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Coherent demodulation is much more applied in practice than differential demodulation. As the main technique of coherent demodulation, channel estimation is particularly important.
The channel estimator is a very important part of the receiver. In the OFDM system, there are two problems in the design of the channel estimator: ** One is the choice of pilot information. Due to the time-varying characteristics of the wireless channel, the receiver needs to keep track of the channel, so the pilot information must also Continuous transmission: The second is the design of a channel estimator that has both low complexity and good pilot tracking capabilities. Under the conditions of determining the pilot transmission mode and channel estimation criteria, find the best channel estimator structure. **In actual design, the selection of pilot information and the design of the best estimator are usually related to each other, because the performance of the estimator is related to the way the pilot information is transmitted.
1. Basic introduction
Channel estimation can be used as a mathematical expression of the influence of the channel on the input signal. A good channel estimation is an algorithm that minimizes the estimation error.
Through the channel occupancy calculation method, the receiver can obtain the impulse response of the channel. In modern wireless communication systems, the channel information has been fully utilized. The adaptive channel equalizer uses channel estimation to counter the effects of ISI. Diversity technology makes use of channel occupancy to achieve a receiver that best matches the received signal. Maximum likelihood detection minimizes the error probability at the receiving end through channel estimation. In addition, an important benefit of channel estimation is that it makes coherent demodulation possible. Because coherent demodulation needs to know the phase information of the signal, compared with incoherent demodulation, it can improve the overall performance of the system, and channel estimation technology makes it possible.
Generally speaking, there are two kinds of channel estimation algorithms, one is the estimation algorithm based on the training sequence, and the other is the blind estimation algorithm.
The channel estimation algorithm based on the training sequence refers to the channel estimation using the information known by the receiver. One of its advantages lies in its wide range of applications and can be used in almost all wireless communication systems. Its shortcomings are also obvious. The training sequence occupies information bits, which reduces the effectiveness of channel transmission and wastes bandwidth. In addition, at the receiving end, the entire frame of the signal must be received before the training sequence can be extracted for channel estimation, which brings an unavoidable delay. Therefore, restrictions on the frame structure are required. For example, in the fast channel, due to the channel The correlation time may be less than the frame length, and the application of channel estimation algorithms based on training sequences is restricted.
Blind estimation does not require a training sequence. The realization of the blind estimation algorithm needs to utilize the inherent mathematical information of the transmitted data. Although this algorithm saves bandwidth compared with the algorithm based on training sequence, it still has its own shortcomings. The computational complexity of the algorithm is too large, the flexibility is very poor, and its application in real-time systems is restricted. However, the blind estimation algorithm does not require a training sequence. Compared with the channel estimation algorithm based on the training sequence, the efficiency of the system is improved. Therefore, its application in wireless communication has attracted more and more attention.
Usually communication systems use channel estimation algorithms based on training sequences. For different channel conditions, we divide channel estimation based on training sequence into channel estimation based on slow fading channel and channel estimation based on fast fading channel, corresponding to block pilot and comb pilot respectively. It should be noted that the slow fading and fast fading channels here are different from the steam and fast fading channels in the normal sense. The fast fading and slow fading mentioned here are determined according to the relative relationship between the channel and the signal change speed. We define that if the channel remains quasi-static for one frame of the OFDM signal, it is called a slow fading channel; if it changes significantly within a frame, it is called a fast fading channel.
2. Channel estimation algorithm under slow fading channel
The first is the least square channel estimation algorithm. The LS algorithm is greatly affected by Gaussian white noise and inter-subcarrier interference (ICI), so the accuracy of this estimation algorithm is limited.
Based on the minimum mean square error (MMSE, Minimum Mean Square Error) channel estimation algorithm, it has a good suppression effect on sub-ICI and Gaussian white noise, so the effect of the MMSE algorithm is better than that of the LS algorithm. Under the same MSE, the MMSE algorithm In terms of SNR: better than LS algorithm by about 10dB~15dB. But the biggest disadvantage of the MMSE algorithm is that the complexity of the algorithm is too high, which increases exponentially with the sampling points.
In order to reduce the complexity of the algorithm, a low-order algorithm based on frequency domain correlation has attracted people's attention, called low-order LMMSE (Low Rank Linear MMSE). Its core idea
is to obtain the optimal low-order estimator by using the different value decomposition of life, and its performance is similar to that of MMSE.
The basic idea of the channel estimation method based on the training sequence is to use the sequence known by both the sender and the receiver to perform channel estimation.
Channel estimation methods based on training sequences can be roughly divided into two categories: one is channel estimation in the frequency domain, and the other is estimation in the time domain. According to the basic structure of OFDM, the pilot can be inserted in the time domain and frequency domain. There are many forms of pilot insertion. We will study two typical insertion methods, block pilots and comb pilots, which correspond to slow fading and fast fading channel conditions, respectively.
Block pilots are periodically inserted into specific OFDM symbols in the time domain and transmitted in the channel. This kind of pilot insertion method is suitable for slow fading wireless channels, that is, in an OFDM block, the channel is regarded as quasi-stationary. Because this training sequence includes all sub-carriers and does not require interpolation in the frequency domain at the receiving end, this pilot design is not very sensitive to frequency selectivity. This channel estimation algorithm is generally extended to LS and MMSE [8].
The comb pilots are evenly divided into each OFDM block. Assuming that the pilot load of the two pilots is the same, the comb pilot has a higher retransmission rate, so the comb pilot has a better estimation effect in the fast fading channel. But in the case of comb pilot, the channel characteristics on the non-pilot sub-carriers can only be obtained by interpolation of the channel characteristics on the pilot sub-carriers, so this pilot type is more sensitive to frequency selective fading. . In order to effectively combat frequency selective fading, the sub-carrier spacing is required to be much smaller than the relevant bandwidth of the channel.
1. Channel estimation algorithm based on DFT
The symbol structure of OFDM enables the channel estimation of the system to be performed simultaneously in the time domain and the frequency domain. This channel estimation algorithm is based on inserting the number frequency into a two-dimensional time-frequency trellis diagram. But this kind of algorithm is too complicated and is limited in practical application. In order to reduce the complexity of two-dimensional channel estimation, channel estimation can be carried out in the time domain and the frequency domain respectively, that is, two one-dimensional channel occupations are carried out, so people propose a way to carry out channel estimation in the time domain first, and then carry out the frequency domain estimation Channel estimation algorithm. **This algorithm uses two independent finite impulse response Wiener filters, which are applied in the time domain and frequency domain respectively. **Further simplification, channel estimation can be performed only in the time domain or only in the frequency domain. This algorithm is simple and easy to implement and has a wide range of applications.
The channel estimation algorithm based on DFT has attracted much attention because of its easy implementation and good performance. The channel estimation algorithm based on DFT first performs the channel estimation of the LS algorithm, then enters the time domain through IDFT, performs linear transformation in the time domain (the specific transformation methods are different, and will be discussed in the following pages), and finally enter through DFT Frequency domain. This algorithm uses the channel energy in the time domain to concentrate on a relatively small number of sampling points, and proposes three simplified algorithms, which are: treat the low-energy sampling point as zero, ignore the cross-correlation of the sampling point, and ignore the sampling The difference in point variance.
2. Channel estimation algorithm based on SVD
The LMMSE estimation algorithm only uses the correlation in the frequency domain, so the complexity is lower than that of the ordinary two-dimensional time-frequency algorithm, but the algorithm complexity is still very high, and it is limited in practical applications: DFT-based algorithms are in channel synchronization When the timing is not ideal, there will be a defect of sampling mismatch. In order to further improve the performance of channel estimation, one method is to use the best low-order theory to simplify the LMMSE algorithm, and another low-order approximation algorithm is based on DFT, which simplifies the LMMSE algorithm. The simplified algorithm is implemented by SVD (Singular Value Decomposition).
3. Channel estimation algorithm based on filter
(1) The frequency domain Wiener filter proposed by Hoeher is composed of a finite-length unit impulse response filter (FIR). The disadvantage is that the hardware complexity is very high, which has been introduced before.
(2) Fixed tap filter, using a filter with a fixed tap in the frequency domain, can eliminate noise by averaging the subcarrier signal vector, thereby improving the accuracy of channel estimation. This filter acts as an equalizer. effect. Moreover, this FIR filter uses a shift instead of a multiplier, thereby reducing the complexity of the device.
(3) Adjustable filter (Adaptive filter) In order to track the channel and reflect the change of the channel in time, and improve the performance of channel estimation, an adjustable filter is used, that is, the tap parameter of the filter is changed. This change is based on each sub Carrier amplitude and the difference between adjacent sub-carrier vectors.
4. Maximum likelihood estimation algorithm
Maximum likelihood algorithm (ML, Maxirmum Likelihood) is a basic method in accounting and detection algorithms. Although its application is limited due to its large complexity, it does not hinder its application in detection and estimation. , Especially in theoretical analysis.
First, briefly introduce the maximum likelihood algorithm and the maximum posterior probability (MAP, Maximum A Posterior Probability) estimation algorithm. Suppose the signal at the transmitting end is x(1) and the signal at the receiving end is y(t). In order to minimize the error at the receiving end, the posterior probability P(x(t)|y(t)) is required to be maximized. By Bayesian formula:
After derivation, the relationship between MAP and ML can be obtained, that is, satisfying the ML criterion must satisfy the MAP criterion, but satisfying the MAP criterion does not necessarily satisfy the ML criterion.
Therefore, based on the ML criterion, the OFDM channel estimation algorithm is studied. The algorithm adopts an iterative method. First, the initial state of the channel is calculated by using the pilot or the previous OFDM symbol, and then the direct decision (Decision Directed) mode is used for iterative calculation to track the channel changes. The structural characteristics of the OFDM system provide convenience for this algorithm.
The ML algorithm starts from the OFDM symbol containing the pilot. The ML estimation of the initial channel is only obtained from the pilot symbol. On this basis, the first estimated value of the transmitted signal can be obtained, and then the pilot symbol and the estimated value are sent The symbol is fed back, and iteratively obtains more accurate channel characteristics until the estimation is accurate to the preset standard.