELE 6333: Wireless Commuications - Ch.7 Dr. Musbah Shaat 16 / 19
Transmitter Diversity Channel Known at Transmitter... 1 In transmit diversity there are multiple transmit antennas with the transmit power divided among these antennas. Transmit diversity is desirable in systems such as cellular systems where more space, power, and processing capability is available on the transmit side versus the receive side. Consider a transmit diversity system with M transmit antennas and one receive antenna. Assume the path gain associated with the i th antenna given by r i e jθ i is known at the transmitter. This is referred to as having channel side information (CSI) at the transmitter. Let s(t) denote the transmitted signal with total energy per symbol E s. This signal is multiplied by a complex gain α i = a i e jθ i and sent through the i th antenna. EELE 6333: Wireless Commuications - Ch.7 Dr. Musbah Shaat 17 / 19
Transmitter Diversity Channel Known at Transmitter... 2 This complex multiplication performs both co-phasing and weighting relative to the channel gains. When the CSI is known, the system is very similar to receiver diversity. The only difference results from having to divide the transmit power among all the transmit antennas. Receiver diversity collects energy from all receive antennas, so it does not have this penalty. This is referred to as having channel side information (CSI) at the transmitter. Hence, The analysis for MRC, EGC and SC assuming transmitter channel knowledge is the same as under receiver diversity, except that the transmit power must be divided among all transmit antennas. EELE 6333: Wireless Commuications - Ch.7 Dr. Musbah Shaat 18 / 19
Next Week Next week we will take the lecture on Wednesday instead of Tuesday. In the same room and time. EELE 6333: Wireless Commuications - Ch.7 Dr. Musbah Shaat 19 / 19