Symbol detection method for ZP-OTFS system based on serial interference cancellation algorithm

Abstract

This invention discloses a symbol detection method for a ZP-OTFS system based on a serial interference cancellation algorithm. This method estimates transmitted symbols based on received symbols consisting of only one transmitted symbol, and uses the estimated transmitted symbols to eliminate interference in the received data frame, thereby continuing the linear complexity process of estimating the transmitted symbols and eliminating interference. This method overcomes the problems of high complexity, high power consumption, and difficult hardware implementation associated with existing symbol detection techniques in ZP-OTFS communication systems. This method fully utilizes the zero-padding characteristic of the ZP-OTFS system to partition the non-signed interference region, selecting non-signed interference regions that are more conducive to the performance of the serial interference algorithm and reducing the impact of error propagation on the performance of the serial interference algorithm. This method also achieves good bit error performance and low complexity in scenarios where the total number of symbols in the ZP-OTFS system's transmitted data frames is relatively large.

Description

Technical Field

[0001] The present invention belongs to the field of communications technology, and more specifically, relates to a symbol detection method for a zero-padding-orthogonal time-frequency space (ZP-OTFS) system based on a successive interference cancellation (SIC) algorithm in wireless communications technology. The present invention can be used to detect data symbols in transmitted data frames from received signals in a ZP-OTFS system under low-complexity conditions. Background Art

[0002] Orthogonal Frequency Division Multiplexing (OFDM) technology has been widely adopted in 4G, 5G, and various Wi-Fi wireless networks. However, in high-mobility scenarios, OFDM systems introduce severe inter-carrier interference (ICI), which impacts the performance of OFDM communications. OTFS is a novel multi-carrier modulation technique that has emerged in recent years. This technique transforms time-varying multipath channels into the delay-Doppler (DD) domain, ensuring that all symbols in a transmission unit experience a nearly identical, slowly varying, sparse channel. Due to its excellent adaptability to Doppler frequency offset and delay, OTFS has gained widespread application in highly dynamic communication scenarios. ZP-OTFS, a variant of OTFS, features zero padding by inserting null symbols into the transmitted symbol grid in the DD domain according to a specific pattern. Zero padding simplifies the relationship between DD input and output symbols, avoiding inter-block interference of transmitted data in the time domain, thereby reducing signal detection complexity. Zero padding can also serve as a guard band for pilot signals in the DD domain and is therefore applicable to channel estimation.

[0003] In high-speed wireless communication scenarios, the channel environment is rapidly time-varying. Therefore, to ensure real-time communication, the signal processing algorithms implemented in the ZP-OTFS receiver must be minimally complex. Signal detection and channel estimation, as key components of a communication system receiver, have a crucial impact on system performance. Therefore, further research into signal detection techniques based on ZP-OTFS systems will significantly advance the application of ZP-OTFS technology and address the high Doppler shift issues encountered in high-speed mobile scenarios.

[0004] In their paper "Low Complexity Iterative Rake Decision Feedback Equalizer for Zero-Padded OTFS Systems" (IEEE transactions on vehicular technology, 2020), Tharaj Thaj, Emanuele Viterbo, and others proposed a symbol detection method for the ZP-OTFS system based on Maximum Ratio Combining (MRC). The ZP-OTFS system is characterized by the need to insert null symbols as zero padding in the DD domain grid. In this system, the MRC detection method extracts and combines the multipath components of the received transmission symbols in the DD domain grid, and then uses the maximum ratio combining method to improve the signal-to-noise ratio of the combined signal. However, the method still has the disadvantage that it requires a good initial estimate of the DD domain transmitted symbols and has an iterative structure, resulting in a high detection complexity. This results in excessive system power consumption for the received symbol detection in the OTFS communication system, resulting in a high overall power consumption of the communication system receiver and high hardware implementation difficulty.

[0005] Beijing University of Posts and Telecommunications disclosed a method for detecting received symbols in an OTFS system based on a neural network and a factor graph in its patent application “A Signal Detection Method and Device for an OTFS System” (patent application number 202010158335.1, publication number CN111478868B). This method obtains optimized signal detection performance parameters through neural network training, thereby improving signal detection performance. The disadvantage of this method is that the neural network training process and the iterative AMP algorithm used increase the complexity of the detection method. When the number of symbols transmitted per frame is large, the number of algorithm iterations increases accordingly, and the corresponding detection complexity will also increase significantly. Therefore, it is not suitable for scenarios with a large amount of data in the transmitted data frame. Summary of the Invention

[0006] The purpose of the present invention is to address the deficiencies of the above-mentioned prior art and provide a ZP-OTFS system symbol detection method based on a serial interference cancellation algorithm. The present invention aims to solve the problems of the current ZP-OTFS communication system, such as the high complexity of the symbol detection method, the high power loss of the communication receiver, the high difficulty of hardware implementation, and the unsuitability for transmitting large amounts of data in data frames.

[0007] The idea behind achieving the objectives of the present invention is to estimate transmitted symbols based on received symbols consisting of only one transmitted symbol, and use the estimated transmitted symbols to eliminate interference in the received data frame, thereby continuing the linear complexity process of estimating the transmitted symbols and eliminating interference. Because the linear complexity process of eliminating interference avoids the complex processing steps required by the prior art, such as channel matrix inversion, multiple iterative calculations, and the construction of a training model, the present invention reduces complexity and is suitable for scenarios in which the symbol detection algorithm occupies limited resources and has low power consumption in communication systems, making it more conducive to hardware implementation. The present invention fully utilizes the zero-padding characteristics of the ZP-OTFS system, namely the zero padding in the DD domain transmitted data frame, to simplify the input and output symbol relationship of the system, resulting in the presence of some received symbols without inter-symbol interference in the DD domain received data frame at the receiving end, forming a non-symbol interference region. The non-symbol interference region is divided, and non-symbol interference regions that are more conducive to the performance of the serial interference algorithm are selected, reducing the impact of error propagation on the performance of the serial interference algorithm. This ensures that the present invention also has good error performance and low complexity characteristics in scenarios where the total number of symbols in the ZP-OTFS system transmitted data frame is large.

[0008] The scheme for realizing the object of the present invention comprises the following steps:

[0009] Step 1: Generate a time domain signal according to the structure of the data frame sent in the DD domain of the ZP-OTFS system, and send the time domain signal through the antenna;

[0010] Step 2: The ZP-OTFS system receiver receives the time domain signal from the transmitter and converts the time domain signal into a DD domain receive data frame.

[0011] Step 3: Obtain the estimated transmitted symbol from one of the two symbol-free interference regions:

[0012] Step 3.1: According to the input and output relationship of the DD domain symbols of ZP-OTFS, determine the inter-symbol interference-free region in the received data frame and divide the inter-symbol interference-free region into two regions S1 and S2;

[0013] Step 3.2: Select one unsigned interference region from the two unsigned interference regions based on the channel complex gain, and use the estimated transmitted symbols from the received symbols in the region as the estimated transmitted symbols;

[0014] Step 4: Estimate the transmitted symbol by eliminating interference in the received data frame:

[0015] Step 4.1, selecting a received symbol containing an estimated transmitted symbol from the current received data frame, and subtracting interference generated by the estimated transmitted symbol from the selected received symbol;

[0016] Step 4.2: Determine whether there is a received symbol consisting of only one transmitted symbol among the received symbols after subtracting the interference. If so, add the transmitted symbol estimated from the received symbol to the estimated transmitted symbol and then execute step 4.1. Otherwise, execute step 5.

[0017] Step 5: Obtain all estimated symbols in the transmitted data frame.

[0018] Compared with the existing technology, the present invention has the following advantages:

[0019] First, the present invention uses the estimated transmitted symbols to eliminate interference in the received data frame, thereby continuing to estimate the transmitted symbols. This overcomes the problems of high complexity of existing symbol detection technologies in ZP-OTFS communication systems, resulting in excessive power loss in communication receivers and high difficulty in hardware implementation. The present invention has lower complexity and is suitable for scenarios in ZP-OTFS communication systems where the symbol detection algorithm occupies limited resources and has low power loss, and is more conducive to hardware implementation.

[0020] Second, the present invention divides the unsigned interference area under the ZP-OTFS system and selects the unsigned interference area that is more conducive to the performance of the serial interference algorithm, thereby reducing the impact of error propagation on the serial interference algorithm in the prior art. This enables the present invention to have good error performance and low complexity in scenarios where the total number of symbols in the data frames sent by the ZP-OTFS system is large. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Figure 1 is a flow chart of the present invention;

[0022] Figure 2 It is a structural diagram of a sending data frame of the present invention;

[0023] Figure 3 It is a simulation result diagram of the present invention. DETAILED DESCRIPTION

[0024] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0025] Reference Figure 1 , further describing the implementation steps of the embodiment of the present invention.

[0026] Step 1: Generate a time domain signal according to the structure of the data frame sent in the DD domain of the ZP-OTFS system, and send the time domain signal through an antenna.

[0027] Step 1.1: Determine the structure of the data frame sent by the DD domain as follows:

[0028]

[0029] Where M represents the total number of subcarriers in the ZP-OTFS system, l m represents the size of the maximum delay tap in the multipath channel, l represents the delay index in the DD domain transmission data frame, k represents the Doppler index in the DD domain transmission data frame, x1[k,l] represents the data symbol in the transmission data frame, and x[k,l] represents the transmission symbol with the lth delay and the kth Doppler in the DD domain transmission data frame, where l = 0, ..., M-1, k = 0, ..., N-1, and N represents the total number of symbols in the ZP-OTFS system.

[0030] In the embodiment of the present invention, M is 16, N is 16, and l m is 3, and the data symbol x1[k,l] comes from the QPSK constellation mapping point.

[0031] Reference Figure 2 , further describes the structure of the sent data frame.

[0032] Figure 2 The horizontal axis is time delay, the vertical axis is Doppler, and the cross marks x1[k,l] and x j represents the transmitted symbol vector of size 16×1, x j The elements are x[k,j], where j=0,...,15, k=0,...,N-1, and x 13 , x 14 , x 15 The elements in the three vectors are all 0, which represents the zero filling of the ZP-OTFS system, such as Figure 2 The area shown in the red box.

[0033] Step 1.2: Generate a time domain signal according to the transmitted data frame, and transmit the time domain signal through an antenna.

[0034] The transmitted data frame is subjected to an inverse sigmoid Fourier transform (ISFFT) to obtain time-frequency domain data, which is then subjected to a Heisenberg transform to obtain a time domain signal, which is then transmitted through an antenna.

[0035] Step 2: The ZP-OTFS system receiver receives the time domain signal from the transmitter and converts the time domain signal into a DD domain receive data frame.

[0036] The received time domain signal is subjected to a Wigner transform to obtain a time-frequency domain signal, which is then subjected to a sigmoid Fourier transform (SFFT) to obtain the received symbol y[k,l] in the DD domain received data frame. y[k,l] represents the received symbol at the lth time delay and the kth Doppler in the received data frame.

[0037] Step 3: Use the serial interference cancellation algorithm to detect the transmitted symbols of the ZP-OTFS system:

[0038] In step 3.1, according to the DD domain symbol input and output relationship of ZP-OTFS, the inter-symbol interference-free region in the received data frame is determined, and the inter-symbol interference-free region is divided into two regions S1 and S2.

[0039] The unsigned interference area in the received data frame is determined by the following DD domain input and output symbol relationship:

[0040]

[0041]

[0042] Wherein, without considering the noise, the non-interference region represents the region without ISI symbols in the received data frame. The non-interference symbol means that the symbol consists of only one transmitted symbol. P represents the total number of channel multipaths, and h i represents the channel gain of the i-th path in the channel, α i (k,l) represents the phase offset of the i-th path in the channel, represents the integer Doppler tap of the ith path in the channel, represents the integer delay tap of the i-th path in the channel, As i increases, w[k,l] represents additive noise, [.] N Indicates modulo N operation, [.] M Represents the modulo M operation.

[0043] S1 means satisfied The area formed by y[k,l] in the received data frame of the condition, S2 represents the area that satisfies The area formed by y[k,l] in the conditional receiving data frame, represents the delay tap of the P-1th path in the channel, represents the delay tap of the Pth path in the channel, represents the delay tap of the first path in the channel, Indicates the delay tap of the second path in the channel.

[0044] In the embodiment of the present invention, P is 3, 1 m is 3,h i The generation of follows a complex Gaussian distribution, is 0, is 1, is -1, is 0, is 2, is 3, is 2, is 3, take y j Represents the received symbol vector of size 16×1, y j The elements are y[k,j], where j=0,...,15, k=0,...,15, and S1 represents the vector y 15 S2 represents the area composed of the elements in vector y0 and vector y1.

[0045] In step 3.2, one unsigned interference region is selected from the two unsigned interference regions according to the channel complex gain, and the transmitted symbols estimated from the received symbols in the region are used as the estimated transmitted symbols:

[0046] The symbols in regions S1 and S2 are all received symbols without inter-symbol interference. Due to the influence of error propagation, the region that can more accurately estimate the transmitted symbols should be selected first. According to the relationship between the input and output symbols in the DD domain, it can be obtained that the selection method is related to the complex gain of the channel. If |h (1) |>|h (2) |, at this time, the transmitted symbols contained in the received symbols in the area should be estimated through area S1, otherwise, the transmitted symbols contained in the received symbols in the area should be estimated through area S2, where h (1) represents the complex gain corresponding to the maximum delay tap path in the channel, h (2) represents the complex gain corresponding to the minimum delay tap path in the channel, and |·| represents the modulo operation on the complex number.

[0047] In the embodiment of the present invention, (1) For h3, h (2) For h1, |h (1) |>|h (2) |, then we should select region S1 to estimate the transmitted symbol, region S1 represents the vector y 15 The area formed by the elements in the vector y 15 The elements in the ZF algorithm are used to get the transmitted symbol vector x 12 The estimated vector is The vector The elements in are added to the set G, and each element in the set G is an estimated transmitted symbol.

[0048] Step 3.3, obtain the receiving symbol containing the elements in the set G.

[0049] Find the received symbol containing the elements in the set G from the current received data frame, and mark its position in the received data frame.

[0050] In step 3.4, the interference caused by the elements in the set G is subtracted from the received symbol whose position is marked.

[0051] The interference caused by the elements in the set G is subtracted from the received symbol with the marked position in the received data frame to obtain an updated received data frame, wherein the interference is the result of the transmitted symbol acting on the corresponding received symbol through the DD domain input-output relationship.

[0052] Step 3.5, find the received symbol with the marked position in the updated received data frame, and add it to the marked queue. Each element in the marked queue is a received symbol with the marked position. Determine whether there is an element in the marked queue consisting of only one transmitted symbol. If so, add the estimated transmitted symbol obtained by the ZF algorithm for this element to the set G to obtain the updated set G, clear the marked queue, and execute step 3.3. Otherwise, execute step 4.

[0053] Step 4: Obtain estimated values ​​of the transmitted symbols in all transmitted data frames based on the G set, and complete the ZP-OTFS system symbol detection.

[0054] The effect of the present invention can be further illustrated by the following simulation experiments:

[0055] 1. Simulation conditions:

[0056] The hardware platform of the simulation experiment of the present invention is: the processor is Intel i3 8100CPU, the main frequency is 3.5GHz, and the memory is 12GB.

[0057] The software platforms for the simulation experiment of the present invention are: Windows 10 operating system and MATLAB R2021a.

[0058] The total number of subcarriers M of the ZP-OTFS system used in the simulation experiment of the present invention is 64, the total number of symbols N is 16, the digital modulation mode of sending data adopts QPSK modulation, the channel type used is Ricean fading channel, the Ricean factor K is 2, the total number of channel paths P is 3, the delay taps are 0, 2, and 3, respectively, and the Doppler taps are 3, -1, and 1, respectively. The delay tap corresponding to the direct path in the channel is 0, the Doppler tap is 3, and the number of cycles for statistical bit error rate is 100,000 times.

[0059] 2. Simulation content and results analysis:

[0060] The simulation experiment of the present invention is to use the present invention and two existing technologies (MRC symbol detection method and MP symbol detection method) to perform symbol detection on a number of 64*16*100000 received symbols under the ZP-OTFS system, and obtain the bit error rate of each method under 5 different signal-to-noise ratios. The relationship between the obtained bit error rate and the signal-to-noise ratio is plotted as shown below: Figure 3The three curves shown in the figure have five different signal-to-noise ratios of 8dB, 10dB, 12dB, 14dB, and 16dB.

[0061] In the simulation experiment, the two existing technologies used are:

[0062] Prior art 1 refers to the MRC symbol detection method proposed by Tharaj Thaj et al. in their paper “Low Complexity Iterative Rake Decision Feedback Equalizer for Zero-Padded OTFS Systems” (IEEE transactions on vehicular technology, 2020).

[0063] Prior art 2 refers to the MP symbol detection method proposed by P. Raviteja et al. in their paper “Interference Cancellation and Iterative Detection for Orthogonal Time Frequency Space Modulation” (IEEE transactions on wireless communications, 2018).

[0064] The complexity of the present invention is analyzed below:

[0065] Considering the complexity through the number of complex multiplications, a received symbol is affected by at most P transmitted symbols. It is necessary to eliminate the interference caused by P-1 transmitted symbols in order to estimate a transmitted symbol. The complexity of the process of calculating the interference caused by P-1 transmitted symbols and estimating a transmitted symbol is The total number of data symbols sent is N(M1 m ), for each transmitted data symbol estimated, the complexity of the process is linear, that is, the complexity of the overall algorithm is approximately Table 1 shows the complexity of the detection algorithm.

[0066] Table 1: Comparison of detection algorithm complexity

[0067]

[0068] In Table 1, the complexity of the MRC algorithm is given by Tharaj Thaj et al. in their paper “Low Complexity Iterative Rake Decision Feedback Equalizer for Zero-Padded OTFS Systems” (IEEE transactions on vehicular technology, 2020); the complexity of the MP algorithm is given by P. Raviteja et al. in their paper “Interference Cancellation and Iterative Detection for Orthogonal Time Frequency Space Modulation” (IEEE transactions on wireless communications, 2018). iter represents the number of iterations of the detection algorithm, is the modulation alphabet size, L is the number of different delay taps between P paths, and under the channel conditions of the present invention, L is P. As can be seen from Table 1, the method of the present invention has the advantage of lower complexity than the MRC symbol detection method and the MP symbol detection method.

[0069] Combined with simulation Figure 3 The effect of the present invention is further described:

[0070] Figure 3 The horizontal axis represents the signal-to-noise ratio of the transmitted symbol, in dB; the vertical axis represents the bit error rate of the symbol detection method. Among them, the curve marked with a cross represents the relationship curve between the bit error rate and the signal-to-noise ratio obtained by simulating the prior art 1; the curve marked with a diamond represents the relationship curve between the bit error rate and the signal-to-noise ratio obtained by simulating the prior art 2; the curve marked with a plus sign represents the relationship curve between the bit error rate and the signal-to-noise ratio obtained by the detection method proposed in the present invention. It can be seen from the figure that the bit error rate performance of the present invention is slightly worse than that of the MP algorithm and the MRC algorithm when the signal-to-noise ratio is 8dB, 10dB, and 12dB. When the signal-to-noise ratio is 14dB, the bit error rate performance of the present invention is basically the same as that of MRC but slightly worse than the MP algorithm. When the signal-to-noise ratio is 16dB, the bit error rate performance of the present invention is better than that of the MP algorithm and the MRC algorithm. According to the trend of the curve in the figure, it can be seen that the method of the present invention has better bit error rate performance under high signal-to-noise ratio.

[0071] The above complexity analysis table and simulation experiments show that the method of the present invention uses a serial interference algorithm to implement symbol detection for the ZP-OTFS system, overcoming the high complexity disadvantage of the existing technology in the ZP-OTFS system. This makes the present invention suitable for scenarios in the ZP-OTFS communication system where the symbol detection algorithm occupies limited resources and is more conducive to hardware implementation. At the same time, due to the reduced error propagation under high signal-to-noise ratio, the method has good bit error rate performance under high signal-to-noise ratio.

Claims

1. A ZP-OTFS system symbol detection method based on a serial interference cancellation algorithm, characterized in that: Obtaining estimated transmission symbols based on the inter-symbol interference-free region, and using the estimated transmission symbols to eliminate interference in the received data frame; the detection method comprises the following steps: Step 1: Generate a time domain signal according to the structure of the data frame sent in the DD domain of the ZP-OTFS system, and send the time domain signal through the antenna; Step 2: The ZP-OTFS system receiver receives the time domain signal from the transmitter and converts the time domain signal into a DD domain receive data frame. Step 3, obtaining an estimated transmitted symbol from one of the two symbol-free interference regions; Step 3.1: According to the input and output relationship of the DD domain symbols of ZP-OTFS, determine the inter-symbol interference-free region in the received data frame and divide the inter-symbol interference-free region into two regions S1 and S2; The unsigned interference region in the received data frame is determined by the following formula: Where y[k,l] represents the area in the received data frame that is composed of symbols without inter-symbol interference (ISI) without considering noise. IISI means that the symbol is affected by only one data symbol in the transmitted data frame. k represents the Doppler index in the DD domain transmitted data frame, l represents the delay index in the DD domain transmitted data frame, P represents the total number of channel multipaths, and h represents the number of channel multipaths. i represents the channel gain of the i-th path in the channel, α i (k,l) represents the phase offset of the i-th path in the channel, represents the integer Doppler tap of the ith path in the channel, [.] N Represents the modulo N operation, represents the integer delay tap of the i-th path in the channel, As i increases, [.] M represents the modulo M operation, w[k,l] represents the additive noise, and M represents the total number of subcarriers in the ZP-OTFS system; The non-signed interference region is divided into two regions S1 and S2: S1 represents the region that satisfies The area formed by y[k,l] in the received data frame of the condition, S2 represents the area that satisfies The area formed by y[k,l] in the conditional receiving data frame, l m Indicates the size of the maximum delay tap in the multipath channel, represents the delay tap of the P-1th path in the channel, represents the delay tap of the Pth path in the channel, represents the delay tap of the 1th path in the channel, represents the delay tap of the second path in the channel; Step 3.2, select one unsigned interference region from the two unsigned interference regions according to the channel complex gain, and use the estimated transmitted symbols from the received symbols in the region as the estimated transmitted symbols; the steps are as follows: if |h(1)|>|h(2)|, then the transmitted symbols contained in the received symbols in the region should be estimated through region S1 first, otherwise, the transmitted symbols contained in the received symbols in the region should be estimated through region S2; where h (1) represents the complex gain corresponding to the maximum delay tap path in the channel, h (2) represents the complex gain corresponding to the minimum delay tap path in the channel, and |·| represents the modulo operation; Step 4: Estimate the transmitted symbol by eliminating interference in the received data frame: Step 4.1, selecting a received symbol containing an estimated transmitted symbol from the current received data frame, and subtracting interference generated by the estimated transmitted symbol from the selected received symbol; Step 4.2: Determine whether there is a received symbol consisting of only one transmitted symbol among the received symbols after subtracting the interference. If so, add the transmitted symbol estimated from the received symbol to the estimated transmitted symbol and then execute step 4.

1. Otherwise, execute step 5. Step 5: Obtain all estimated symbols in the transmitted data frame.

2. The ZP-OTFS system symbol detection method based on the serial interference cancellation algorithm according to claim 1 is characterized in that: The structure of the data frame sent by the DD domain in step 1 is as follows: Where x1[k,l] represents the data symbol in the transmitted data frame, and x[k,l] represents the transmitted symbol at the lth delay and kth Doppler in the DD domain transmitted data frame, where l = 0, ..., M-1, k = 0, ..., N-1, and N represents the total number of symbols in the ZP-OTFS system.

3. The ZP-OTFS system symbol detection method based on the serial interference cancellation algorithm according to claim 2 is characterized in that: The process of generating the time domain signal in step 1 is as follows: performing an inverse sigmoid Fourier transform (ISFFT) on the DD transmission data frame to obtain time-frequency domain data, and then performing a Heisenberg transform on the time-frequency domain data to obtain a time domain signal.

4. The ZP-OTFS system symbol detection method based on the serial interference cancellation algorithm according to claim 3 is characterized in that: The conversion of the time domain signal into the DD domain received data frame in step 2 refers to: performing a Wigner transform on the received time domain signal to obtain a time-frequency domain signal, and then performing a sigmoid Fourier transform (SFFT) operation on the time-frequency domain signal to obtain a received symbol y[k, l] in the DD domain received data frame.

5. The ZP-OTFS system symbol detection method based on the serial interference cancellation algorithm according to claim 1, characterized in that: The interference described in step 4.1 refers to the influence of the estimated transmitted symbols on the received symbols through the DD domain symbol input-output relationship.

6. The ZP-OTFS system symbol detection method based on the serial interference cancellation algorithm according to claim 1, characterized in that: The estimation described in step 3.2 or step 4.2 refers to making a decision on a received symbol consisting of only one transmitted symbol to obtain an estimated value of the corresponding transmitted symbol.

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