Welcome back to my lecture. This is the third part. I want to explain the diversity content. The question now is, how can you improve a link reliability, especially in the highest innovation? Before, among the main three multiple-antenna gains, we have covered the array gain. And let's move on to the diversity gain. The diversity gain is different from the array gain. The diversity gain benefits from independent fading paths. It could be a space, time, and/or frequency domains. We reduce durability and eventually minimize error rates, this gain can be achieved at both the transmitter and the receiver side unlike an array system. Arrays antenna system we cover in the previous part. It is required to have uncorrelated channels for diversity techniques since it relies on statistically independent channel environment. Thus, with the uncorrelated channel from now on. In urban and indoor environments, there is no clear line of sight between the transmitter and the receiver. If [INAUDIBLE] the signal is refracted along multiple passes before finally being received. In addition to these macro level study obstacles, we may also have more reflections and doppler effect generated by the moving neighbors. They see the change in frequency of a wave for a moving relative to its source. These macro and micro scatterers introduced three ships time the length, attenuations and distorsion that can destruct heavily in the fear with one another at a percher of the receiving antenna. Here, we have plot that this cart the China fluctuations for really fading. We could observe that there is a huge difference the maximum and the minimum values of the amplitude. It is approximately. We also have similar percher in frequency and spacial domain. The multipath angular spread is simply defined by a ratio of the diameter of the here it's D and the distance between the transmitter and the receiver L. If there is no optical near the receiver, angular spread becomes asymptotic laser. Also, the spatial correlation is defined like this, as simply the wider the agitation and entire distance. The lower the space are correlation and which are default several times. As the market pass angular spread increases, this pressure correlation decreases which is what we desire to achieve the diversity key to enjoy the independence of the channel. Why is this independent passer important? The antenna diversity is especially effective at mitigating the multipath situation. This is because the multiple antennas offer a receiver several activations of the same signal. Each antenna will experience a different one in a environment. By simply summing up the two received signals here the channel is not likely to fluctuate greater in amount. It just looks like antenna. Again, if one antenna is experiencing a deflate, it is likely that another has sufficient signal, reactively system can provide a link. Well, this is [INAUDIBLE] in the receiving system, or receiver diversity, diversity reception. The analog has always proven valuable for transmitting system and transmit diversity as well. Transmit diversity is quite similar to the receiver diversity, except one thing. No channel state information is available at the node. Suppose we have three alphabets to transmit. The single data string goes through the space-time and it repeats. The guarantee its symbol suffers from two independent antennas. You might think, it's not an efficient system because it adds some redundancy. But a sense to days, we can improve the quality. We might ask that or we'll write in wrong a technically, we'd use to error rate then what is the difference between array gains, a cheap buy the informing light solutions and special diversity? The big difference is antenna structure. Yes, as you correctly remember, the perfectly correlated channel was chief rating. And on correlated the diversity came. So, the distance between adjacent antenna is different. See half lambda, and oval, ten-lambda distances. It gives quite good intuition for the array gain part, the input signal is experiencing the same channel, and the output signal is the same as the input signal. But the received power increases. Due to the increased power we have linear shift in error probabilities for [INAUDIBLE] fading channel. On the other side, the antenna diversity utilizes two independent channels. And output signal becomes flat and it shows bit-error characteristics. As the number of antenna increases, the slope of the pattern become increases. From these curves, we could learn that the array gain is quite useful for new SNR scenarios, like. And the diversity gain is quite powerful for high SNR. So far, we have focused on the concept of the diversity system here. Let me introduce some of the representative diversity techniques. For simplicity, let's assume one Tx and half and multiple Rxs antennas. This kind of configuration has been used for over 50 years. For this setup, we are not able to increase the data rate, since we have a single mouth here at the transmitter but we could achieve diversity gain. The simplest way of enjoying the multiple antennas is antenna selection. Here, as we played a lot before, two antennas or separated with sufficient spacing. That idea is quite simple, we are quite familiar with the single antenna system and we just select one antenna that has the highest antenna gain, if you look at the channel variation of the first antenna, we have red part and the green parts. Red means bad channel, and green means good channel. Thus, we select the second antenna for a certain period and switch the first antenna, okay? Switch to the second antenna and so on based on the channel condition. In doing so, we have a new size assistant with quite good channel conditions. However, as we all could guess the antenna selection is not the optimum solution. We could do better if we use the channel coefficients at the receiver. This is the optimal solution called the maximum ratio combining, MRC. In this lecture, I'm not going to go to introduce all of the details, but conceptually, this is the MRC. The signal from each antenna is rotated and weighted according to the face and strength of the channel such that the signals from all antennas are combined. The maximum ratio between signal and noise terms. More specifically, the received signal can be reach in. Here, we have two unknown coefficients. We next derived the SNRX pressure for the system and optimize define two coefficients. Then we have the a, b or complex conjugates of the channel coefficients. M or c is for simulcases, mesh memories are combing for simul cases. It's not really straightforward how to achieve the diversity gain for my two cases, multiple antennas at the transmitter side. It's been an open question until Alamouti published his landmark paper in 1998. Let me ask you a quick question, wouldn't the Tx diversity be the same as the Rx diversity? Do we just need to apply the same concept for Tx diversity? And then the Tx diversity is the same as the Rx diversity, if the signal from two different antennas are separated. We could not rely only on the space domain. We also need to exploit time and spacial domains to separate the signal. Alamouti, he invented the simplest of all the antenna Tx diversity in 1998. It was designed for two a transing antenna system and has the following putting matrix. It's readily apparent that this is grade one code. It takes two times slots to transmit two symbols using the optimal decoding scheme here, the beat that our rates of this Tx diversity is equivalent to n Rx branch maximum ration combining. That's, we already learned, deeper rights. This is a picture of the perfect between the symbols after it's been processing. There are two copies of its symbol transmitting. Since they also want a this on a transmit signal. We could easily decouple the signal by multiplying a of the with H. This means that the space diversity is designed such that the vectors will project in pairs of columns taken from the coding matrixes with original of this is simple, linear, and optimal decoding at the receiver. Here, we compare the bit error rate performances of MISO, Alamouti, SIMO, MRC, and SISO systems. It can be after that MRC and Alamouti have the same slope, ensure a better performance or precise assistance. Especially in the high senr reason. All right, we have mentioned the third part. We have learned the concept of space-diversity and the difference between the diversity gain and array gain. As a specific technique, we have also learned MRC for Rx diversity and a Alamouti code for Tx diversity. Please note that for space diversity, its most serious disadvantage is that we must sacrifice some proportion of their data rates. Indeed, the data rate is still one for Alamouti case like SISO/G systems. In the next part, I will introduce a technique to enhance the data rate by sending multiple messages.
