CN104811974B - Data processing method based on IEEE802.11n standards in WiFi comprehensive test instruments - Google Patents

Abstract

The invention discloses a data processing method based on the IEEE802.11n standard in a WiFi comprehensive tester, and aims to solve the problem of realizing the real-time and accuracy of data processing when the received data in the WiFi comprehensive tester conforms to the IEEE802.11n standard, and truly reflect the waiting time. performance of the test piece. The method is as follows: the joint timing synchronization based on energy packet detection and local training sequence cross-correlation can realize precise synchronization; the method of estimating carrier frequency offset based on time-domain data-assisted maximum likelihood can accurately estimate the frequency offset value; using LS channel Estimation and fitting achieve accurate estimation of channel characteristics. After the received data intercepts a frame of valid data, it first goes through timing synchronization and frequency offset estimation, then performs frequency compensation on the data, demodulates the data after removing the cyclic prefix, then performs channel estimation, and analyzes the signal domain, and finally the data Perform phase compensation to obtain EVM, which can truly reflect the performance of the DUT.

Description

Data processing method based on IEEE802.11n standard in WiFi comprehensive tester

technical field

The invention belongs to the field of signal processing, data processing and instrument measurement industry, in particular to a data processing method based on the IEEE802.11n standard in a WiFi comprehensive tester.

Background technique

In the past ten years, wireless LAN technology has the characteristics of high speed, flexible and low-cost layout, and has been widely used in many places, with a huge market scale and a wide range of user groups. With the development of wireless LAN, the demand for wireless network chips will continue to increase. It is particularly important for a reliable and efficient WiFi comprehensive tester to accurately detect the chip. At present, WiFi comprehensive testers in the global market are basically monopolized by foreign manufacturers, but my country is still in a backward position in the field of research and development of WiFi comprehensive testers. The integrity and security of the chain are of great significance.

The data processing of the WiFi comprehensive tester mainly includes timing synchronization, frequency synchronization and channel estimation. Synchronization is an important task for any WiFi comprehensive tester. Without accurate synchronization, the receiving end cannot recover the received data reliably, resulting in the failure of subsequent work. Timing synchronization and frequency synchronization must be performed before demodulating subcarriers, where timing synchronization includes frame synchronization and symbol synchronization. Frame synchronization is to detect the arrival of the frame and estimate the starting position of the data frame symbol, and prepare for the next step of synchronization. Symbol synchronization is to estimate the starting position of FFT data demodulation. If the symbol synchronization error is large, it will introduce inter-symbol interference, and even destroy the orthogonality between subcarriers, resulting in serious ICI. The purpose of frequency synchronization is to estimate and correct the frequency offset present in the signal.

During the wireless channel transmission, the signal will be seriously affected by the channel, which will lead to a sharp decline in the performance of the receiving end. However, channel coding technology and data interleaving technology cannot completely solve this kind of problem. It is necessary to obtain channel parameters after channel estimation of the received signal, and then equalize the signal, so as to improve the accuracy of the comprehensive tester test. The accuracy of channel estimation directly affects the performance of the entire comprehensive tester, and it is very important for the comprehensive tester to accurately reflect the performance of the DUT to obtain detailed channel information and correctly demodulate the transmitted signal at the receiving end.

Contents of the invention

Purpose of the invention: In view of the deficiencies in the prior art, the purpose of the present invention is to provide a data processing method based on the IEEE802.11n standard in a WiFi comprehensive tester, to solve the problem of realizing data processing when the received data conforms to the IEEE802.11n standard in the WiFi comprehensive tester Real-time and accuracy, truly reflect the performance of the DUT.

Technical solution: In order to achieve the above-mentioned purpose of the invention, the present invention adopts the following technical solutions:

A data processing method based on the IEEE802.11n standard in a WiFi comprehensive tester, for testing the EVM (Error Vector Magnitude, error vector magnitude) value of the DUT supporting the IEEE802.11n standard, it is characterized in that, comprising the steps:

(1) Receive the data sent by the DUT, and intercept a frame of valid data according to the signal energy distribution;

(2) Using a joint timing synchronization algorithm based on energy group detection and local training sequence cross-correlation to accurately synchronize the intercepted effective data;

(3) Using the method of estimating carrier frequency offset based on time-domain data-assisted maximum likelihood to calculate and obtain the frequency offset value, and perform frequency offset compensation on the intercepted effective data;

(4) Down-sampling, cyclic prefix removal and FFT demodulation are performed sequentially on the frequency-compensated data;

(5) Utilize the long training sequence in the data frame to use the least squares channel estimation algorithm to calculate the channel impulse response function and perform channel estimation by a method of fitting the impulse response function;

(6) After performing deinterleaving, decoding and descrambling in sequence on the signal domain after frequency offset compensation and channel equalization, the modulation mode and effective data length are extracted;

(7) Analyze the data field, and perform phase compensation to the signal of the data field;

(8) Calculate the EVM value.

When intercepting a frame of valid data according to the signal energy distribution in the described step (1), the discriminant formula according to is as follows:

Among them, r(n) represents the received signal, r(n) ² represents the energy of the received signal, N represents the total length of the received data, and I(i) is used to record that the signal energy is less than the average energy; when I(i) appears two When there are two non-adjacent consecutive "1", it means that the valid signal is between the consecutive "1".

In described step (2), comprise:

(21) In a frame of data intercepted, when continuous "0" occurs in I(i), the position of "0" that occurs for the first time is regarded as the position of coarse synchronization;

(22) Then the received signal r(n) is cross-correlated with the local long training sequence S _m , namely

Among them, L is the length of two repeated symbols, which is 64; the energy of the cross-correlation value is calculated, namely:

Wherein, N represents the length of one frame of valid data intercepted.

(23) obtaining the position corresponding to the first maximum value in P _n is a rough estimate of the first long training sequence starting position;

(24) Correspondingly add the cross-correlation values of the two long training sequences before and after, and the position corresponding to the maximum value is an accurate estimation of the starting position of the first long training sequence.

In the step (3), the method for calculating and obtaining the frequency offset value based on time-domain data-assisted maximum likelihood estimation of carrier frequency offset is adopted, and the calculation formula of the frequency offset estimated value is: Among them, z is an intermediate variable that performs time-domain correlation operations on the two received repeated symbols, specifically

Among them, f _Δ is the carrier frequency difference between the sending end and the receiving end, T _s is the sampling time, L is the length of two repeated symbols, and D is the delay of the same value of the two repeated symbols;

In described step (3), comprise the following steps:

(31) Utilize the short training sequence to realize coarse frequency offset estimation, perform cross-correlation operation on the 3-6 subsequences of the short training sequence and the 4-7 subsequences of the short training sequence, and obtain 64 frequency offset values. After averaging the values, a rough frequency offset estimate is obtained;

(32) Use the coarse frequency offset estimation value to perform frequency offset compensation on the signal, and then use the long training sequence to realize the fine frequency offset estimation, take the midpoint of the cyclic prefix as the starting point of the fine frequency offset estimation, and add 64 consecutive points after this point The sequence is cross-correlated with the next 64 points of the sequence, and the final frequency offset value is the average value of these 64 frequency offset values.

In described step (8), the formula of calculating EVM value is:

Calculate the average value of all effective value (RMS) errors in the frame, the calculation formula is as follows:

where N _f is the number of measured frames, I ₀ (if , _{i s} , i _ss , i _sc ), Q ₀ (if , _{i s} , i _ss , i _sc ) means the subcarrier i _sc , the spatial data stream i _ss and the ideal constellation symbol point corresponding to OFDM symbol _{i s} in frame if. I(if , _{i s} ,i _ss ,i _sc ), Q(if , _{i s} ,i _ss ,i _sc ) means the subcarrier i _sc , the spatial data stream i _ss corresponds to the OFDM symbol _{i s} in the frame if , P ₀ is the average power of the constellation, N _SYM is the number of data fields in OFDM symbols, N _SS is the number of air data streams, and N _ST is the total number of subcarriers.

Beneficial effects: Compared with the prior art, the patent of the present invention proposes a data processing method based on the IEEE802.11n standard in the WiFi comprehensive tester, and adopts new timing synchronization, frequency synchronization and channel estimation algorithms. It can ensure that the received signal is processed accurately in the WiFi comprehensive tester, can truly reflect the performance of the device under test, and the test results have high stability and high accuracy. Timing synchronization proposes a joint algorithm based on signal energy and local training sequence cross-correlation. Firstly, the energy packet detection is used to achieve coarse synchronization of signals, and then the local long training sequence cross-correlation algorithm is used to achieve fine synchronization. Frequency offset estimation obtains more accurate frequency offset estimation by changing the starting position of frequency offset estimation and increasing the number of points for calculating frequency offset values. Channel estimation combines the characteristics of the high signal-to-noise ratio of the channel in the comprehensive tester. On the basis of the LS algorithm, a method for fitting the impulse response function is proposed, which can accurately estimate the channel impulse response function. After the phase compensation of the data field, the EVM value is calculated, and compared with the test results of Aeroflex's PXI3000 series solution, which is the industry's leading WiFi comprehensive tester manufacturer, it has the characteristics of high stability and high accuracy.

Description of drawings

Fig. 1 is based on IEEE802.11n standard test flowchart in the WiFi comprehensive measuring instrument of the present invention;

Figure 2 is a block diagram of a receiver based on the IEEE802.11n protocol;

Fig. 3 is a schematic diagram of the frame structure of the HT-mixed mode adopted by the embodiment of the present invention;

FIG. 4 is a schematic diagram of realizing coarse frequency offset estimation by using short training sequences in the method of the present invention;

Fig. 5 is a schematic diagram of realizing fine frequency offset estimation by using a long training sequence in the method of the present invention;

Fig. 6 is a schematic diagram of a descrambler in the method of the present invention.

Detailed ways

The specific implementation will be further elaborated below in conjunction with the accompanying drawings.

The data processing process in the WiFi comprehensive tester is the same as the general receiver processing process. Figure 2 is a block diagram of a receiver based on the IEEE802.11n protocol. First, the received signal is converted into a baseband signal through a down-conversion, and then undergoes AGC (automatic gain control) and analog-to-digital conversion, and then performs frame detection and time domain synchronization, so that the system can obtain the arrival time of the signal, and then perform carrier wave on the received signal Frequency offset compensation. After that, the cyclic prefix is removed from the signal, and the signal is converted from the time domain to the frequency domain through FFT (FastFourier Transformation) transformation. After FFT transformation, the received long training sequence is used for channel estimation, and finally the original signal is obtained through constellation inverse mapping and deinterleaving.

According to the IEEE802.11n standard, there are three working modes: Non-HT (Non-high-throughput) mode, HT-mixed (High-throughput-mixed) mode and HT-greenfield (High-throughput-greenfield) mode, the present invention Taking the HT-mixed mode with a bandwidth of 20M as an example to describe in detail, Figure 3 shows the frame structure of the HT-mixed mode. The L-STF (Non-HT Short Training field) training sequence is used for timing synchronization, coarse frequency offset estimation and AGC; the L-LTF (Non-HT Long Training field) is used for fine frequency offset estimation and channel estimation. The channel is divided into 64 subcarriers, numbered from -32 to 31, and the subcarrier numbered 0 is the center DC, where the subcarriers numbered from -28 to -1 and 1 to 28 are used to transmit signals, and the pilot subcarriers are The labels are ±7 and ±21.

As shown in Figure 1, a data processing method based on the IEEE802.11n standard in a WiFi comprehensive tester provided by the embodiment of the present invention mainly includes the following steps:

(1) Receive the data sent by the DUT, and intercept a frame of valid data according to the signal energy distribution.

Before and after a complete frame of data, there is a period of power value that is much lower than the average power data. The power value is judged as follows:

Where r(n) represents the received signal, r(n) ² represents the energy of the received signal, N represents the total length of the received data, and I(i) is used to record that the signal energy is less than the average energy. When two non-adjacent consecutive "1"s appear in I(i), it means that the valid signal is between the consecutive "1".

(2) Using a joint timing synchronization algorithm based on signal energy and local training sequence cross-correlation to accurately synchronize the intercepted effective data.

In one frame of intercepted data, when consecutive "0"s appear in I(i), the position of the first occurrence of "0" can be regarded as the position of coarse synchronization. Then the received signal r(n) is cross-correlated with the local long training sequence S _m , namely

Where L is the length of two repeated symbols, which is 64. Find the energy of the cross-correlation value, that is:

Where N represents the length of one frame of valid data intercepted.

The positions corresponding to the two points with the largest energy value calculated by the above formula are respectively the starting point of the first long training sequence and the starting point of the second long training sequence, and the position corresponding to the first maximum value in P _n is calculated, which is:

above formula The position of is a rough estimate of the starting position of the first long training sequence. In order to accurately estimate the starting position of the first long training sequence, the cross-correlation values of the two long training sequences before and after are added correspondingly, and the maximum value corresponds to The position of is the position corresponding to the starting point of the first long training sequence which is:

(3) The method of estimating carrier frequency offset based on time-domain data-assisted maximum likelihood is used to calculate and obtain the frequency offset value, and perform frequency offset compensation.

Where s(n) is the complex baseband signal at the transmitter, f _Δ is the carrier frequency difference between the transmitter and the receiver, and T _s is the sampling time. Perform time-domain correlation operations on the received two repeated symbols, assuming an intermediate variable z:

Where L is the length of two repeated symbols, D is the delay of the same value of the two repeated symbols, and the final estimated frequency offset is:

The IEEE802.11n standard stipulates that the short training sequence is used for coarse frequency offset estimation, and the long training sequence is used for fine frequency offset estimation. The short training sequence is used to realize coarse frequency offset estimation. The specific implementation steps are shown in Figure 4. The cross-correlation operation between 3-6 of the short training sequence and 4-7 of the short training sequence can obtain 64 frequency offset values. After the 64 frequency offset values are averaged, a rough frequency offset estimation value can be obtained. The frequency offset compensation is performed on the signal by using the coarse frequency offset estimation value. Then use the long training sequence to realize fine frequency offset estimation. The specific implementation steps are shown in Figure 5. Take the midpoint of the cyclic prefix as the starting point of fine frequency offset estimation, and combine the continuous 64 point sequence after this point with the next sequence of this sequence 64 points are cross-correlated, and the final frequency offset value is the average value of these 64 frequency offset values.

(4) Perform down-sampling on the frequency-compensated data and remove the cyclic prefix, and perform FFT demodulation on the data.

(5) Use long training sequences for channel estimation.

In the 802.11n frame structure, the L-LTF in the preamble is used to calculate the channel estimation, extract the pilot information corresponding to the data subcarrier position of the data field in the L-LTF field in the received signal, and then use the minimum The square channel estimation algorithm calculates the channel impulse response function, namely:

H _LS ＝X ^- 1Y

Where X is the L-LTF field in the transmitted signal, Y is the pilot information corresponding to the position of the data subcarrier in the transmitted data field in the L-LTF field of the received signal, and linear fitting is performed on the obtained _HLS . Finally, the data in the signal field and the data field are used for channel equalization with the fitted channel impulse function.

(6) Analyzing the HT-SIG (High-throughput-signal) field to extract the modulation mode and effective data length.

Analyze the HT-SIG field after frequency offset compensation and channel equalization, first deinterleave the HT-SIG field, use j to represent the sequence number of the original received bit before the first permutation, and i represent the first permutation, The sequence number before the second permutation, k represents after the second permutation, s represents the received signal bits, and N _CBPS represents the number of coded bits per OFDM symbol.

The first replacement is carried out as follows:

i=s×floor(j/s)+(j+floor(16×j/N _CBPS )) mods j=0,1,...,N _CBPS -1

The second replacement is carried out as follows:

k=16×i-(N _CBPS -1) floor(16×j/N _CBPS )i=0,1,...,N _CBPS -1

Then use the Viterbi decoder to decode the deinterleaved HT-SIG field, and finally descramble the HT-SIG field. The descrambler is shown in Figure 6, and the descrambling polynomial is:

S(x)＝x ⁷ +x ⁴ +1

The modulation mode and effective data length can be extracted from the HT-SIG field after deinterleaving, decoding and descrambling.

(7) Phase compensation is performed on the signal of the data field.

Since each OFDM symbol in the data field contains 4 pilot points, the transfer function H _m (k) of these 4 points is calculated.

Where Y _m (k) represents the received frequency domain data of the mth symbol frequency point k, and X(k) represents the known frequency domain data of the frequency point. And through data interpolation (such as: linear interpolation, quadratic interpolation, etc.), the transfer function H _m (k), k∈[-32..31] of all points is obtained.

(8) Calculate the EVM (Error Vector Magnitude) value.

Calculate the average value of all effective value (RMS) errors in the frame, the calculation formula is as follows:

where N _f is the number of frames measured. I ₀ (if , _{i s} ,i _ss ,i _sc ), Q ₀ (if , _{i s} ,i _ss ,i _sc ) represents subcarrier i _sc , spatial data stream i _ss and OFDM symbol i in frame i _f The ideal constellation symbol point corresponding to _s . I(if , _{i s} ,i _ss ,i _sc ), Q(if , _{i s} ,i _ss ,i _sc ) means the subcarrier i _sc , the spatial data stream i _ss corresponds to the OFDM symbol _{i s} in the frame if The actual constellation diagram symbol points for . P ₀ is the average power of the constellation diagram, N _SYM is the number of data fields in the OFDM symbol, N _SS is the number of air data streams, and N _ST is the total number of subcarriers.

With the data processing method of the present invention, the test results are close to the test results of the PXI3000 series solutions of the industry's advanced WiFi comprehensive tester manufacturer Aeroflex, and the test stability and accuracy are better than the PXI3000 series solutions.

Claims (2)

1. the data processing method based on IEEE802.11n standards in a kind of WiFi comprehensive test instruments, is supported for testing The Error Vector Magnitude EVM values of the part to be measured of IEEE802.11n standards, it is characterised in that include the following steps：

(1) data that part to be measured is sent are received, one frame valid data of interception are distributed according to signal energy；

(2) timing synchronization algorithm is combined using based on energy interblock interference and local training sequence cross-correlation, to the effective of interception Data carry out precise synchronization；

(3) calculated using the method based on time domain data auxiliary maximum likelihood estimation carrier wave frequency deviation and try to achieve frequency deviation value, and to interception Valid data carry out frequency deviation compensation；

(4) data after frequency compensation are carried out with down-sampled, removal cyclic prefix and FFT demodulation successively；

(5) channel impulse response function is calculated using least square channel estimation method using the long training sequence in data frame And the method being fitted to impulse response function carries out channel estimation；

(6) after the signal domain after overdeviation compensation and channel equalization being deinterleaved, decode and descrambled successively, tune is extracted Molding formula and valid data length；

(7) data field is parsed, phase compensation is carried out to the signal of data field；

(8) EVM values are calculated；

When being distributed one frame valid data of interception according to signal energy in the step (1), the discrimination formula of foundation is as follows：

<mrow> <mi>I</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mrow> <mi>r</mi> <msup> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>&lt;</mo> <mrow> <mo>(</mo> <munderover> <mi>&amp;Sigma;</mi> <mrow> <mi>n</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <mi>r</mi> <msup> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>)</mo> </mrow> <mo>/</mo> <mi>N</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <mi>e</mi> <mi>l</mi> <mi>s</mi> <mi>e</mi> </mrow> </mtd> </mtr> </mtable> </mfenced> </mrow>

Wherein, r (n) represents to receive signal, r (n)²Represent the energy of reception signal, total length of data received by N expressions, I (i) It is less than average energy for tracer signal energy；When there is non-conterminous twice continuous " 1 " in I (i), then it represents that useful signal exists Between this continuous " 1 "；

In the step (2), including：

(21) in a frame data of interception, when continuous " 0 " occurs in I (i), by the position of " 0 " that first appears as thick Synchronous position；

(22) the signal r (n) subsequently received and local long training sequence S_mCross-correlation is carried out, i.e.,

<mrow> <msub> <mi>C</mi> <mi>n</mi> </msub> <mo>=</mo> <munderover> <mi>&amp;Sigma;</mi> <mrow> <mi>k</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>L</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <mi>r</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>+</mo> <mi>k</mi> <mo>)</mo> </mrow> <msubsup> <mi>S</mi> <mi>m</mi> <mo>*</mo> </msubsup> </mrow>

Wherein, L is the symbol lengths of two repetitions；The energy of cross correlation value is asked for, i.e.,：

<mrow> <msub> <mi>P</mi> <mi>n</mi> </msub> <mo>=</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>k</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <mo>|</mo> <msub> <mi>C</mi> <mi>n</mi> </msub> <msup> <mo>|</mo> <mn>2</mn> </msup> <mo>;</mo> </mrow>

Wherein, N represents the length of a frame valid data of interception；

(23) P is asked for_nIn position corresponding to first maximum for first long training sequence initial position rough estimate；

(24) former and later two long training sequence cross correlation values are carried out corresponding to addition, the wherein position corresponding to maximum is first The accurate estimation of a long training sequence initial position；

Calculated in the step (3) using the method based on time domain data auxiliary maximum likelihood estimation carrier wave frequency deviation and try to achieve frequency deviation value In, the calculation formula of offset estimation value is：Wherein, z is that two replicators that will be received carry out The intermediate variable of time-domain related calculation, is specially

<mrow> <mi>z</mi> <mo>=</mo> <munderover> <mi>&amp;Sigma;</mi> <mrow> <mi>n</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>L</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <mi>r</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <msup> <mi>r</mi> <mo>*</mo> </msup> <mrow> <mo>(</mo> <mi>n</mi> <mo>+</mo> <mi>D</mi> <mo>)</mo> </mrow> </mrow>

Wherein, f_ΔIt is the frequency difference of transmitting terminal and receiving terminal carrier wave, T_sFor the sampling time, L is the symbol lengths of two repetitions, D two The delay of the identical sample value of a replicator；

Include the following steps in the step (3)：

(31) coarse frequency offset is realized using short training sequence, by the 4 of 3~6 subsequences of short training sequence and short training sequence ~7 subsequences carry out computing cross-correlation, obtain 64 frequency deviation values, after being averaging to 64 frequency deviation values, obtain coarse frequency offset Value；

(32) frequency deviation compensation is carried out to signal using coarse frequency offset value, realizes that thin frequency deviation is estimated followed by using long training sequence Meter, the midpoint for taking cyclic prefix are the starting point of thin offset estimation, and continuous 64 point sequence and this sequence are following after this is put 64 points progress cross-correlation, the frequency deviation value finally obtained be this 64 frequency deviation values average value.

2. the data processing method based on IEEE802.11n standards in WiFi comprehensive test instruments according to claim 1, its feature It is, in the step (8), the formula for calculating EVM values is：

<mrow> <msub> <mi>EVM</mi> <mrow> <mi>R</mi> <mi>M</mi> <mi>S</mi> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <munderover> <mi>&amp;Sigma;</mi> <mrow> <msub> <mi>i</mi> <mi>f</mi> </msub> <mo>=</mo> <mn>1</mn> </mrow> <msub> <mi>N</mi> <mi>f</mi> </msub> </munderover> <msqrt> <mfrac> <mrow> <munderover> <mi>&amp;Sigma;</mi> <mrow> <msub> <mi>i</mi> <mi>s</mi> </msub> <mo>=</mo> <mn>1</mn> </mrow> <msub> <mi>N</mi> <mrow> <mi>S</mi> <mi>Y</mi> <mi>M</mi> </mrow> </msub> </munderover> <mo>&amp;lsqb;</mo> <munderover> <mi>&amp;Sigma;</mi> <mrow> <msub> <mi>i</mi> <mrow> <mi>s</mi> <mi>s</mi> </mrow> </msub> <mo>=</mo> <mn>1</mn> </mrow> <msub> <mi>N</mi> <mrow> <mi>S</mi> <mi>S</mi> </mrow> </msub> </munderover> <mo>(</mo> <munderover> <mi>&amp;Sigma;</mi> <mrow> <msub> <mi>i</mi> <mrow> <mi>s</mi> <mi>c</mi> </mrow> </msub> <mo>=</mo> <mn>1</mn> </mrow> <msub> <mi>N</mi> <mrow> <mi>S</mi> <mi>T</mi> </mrow> </msub> </munderover> <mo>(</mo> <msup> <mrow> <mo>(</mo> <mrow> <mi>I</mi> <mrow> <mo>(</mo> <mrow> <msub> <mi>i</mi> <mi>f</mi> </msub> <mo>,</mo> <msub> <mi>i</mi> <mi>s</mi> </msub> <mo>,</mo> <msub> <mi>i</mi> <mrow> <mi>s</mi> <mi>s</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>i</mi> <mrow> <mi>s</mi> <mi>c</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>I</mi> <mn>0</mn> </msub> <mrow> <mo>(</mo> <mrow> <msub> <mi>i</mi> <mi>f</mi> </msub> <mo>,</mo> <msub> <mi>i</mi> <mi>s</mi> </msub> <mo>,</mo> <msub> <mi>i</mi> <mrow> <mi>s</mi> <mi>s</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>i</mi> <mrow> <mi>s</mi> <mi>c</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> </mrow> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <mrow> <mi>Q</mi> <mrow> <mo>(</mo> <mrow> <msub> <mi>i</mi> <mi>f</mi> </msub> <mo>,</mo> <msub> <mi>i</mi> <mi>s</mi> </msub> <mo>,</mo> <msub> <mi>i</mi> <mrow> <mi>s</mi> <mi>s</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>i</mi> <mrow> <mi>s</mi> <mi>c</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>Q</mi> <mn>0</mn> </msub> <mrow> <mo>(</mo> <mrow> <msub> <mi>i</mi> <mi>f</mi> </msub> <mo>,</mo> <msub> <mi>i</mi> <mi>s</mi> </msub> <mo>,</mo> <msub> <mi>i</mi> <mrow> <mi>s</mi> <mi>s</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>i</mi> <mrow> <mi>s</mi> <mi>c</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> </mrow> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>)</mo> <mo>&amp;rsqb;</mo> </mrow> <mrow> <msub> <mi>N</mi> <mrow> <mi>S</mi> <mi>Y</mi> <mi>M</mi> </mrow> </msub> <mo>&amp;times;</mo> <msub> <mi>N</mi> <mrow> <mi>S</mi> <mi>S</mi> </mrow> </msub> <mo>&amp;times;</mo> <msub> <mi>N</mi> <mrow> <mi>S</mi> <mi>T</mi> </mrow> </msub> <mo>&amp;times;</mo> <msub> <mi>P</mi> <mn>0</mn> </msub> </mrow> </mfrac> </msqrt> </mrow> <msub> <mi>N</mi> <mi>f</mi> </msub> </mfrac> </mrow>

Wherein N_fFor the frame number of measurement, I₀(i_f,i_s,i_ss,i_sc), Q₀(i_f,i_s,i_ss,i_sc) represent subcarrier i_sc, spatial data i_ssWith frame i_fMiddle OFDM symbol i_sCorresponding ideal constellation symbolic point；I(i_f,i_s,i_ss,i_sc), Q (i_f,i_s,i_ss,i_sc) represent Subcarrier i_sc, spatial data i_ssWith frame i_fMiddle OFDM symbol i_sCorresponding actual constellation symbolic point, P₀For the flat of planisphere Equal power；N_SYMFor the quantity of the data field in OFDM symbol, N_SSFor air-data stream quantity, N_STFor total number of sub-carriers.