OFDM study notes (9) (adaptive technology)

The basic idea of ​​link-level adaptive technology is to adaptively adjust the parameters of signal transmission to make full use of the current channel environment. The basic parameters that can be adjusted include modulation mode, coding mode, transmit power, spreading gain, and signaling bandwidth . The gain of the channel capacity of the system obtained by the adaptive technology is very obvious. This kind of adaptive technology has been widely regarded as one of the important means to effectively improve the spectrum utilization in the wireless channel system, and has been used in the third-generation mobile communication standards including CDMA2000 and WCDMA.

Compared with traditional single-carrier systems, multi-carrier OFDM systems using link-level adaptive technology will have higher flexibility and can achieve better system performance. First introduce the theoretical basics of adaptive strategy; then, briefly introduce the adaptive power allocation methods used in OFDM systems, including the water injection power allocation method based on the optimal channel capacity and the power allocation method based on the bit error rate optimization. Then, it will focus on the various adaptive technologies used in the OFDM system, including adaptive power allocation, adaptive bit allocation, etc.; finally, the use of joint adaptive bit, modulation and power allocation technology, in multi-user conditions Next, joint optimization of system performance.

1 The basis of the adaptive strategy: channel state information

An ideal link adaptation algorithm can adjust various signal transmission parameters according to the current channel environment. As we all know, the mobile channel is different from the wired channel, and its randomness is very strong, so its corresponding probability statistical model is also for different environments. Generally speaking, channel propagation models can be divided into two categories according to the scale of change:
● Large-scale changes, including path loss and its variance near the mean.
●Small-scale changes reflect the characteristics of rapid changes in the received signal due to multipath fading in a short distance or time. For wideband signals, these rapidly changing characteristics correspond to frequency selective fading channels.

The basic principles of the adaptive strategy are:
Define a channel quality indicator variable, or channel state information, which provides some characteristics of the channel.
●Adjust some signal transmission parameters according to channel state information in time, frequency or space.

There are many ways to express channel state information. **Typical signal-to-noise ratio (SNR) or signal-to-noise ratio (SINR) are obtained from the physical layer. At the link layer, the packet error rate obtained from the Cyclic Redundancy Check (CRC) information can be used. **Sometimes, bit error rate can be used. In the next part, I will create a look at each of these ways of representing channel state information. First, consider the traditional use of signal-to-noise ratio measurement and ideal real-time feedback of channel state information. Here will explain the limitations of this method, and further explain more advanced types of channel state information.

1.1 Channel state information based on the mean value of the signal-to-noise ratio

In order to achieve adaptive transmission, effective channel state information must be available at the transmitter or receiver. This information is often composed of the signal-to-noise ratio measured at the receiver. In this case, an adaptive strategy that can be adopted is as follows:

(1) Measure the signal-to-noise ratio at the receiver.
(2) According to each candidate working mode, the signal-to-noise ratio information is converted into corresponding bit error rate information.
(3) Based on the target bit error rate, within the bounds of guaranteeing the target bit error rate, select the working mode that can produce the maximum throughput.
(4) Feed back the selected working mode to the transmitter.

Step (1) corresponds to the evaluation of channel state information. Step (2) mentioned calculating the threshold of the adaptive algorithm. In this case, the threshold is defined as the minimum signal-to-noise ratio required for a given operating mode to operate at the target bit error rate. Step (3) mentions the selection of the optimal working mode based on the threshold and the measured signal-to-noise ratio. Step (4) is concerned with feeding the information back to the transmitter. Under ideal circumstances, these implementation steps are simple and true. For example, let us consider a channel that only changes in time (for simplicity, the frequency domain is ignored). Only when the average signal-to-noise ratio can be measured in a relatively short time window, can the signal-to-noise ratio be converted into a bit error rate, so in each time window, what must be seen is a constant Non-sorrowful channel. Let us further assume that the signal-to-noise ratio can be measured in real time, and then the purpose of adaptive measurement is to select a set of technically coded M-ary quadrature amplitude modulation methods based on the real-time signal-to-noise ratio. From the closed expression of the bit error rate under the Gaussian white noise channel, it can be seen that in the ideal correlation detection, the bit error rate is a function of the signal-to-noise ratio.

1.2 Channel state information based on high-order probability characteristics of signal-to-noise ratio

Here, we assume that the channel state information can be measured in an arbitrary observation window at the same time. This observation window is two-dimensional, including time domain and frequency domain. The mapping relationship between the signal-to-noise ratio and the bit error rate is determined by the signal-to-noise ratio probability density function. But the problem is that because the probability density function contains many parameters, it cannot be easily obtained. It mainly depends on the following factors:

●Probability characteristics of channel fading in the time and frequency domains (often different distributions);
●The relationship between the length of the observation window in the time domain and the channel correlation time;
●The length of the observation window in the frequency domain is related to the double channel The relationship between bandwidth.

Since the probability density function for estimating the signal-to-noise ratio in the white adaptive observation window is very complicated, we can estimate some limited probability characteristics, such as the k-order characteristics of the signal-to-noise ratio in the adaptive observation window (including the first-order The characteristic is the mean value) to simplify the problem. These probability characteristics only provide some approximations of the probability density function of the received signal-to-noise ratio. However, when k is kept small, these characteristics can also provide sufficient information for the mapping from the signal to the bit error rate. The order characteristic of the signal-to-noise ratio reflects the average power measured at the receiver. The second-order characteristic of the signal-to-noise ratio in the time domain (or frequency domain) reflects the selectivity of the channel in the adaptive observation window. Higher-order features give more information about the probability density function. However, these characteristics require higher computational complexity to obtain. Therefore, it is necessary to strike a balance between accuracy and complexity.

When the high-order characteristics based on the signal-to-noise ratio are used to reflect the channel state information, the threshold value in the adaptive strategy will be a function of the high-order characteristics of the signal-to-noise ratio of the received signal. Because the threshold is no longer dependent on any characteristic of the channel environment, the adaptive strategy is more flexible and simple. The adaptive strategy is applicable to any Doppler spreading and delay spreading, and in a multi-
antenna system, it will not depend on factors such as the number of transmitting and receiving lines, the polarization of the antenna, and so on. Because the influence of these internal elements can be reflected by the k-order characteristics of the signal-to-noise ratio, and to a considerable extent, only the first-order and second-order characteristics are required.

1.3 Channel state information based on packet or bit error information

In some cases, the channel state information is related to the error rate of received data packets corresponding to various candidate working modes. Update and save the data reception status until all working modes have been trained. There is a corresponding relationship between the working mode and the packet error rate. Different from the original method that relied on the theoretical curve of bit error rate, this adaptive working mode clearly provides observable link quality information for each possible candidate working mode. However, this method is limited in Obtain the number of packets in the observation window. This method relies on the probability characteristics of the packet error rate, and the probability characteristics of the packet error rate are expected to be reliable after sending thousands of packets in a given working mode. Therefore, this may make the adaptive process very slow. Unless the training sequence is constantly transmitted frequently, this adaptive strategy can only be applied to the adaptation of large-scale channel changes. In addition, these methods depend on the service, which makes it difficult to control the response time of the algorithm (for example, compared with the method based on the signal-to-noise ratio), and it is impossible to monitor the quality of the channel when the user does not send or receive the service. Especially when there is a
lack of service, the user will lose the best tracking of the channel quality and have to restart a new adaptive process.

1.4 Based on the channel state information obtained by combining the signal-to-noise ratio and error statistical information

The types of channel state information mentioned above have their advantages and disadvantages. The channel state information based on the signal-to-noise ratio provides the flexibility to adjust the working mode on a faster basis, but this information depends on the calculated thresholds for station adaptation, and these thresholds are not necessarily correct. of. The accuracy of the threshold mechanism can be improved by considering the higher-order probability characteristics of the signal-to-noise ratio rather than just the mean value. Channel state information based on errors can obtain the performance of the accuracy of the working mode. However, this accuracy can only be obtained after observing the big business of Gandang, especially in the range of low error probability, but this will cause The adaptation process is very slow. Therefore, in the research of Momi, how to effectively combine all the types of small channel state information will surely become an important topic.

2. Adaptive power allocation

2.1 Based on the principle of channel capacity optimization

People have done a lot of research on the link white adaptation strategy in OFDM system, and put forward a series of link adaptation algorithms. Among these algorithms, the most basic algorithm is the power distribution algorithm based on the principle of water injection, and many algorithms originated here. Therefore, it is necessary to first introduce the principle of water injection here.

** Shannon has proved theoretically that if the data information rate is not greater than the channel capacity, it is possible to transmit on a given channel with an arbitrarily small bit error rate. ** Therefore, the channel capacity is the limit data rate for reliable transmission. In order to achieve as high an information rate as possible in a limited channel bandwidth, researchers have proposed various novel technologies, including compression coding, error control, and various adaptive coding and modulation techniques. Here, it is necessary to analyze the channel capacity of the multi-carrier system first.



In the OFDM system, the entire bandwidth is divided into multiple equally spaced sub-channels, so the basic unit of the allocation algorithm is the width of the sub-channels. Starting from the principle of water injection, we can adopt various adaptive modulation and coding techniques, bit allocation and power allocation strategies to expect better channel capacity. More power will be allocated to sub-channels with better channel characteristics or lower noise power.

2.2 The principle of optimizing performance based on bit error rate

Different from the above-mentioned power allocation method for maximizing system capacity, here, we will introduce an algorithm for optimizing the transmit power that directly improves the system's bit error rate performance as a starting point. In order to reduce the impact of mourning, the receiver diversity technology can be added. While giving the optimal algorithm, we will also introduce a sub-optimal algorithm with lower complexity. The system block diagram considered here is shown in the figure below.

2.2.1 Equal power distribution method

When the transmitter cannot obtain the channel state information, it naturally can only split all the transmit power equally among the sub-carriers.

2.2.2 Optimal power allocation based on bit error rate optimization

In order to obtain the optimal power allocation method, we first show the total bit error rate as a function of the transmit power {p:lk=I, 2, ", K} on K sub-carriers, and then find a set of {px} Minimize the total bit error rate.

2.2.3 Suboptimal power allocation based on bit error rate optimization

When the closed expression of the bit error rate cannot be obtained, as described above, an adaptive method can be used to find the optimal solution. However, it takes many iterations to approach the optimal solution. A more simplified method can be used to obtain a set of values ​​close to the optimal solution by using an approximation rather than an exact value of the bit error rate. Through this method, we obtain the closed expression of the sub-optimal solution under the M-phase QAM modulation mode. This approximate method of finding the sub-optimal solution can be easily used in other modulation methods.

2.2.4 Distribution method of equal signal-to-noise ratio

When the ratio of the gain of the combined subchannel to the noise power is large enough, we can regard the sub-optimal probability allocation as a strategy for equal SNR allocation. Compared with the equal power allocation method, the equal signal-to-noise ratio allocation method improves the relatively poor sub-channel receiving signal-to-noise ratio and reduces the relatively good sub-channel receiving signal-to-noise ratio.

However, this method is only more suitable for high signal-to-noise ratios. When the signal-to-noise ratio is relatively low, it is more suitable for the equal power distribution method.

3. Adaptive modulation technology

Adaptive modulation, as the name implies, is to adjust the modulation mode of each subcarrier according to the channel conditions. Simply put, the principle of adaptive modulation is to use high-order modulation when the channel conditions are good, and use low-order modulation when the channel conditions are bad.

The adaptive modulation strategy is similar in principle to the adaptive power allocation strategy described above. The modulation method can be selected based on maximizing channel capacity or minimizing bit error rate, so the principles of various algorithms are not described in detail. The algorithm of adaptive modulation is simpler than the algorithm of adaptive power allocation. Under the principle of optimizing the performance of bit error rate, some algorithms provide closed-form solutions, which greatly reduces the complexity of the algorithm.

The white adaptive modulation can also use the water injection principle to maximize the channel capacity. However, the complexity of directly applying the principle of water injection is too high, and because the types of modulation signal constellations are limited, it is impossible to perform precise adjustments according to channel conditions. Therefore, it is necessary to study practical adaptive modulation technology.

3.1 Chow algorithm

The Chow algorithm allocates bits according to the channel capacity of each sub-channel. Its optimization criterion is to optimize the spectrum efficiency of the system while maintaining the target bit error rate. This algorithm is mainly completed by three steps. First, determine the threshold Y mangin that makes the system performance optimal, then determine the modulation mode of each sub-carrier, and finally adjust the power of each sub-carrier. Here are the steps of this algorithm:

3.2 Fischer algorithm

Unlike the Chow algorithm, the Fischer algorithm does not allocate bits based on the channel capacity. Its optimization criterion is to optimize the system's bit error rate performance under the premise of maintaining a constant transmission rate and a given total transmit power . When the bit error rate on all sub-carriers is equal, the bit error rate of the system reaches the minimum value. Fischer algorithm gives a
closed-form solution for bit allocation . It first stores the noise power value log2Ni on each sub-carrier, and then only needs to perform some addition and division by integers, so it is more complex than Chow The algorithm has been progressively reduced. A brief description of the algorithm is given below.

3.3 Simple packet bit allocation algorithm (SBLA)

SBLA (Simple Block Loading Algorithm) is a simple packet bit allocation algorithm. SBLA is an adaptive modulation technology to enhance the HIPERLAN/2 air interface. It further simplifies the bit allocation algorithm, and bundles the sub-carriers into groups. The same group of sub-carriers uses the same modulation method, which further reduces the signal overhead and the amount of calculation.

SBLA determines which modulation method to use based on the average signal-to-noise ratio of each group of sub-carriers. First, all sub-carriers are divided into Ng groups, and their signal-to-noise ratios are calculated separately according to channel conditions. Then determine the modulation mode of each group of sub-carriers according to the series of signal-to-noise ratio thresholds. The absolute value of the signal-to-noise ratio threshold is variable, but the interval between the thresholds remains unchanged. The absolute position of this "ruler" is determined by the average signal-to-noise ratio of the carrier. The thresholds on the "scale" are
obtained from the value at 103 of the BER curves of various modulation modes under the root AWGN channel. The signal-to-noise ratio threshold is shown in the figure.


Since this algorithm mainly uses addition and subtraction operations, the complexity is very low.

4. Joint adaptive bit, modulation and power allocation

Previously discussed adaptive power allocation and bit allocation technology, the following will introduce how to combine adaptive bit, modulation, and power allocation technologies in a multi-user environment to optimize the overall performance of the system.

Next, consider extending OFDM with adaptive modulation to a multi-user frequency selective fading environment. When OFDM with adaptive modulation is applied in a frequency selective fading environment, a considerable part of the subcarriers may not be used. There are some typical subcarriers that are in deep fading and do not have enough power to carry any information bits. In a multi-user system that uses static time division multiplexing (TDMA) or frequency division multiplexing (FDMA) as a multiple access technology, each user applies adaptively modulated OFDM in a predetermined time slot or frequency band. As a result, these sub-carriers that are not used in the time slot or frequency band allocated by a certain user (due to adaptive modulation) will be wasted, and other users will not use these sub-carriers. However, the sub-carriers that exhibit deep fading in one user are not necessarily in deep fading in other users. In fact, it is almost impossible for a subcarrier to be in deep fading among all users, because the fading parameters of different users are completely independent. This leads us to consider an adaptive multi-user sub-carrier allocation method that allocates sub-carriers to each user according to the instantaneous channel characteristics. This method enables all sub-carriers to be used more effectively, because a sub-carrier is only discarded when it is in deep fading among all users.

Consider a multi-user subcarrier, bit, and power allocation method in which all users transmit data in all time slots. Our goal is to minimize all levels, assign sub-carriers to users according to the instantaneous fading characteristics of all users, and determine the number of bits and power level transmitted by each sub-carrier L. We formulate the allocation of multi-user sub-carriers, bits and power, and propose a cyclic algorithm to complete the allocation of multi-user carriers. Once the allocation of sub-carriers is determined, the allocation algorithm of bits and power can be applied to the sub-carriers allocated by each user.

4.1 System Model

4.2 Single-user bit allocation algorithm

First introduce the bit allocation algorithm in a single-user environment.


The idea of ​​this algorithm is very simple, and many similar algorithms are also based on the previously mentioned principles. In fact, the Chow algorithm and Fischer algorithm are more effective, and these algorithms can greatly increase the speed of bit allocation.

More similar to the common greedy algorithm!

4.3 Multi-user sub-carrier and bit allocation

As we all know, in a single-user environment, the greedy algorithm (that is, only one bit is allocated to the carrier that requires the least additional power at a time) is an optimal allocation algorithm, which minimizes the total transmission power. But this algorithm becomes more complicated in a multi-user environment. Since multiple users cannot share the same subcarrier, allocating bits to one subcarrier severely hinders other users from using this subcarrier. This dependence makes the greedy algorithm not the optimal solution. Experiments show that the optimal algorithm is likely to not allocate any user's bit information on the best subcarrier of a certain user. This may happen when the best subcarrier of a user happens to be the best subcarrier of another user, and the latter happens to have no other better subcarriers. Therefore, the allocation of multi-user sub-carriers and bits is more complicated than the single-user situation.

4.4 Performance comparison

The MAO algorithm is compared with the original three static multi-user sub-carrier allocation methods.

(1) OFDM-TDMA, each user is allocated a predetermined TDMA time slot, and all sub-carriers can be used in its dedicated time slot.

(2) OFDM-FDMA, each user is allocated a predetermined sub-carrier frequency band, and can only use its dedicated sub-carrier in one OFDM symbol. In a frequency selective fading channel, the channel gains of adjacent sub-carriers have a high degree of correlation. In order to avoid all sub-carriers of a user in deep fading, an enhanced OFDM-FDMA algorithm is proposed. We can call it OFDM interleaved-FDMA (OFDM interleaved-FDMA).

(3) OFDM interleaved-FDMA: Except that the subcarriers of one user and the subcarriers of other users are interleaved on the frequency city, other aspects are the same as OFDM-FDMA.

When the BER is required to satisfy Pe 0.0001 and the number of users is 5, the average bit signal-to-noise ratio required by the three different OFDM algorithms under different rms delay spreads. The average bit signal-to-noise ratio is defined here as the ratio of the average transmit power to the PSD value N0.

It is not difficult to see that the MAO algorithm is better than the static algorithm. In addition, the performance of OFDM-FDMA and OFDM-TDMA is similar, and the performance is better than OFDM-FDMA.

When the root mean square value of the time delay spread is 100ns, in order to achieve the same BER value, different average bit signal-to-noise ratios are required for different numbers of users. It can be seen that the performance of the MAO algorithm is basically the same as that of other algorithms in this case.

The above figure also shows the degree of improvement of the system performance by the bit allocation algorithm under the requirement of the bit signal-to-noise ratio. It can be seen that the performance of the MAO algorithm is improved by at least 3-4db compared to other algorithms.

If it is assumed that the maximum transmission power of the base station has been set, the effect of bit and subcarrier allocation is explained by the given stall frequency.

Assuming that a certain cell has five users distributed on the edge of the cell, the triangle in the figure is the location of the user. Normalized when the cell radius is set. It is not difficult to see from the following two figures that at the same distance, the stall probability of the MAO algorithm is much lower than that of other algorithms.