SC-FDE system frequency selection I / Q imbalance compensation method based on ZC sequence

Abstract

The invention discloses an SC-FDE system frequency selection I / Q imbalance compensation method based on a ZC sequence. The method comprises the following steps: step 1, establishing a receiving signal model containing amplitude deviation, phase deviation and filter, namely ADC system response; 2, compensating the received signal y by using an FIR filter eta to generate a compensation signal zl; 3, converting the compensation signal to a frequency domain, and constructing a frequency domain vector G; 4, constructing an auxiliary matrix E; and 5, constructing a minimization problem and converting the minimization problem into a rooting problem. Solving a rooting problem in a Newton iteration mode to obtain an estimated value of a compensation filter eta; the method is high in universality, high in flexibility and low in complexity, the adopted ZC sequence can also be used for timing synchronization, frequency synchronization, channel estimation and other receiving end signal processing modules together, and the pilot frequency utilization rate is improved. In addition, the method has robustness for phase noise.

Description

Technical Field

[0001] The present invention relates to the field of wireless communications, and in particular to a frequency-selective (FD) I / Q imbalance compensation method for a single-carrier frequency-domain equalization (SC-FDE) system, which is applicable to signal processing in millimeter-wave and terahertz communication systems. Background Art

[0002] The terahertz (THz) frequency band provides vast spectrum resources for ultra-high-speed wireless communications. However, THz devices face severe RF impairments, which have become a bottleneck limiting the performance of THz communication systems. One such RF impairment is I / Q imbalance. The wide bandwidth characteristics of THz communication can cause I / Q imbalance to exhibit frequency-selective characteristics, also known as frequency-selective I / Q imbalance. Because THz power amplifiers have low output power and nonlinear effects, and OFDM faces the problem of high peak-to-average power ratio (PAPR), THz communication transceivers are more suitable for single-carrier frequency-domain equalization (SC-FDE) structures. However, low-complexity broadband I / Q imbalance compensation in THz SC-FDE systems is a challenging problem.

[0003] Existing frequency-selective I / Q imbalance compensation methods can be categorized as test tone-based, blind estimation, and pilot-based. Test tone methods require the generation of high-precision multi-tone signals as reference signals, resulting in high equipment costs and limited offline compensation. These methods are currently commonly used in the industry. Blind estimation methods exploit the statistical properties of I / Q imbalance signals, specifically the cyclically symmetric complex Gaussian properties. However, these methods rely on restoring the statistical properties of time-domain signals, requiring large data blocks to implement and resulting in poor real-time performance. Pilot-based compensation methods use pilot signals to jointly estimate the desired channel and the image channel, using these two channels for equalization to achieve I / Q imbalance compensation. These compensation methods typically treat the I / Q imbalance and channel as equivalent channels, jointly estimating both. This complicates the algorithm design and reduces its versatility. Furthermore, this method is robust to phase noise. Summary of the Invention

[0004] The purpose of the present invention is to overcome the shortcomings of the prior art and provide a frequency-selective I / Q imbalance compensation method for an SC-FDE system based on a ZC sequence.

[0005] In order to achieve the above object, the present invention adopts the following technical solutions:

[0006] A frequency-selective (FD) I / Q imbalance compensation method for a single-carrier frequency-domain equalization (SC-FDE) system based on a Zadoff–Chu (ZC) sequence comprises the following steps:

[0007] Step 1: Build a received signal model that includes amplitude deviation, phase deviation, and filter (ADC) system response.

[0008] Step 2: Compensate the received signal y. The received signal is compensated by the compensation filter η to generate a compensation signal. where y * represents the conjugate of y, represents linear convolution;

[0009] Step 3: Convert the compensation signal to the frequency domain and construct the frequency domain vector where ⊙ represents the Hadamard product, Represents the compensated frequency domain signal Z l The conjugation of .

[0010] Step 4: Construct the auxiliary matrix Among them F (:,κ) is a submatrix of the DFT matrix F, consisting of columns in F whose column indices are the set κ, Indicates F (:,κ) The conjugate transpose of .

[0011] Step 5: Solve the minimization problem To estimate the compensation filter η.

[0012] Consider a SC-FDE system where the training sequence is composed of L z The length is N Z The data part consists of L s data blocks, each data block is of length N, and the lth data block signal is represented by a column vector s l The channel time domain response is h, and the diagonal matrix H=diag{[H0,H1,...,H N-1 The diagonal vector of ]} is the frequency domain channel response. Ideally, the lth block of time domain received signal is:

[0013]

[0014] In the formula is a circular convolution, and w is an additive white Gaussian noise vector.

[0015] Ideally, the received signal in the frequency domain is R l =HS l +W l . Where R lis the frequency domain representation of the received signal, S l is the frequency domain representation of the transmitted signal.

[0016] When frequency-selective I / Q imbalance exists, the received signal is:

[0017]

[0018] Where α and β are I / Q imbalance coefficients, which are related to the amplitude deviation ε, phase deviation θ, and the system response of the low-pass filter and ADC. Assume that the system response of the I-channel filter and ADC is g I , Q-path response is g Q ,but

[0019] α=0.5(g I +εg Q e -jθ )

[0020] β=0.5(g I -εg Q e -jθ )

[0021] From equation (2), it can be seen that the received signal is interfered by the image signal. This interference cannot be reduced by increasing the signal transmission power, nor can it be filtered out by a filter.

[0022] A further improvement of the present invention is that a compensation structure based on a two-dimensional FIR filter η=[η1,η2] is designed in step 2. By adjusting the filter η, a useful signal without image interference is obtained.

[0023] The compensated signal is labeled z l , then

[0024] (Both circular and linear convolution can be used here.) (3)

[0025] In order to ensure that the image interference signal is completely suppressed, there should be, At this time, you get

[0026] At this time, there is no η that can make Because this is an overdetermined equation, we can only find the optimal η to suppress the image interference as much as possible.

[0027] A further improvement of the present invention is that the process of constructing the frequency domain vector G in step 3 is as follows:

[0028] Ignoring the noise term, convert the compensated signal to the frequency domain:

[0029]

[0030] in, for The corresponding frequency domain vector matrix. (3) is expressed as a matrix:

[0031]

[0032] in Indicates that the timing starting point of the received signal is shifted to the left by one sampling point. Transforming the above formula into the frequency domain, we have:

[0033]

[0034] in express frequency domain signal.

[0035] Due to s l is a ZC sequence, which still has constant mode properties after FFT transformation, that is, |S (l,k) | 2 =1, k=0,1,...,N z -1. Introducing and designing N-dimensional vectors According to formula (2), we can get

[0036]

[0037] From the above formula, we can see that due to the constant envelope characteristic of the ZC sequence, the vector G is only related to the channel and has nothing to do with the transmitted signal. In other words, the time-frequency characteristics of the vector G are determined by the channel. Specifically, the vector G can be regarded as a frequency domain channel Multiply the signal by its conjugate point. According to the time-domain convolution theorem for signals and systems, convolution in the time domain corresponds to product in the frequency domain. In the terahertz band, due to high signal propagation losses, time-domain channel tap systems typically have very few channels, so the time-domain convolution length between two channels is also very short.

[0038] A further improvement of the present invention is that the specific process of constructing the auxiliary matrix in step 4 is as follows:

[0039] Define Y l =Fy l , Definition of Λ l for

[0040]

[0041] definition According to the definition of vector G,

[0042]

[0043] Among them F (:,κ)is a submatrix of the DFT matrix F, consisting of the columns in F whose column indices are the set κ.

[0044] Then we can get

[0045]

[0046] Introduce the auxiliary matrix E, defined as

[0047]

[0048] A further improvement of the present invention is that the minimization problem in step 5 is constructed as follows:

[0049] Because for the auxiliary matrix λ H The equation Eλ = 0 holds. The equation on the left is a square equation with a non-negative value. It is zero if and only if the I / Q imbalance is perfectly compensated. Therefore, the I / Q imbalance compensation factor η can be estimated by solving the following minimization problem:

[0050]

[0051] Through some derivations, the minimization problem of the above formula can be transformed into a root-finding problem of a nonlinear system of equations. The unknowns are the real and imaginary parts of η, that is, The root-finding problem can be solved by the Newton-Schmidt method, which gives an estimate of the FD I / Q imbalance.

[0052] The design concept of the present invention is as follows:

[0053] Terahertz systems generally face the problem of FD I / Q imbalance. The present invention designs an I / Q imbalance compensation structure based on FIR filters, and then uses the Zadoff–Chu (ZC) sequence commonly used in communication system synchronization and channel estimation as a training sequence to directly estimate the filter parameters. This method is performed before channel estimation, rather than in conjunction with channel estimation. Therefore, this method has strong versatility, high flexibility and low complexity. The ZC sequence used can also perform timing synchronization, frequency synchronization, channel estimation and other receiving-end signal processing modules at the same time, thereby improving pilot utilization. Simulation experiments have verified the effectiveness of the algorithm.

[0054] Compared with the prior art, the present invention has the following beneficial effects:

[0055] The present invention first establishes a received signal model that includes amplitude and phase deviations, and defines a parameter η to compensate for the received signal, obtaining a useful signal without image interference. After ignoring the noise term, the compensated signal is converted to the frequency domain. The frequency domain vector G is constructed using the OFDM constant modulus modulation characteristics. In combination with the channel's time-domain sparsity constraints, G is inverse Fourier transformed into the time domain and the valid index region is filtered to eliminate non-channel-related interference. Furthermore, an auxiliary matrix E is constructed, and the compensation factor η is directly estimated through a closed-form quadratic optimization solution, enabling independent parameter calibration without the need for joint channel estimation. Furthermore, this method is robust to phase noise. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] Figure 1 Schematic diagram of data frame group composition of the present invention;

[0057] Figure 2 This is a structural diagram of the I / Q imbalance compensation of the present invention;

[0058] Figure 3 This is a system IRR curve diagram after I / Q imbalance compensation of the present invention;

[0059] Figure 4 This is a system SER curve diagram after I / Q imbalance compensation according to the present invention. DETAILED DESCRIPTION

[0060] The present invention is described in further detail below with reference to the accompanying drawings:

[0061] A frequency-selective I / Q imbalance compensation method for an SC-FDE system based on a ZC sequence, the specific steps are as follows:

[0062] Step 1: Consider a SC-FDE system, where the training sequence is composed of L z The length is N Z The data part consists of L s data blocks, each data block is of length N, and the lth data block signal is represented by a column vector s l , the data frame is composed of Figure 1 As shown. The channel time domain response is h, the diagonal matrix H=diag{[H0,H1,...,H N-1 The diagonal vector of ]} is the frequency domain channel response. Ideally, the lth block of time domain received signal is:

[0063]

[0064] In the formula is the circular convolution, w l is the additive white Gaussian noise vector.

[0065] Ideally, the received signal in the frequency domain is R l =HSl +W l . Where R l is the frequency domain representation of the received signal, S l is the frequency domain representation of the transmitted signal.

[0066] When frequency-selective I / Q imbalance exists, the received signal is:

[0067]

[0068] Where α and β are I / Q imbalance coefficients, which are related to the amplitude deviation ε, phase deviation θ, and the system response of the low-pass filter and ADC. Assume that the system response of the I-channel filter and ADC is g I , Q-path response is g Q ,but:

[0069] α=0.5(g I +εg Q e -jθ )

[0070] β=0.5(g I -εg Q e -jθ )

[0071] From equation (2), we can see that the received signal is interfered by the image signal. This interference cannot be reduced by increasing the signal transmission power, nor can it be filtered out by a filter. In practical systems, the image rejection ratio (IRR) is often used to measure the severity of I / Q imbalance, which is defined as:

[0072]

[0073] Step 2: Use Figure 2 The compensation structure shown in the figure obtains a useful signal without image interference by adjusting the filter η. A two-dimensional FIR filter is used as the compensation filter.

[0074] Define η = [η1, η2] as the I / Q imbalance compensation coefficient, and the compensated signal is marked as z l , then

[0075]

[0076] In order to ensure that the image interference signal is completely suppressed, there should be, At this time, you get

[0077] At this time, there is no η that can make This is an overdetermined equation. We can only find the optimal η to suppress the image interference as much as possible.

[0078] Step 3: Ignore the noise term and convert the compensated signal into the frequency domain:

[0079]

[0080] in, for The corresponding frequency domain vector matrix. (3) is expressed as a matrix:

[0081]

[0082] in Indicates that the timing starting point of the received signal is shifted to the left by one sampling point. Transforming the above formula into the frequency domain, we have:

[0083]

[0084] in express frequency domain signal.

[0085] Due to s l is a ZC sequence, which still has constant mode properties after FFT transformation, that is, |S (l,k) | 2 =1, k=0,1,...,N z -1. Introducing and designing N-dimensional vectors According to formula (4), we can get

[0086]

[0087] From the above formula, we can see that due to the constant envelope characteristic of the ZC sequence, the vector G is only related to the channel and has nothing to do with the transmitted signal. In other words, the time-frequency characteristics of the vector G are determined by the channel. Specifically, the vector G can be regarded as a frequency domain channel Multiply the signal by its conjugate point. According to the time-domain convolution theorem for signals and systems, convolution in the time domain corresponds to product in the frequency domain. In the terahertz band, due to high signal propagation losses, time-domain channel tap systems typically have very few channels, so the time-domain convolution length between two channels is also very short.

[0088] Step 4: Convert it to the time domain through DFT transformation, and we can get

[0089]

[0090] Assuming the number of channel paths is P, define two index number sets κ = {P, P+1, ..., NP} and Then there is

[0091] g κ =0 (9)

[0092] In order to ensure that the index set κ is not an empty set, the number of channel paths P should satisfy N≥2P. When implementing the algorithm, the cyclic prefix length N can be used. CP Instead of the channel path number P, P is usually unknown in practical scenarios.

[0093] Define Y l =Fy l , Definition of Λ l for

[0094]

[0095] definition According to the definition of vector G,

[0096]

[0097] Among them F (:,κ) is a submatrix of the DFT matrix F, consisting of the columns in F whose column indices are the set κ.

[0098] Then we can get

[0099]

[0100] Introduce the auxiliary matrix E, defined as

[0101]

[0102] Step 5: Since Equation (12) holds for all symbol blocks, we can get

[0103] λ H Eλ=0.

[0104] The above equation is a square form, its value is non-negative, and its value is zero if and only if the I / Q imbalance is perfectly compensated. Therefore, the I / Q imbalance compensation factor η can be estimated by solving the following minimization problem:

[0105]

[0106] By derivation, the minimization problem of the above formula can be transformed into the root-finding problem of a nonlinear system of equations. The unknown number set is the real part and imaginary part of η, that is, The root-finding problem can be solved by Newton's iteration method.

[0107] MATLAB software was used to build the SC-FDE communication system and the algorithm performance was numerically simulated and analyzed. s =4 data blocks for demodulation, each data block length is N = 256, and the cyclic prefix length is CP = 8. The training sequence is composed of L zZC sequences, each ZC sequence is N in length z =32. The digital modulation mode is 8PSK. The channel is set to a frequency-selective Rayleigh fading channel with an order of 2. The amplitude deviation of the two orthogonal paths is ε = 0.1, the phase deviation is θ = 3°, and the time domain response of the I-path RF link is g I =[0.98,0.03], the time domain response of the Q-path RF link is g Q =[1,-0.05]. At this time, the image rejection rate IRR is 15dB on average. Through Monte Carlo simulation experiments, the average IRR curve and symbol error rate (SER) curve of the system after I / Q imbalance compensation using the proposed algorithm are obtained, as shown in Figure 2. Figure 3 and Figure 4 shown.

[0108] Figure 3 It shows that the proposed algorithm can effectively suppress the image interference, and the system average IRR increases with the increase of signal-to-noise ratio. z Increase and strengthen. Figure 4 The results show that compared with the uncompensated I / Q imbalance, the system SER is significantly reduced at high SNR after the proposed algorithm is used. This is because at low SNR, the system SER performance is limited by noise, while at high SNR, the system performance is limited by I / Q imbalance.

Claims

1. A frequency-selective I / Q imbalance compensation method for an SC-FDE system based on a ZC sequence, characterized in that: The following steps are involved: Step 1: Build a received signal model that includes amplitude deviation, phase deviation, and filter (ADC) system response. Step 2: Receive signal y l After compensation, the received signal is compensated by the compensation filter η to generate a compensation signal. in represents y l The conjugate of represents linear convolution; Step 3: Convert the compensation signal to the frequency domain and construct the frequency domain vector where ⊙ represents the Hadamard product, Represents the compensated frequency domain signal Z l conjugation of; Step 4: Construct the auxiliary matrix Among them F (:,κ) is a submatrix of the DFT matrix F, consisting of columns in F whose column indices are the set κ, Indicates F (:,κ) The conjugate transpose of Step 5: Solve the minimization problem To estimate the compensation filter η.

2. The method for frequency-selective I / Q imbalance compensation in an SC-FDE system based on a ZC sequence according to claim 1, characterized in that: The specific process of the received signal being compensated by the compensation filter η in step 2 is as follows: By adjusting the filter η, the compensated signal z is obtained l , which should be a useful signal without image interference: Among them, ρ is a coefficient related to I / Q imbalance, r l It is an ideal receiving signal; Ignoring the noise term, the compensated signal z l Convert to frequency domain: Where F is the DFT matrix, for The corresponding frequency domain vector matrix, s l To send a signal.

3. The method for frequency-selective I / Q imbalance compensation in an SC-FDE system based on a ZC sequence according to claim 2, wherein: The construction process of the frequency domain vector G in step 3 is as follows: Due to s l is a ZC sequence, which still has constant mode properties after FFT transformation, that is, |S (l,k) | 2 =1, k=0,1,...,N z -1; Introduce and design N-dimensional vector According to formula (2), we can get:

4. The method for frequency selective FD I / Q imbalance compensation in an SC-FDE system based on a ZC sequence according to claim 3, wherein: The specific process of constructing the auxiliary matrix E in step 4 is as follows: By DFT transformation, the frequency domain vector G is transformed into the time domain, and we get: Assuming the number of channel paths is P, define two index number sets κ = {P, P+1, ..., NP} and Then we have: g κ ＝0 (5) g κ is a subset of vector g, consisting of the elements of vector g whose index is set κ; In order to ensure that the index set κ is not an empty set, the number of channel paths P should satisfy N≥2P; when implementing the algorithm, the cyclic prefix length N is used. CP Instead of the channel path number P; Define Y l =Fy l , Definition of Λ l for: definition According to the definition of vector G: Among them F (:,κ) is a submatrix of the DFT matrix F, consisting of the columns of F whose column indices are the set κ; Then we can get: Introduce the auxiliary matrix E, which is defined as:

5. The method for frequency selective FD I / Q imbalance compensation in an SC-FDE system based on a ZC sequence according to claim 4, characterized in that: The specific process of solving the minimization problem to estimate the compensation filter η in step 5 is as follows: Since equation (8) holds for all symbol blocks, we have: l H Eλ=0 (10) The above equation is a square form, its value is non-negative, and its value is zero if and only if the I / Q imbalance is perfectly compensated; therefore, the I / Q imbalance compensation factor η is estimated by solving the following minimization problem: By derivation, the minimization problem of the above formula is transformed into the root-finding problem of a nonlinear system of equations; the set of unknowns is the real and imaginary parts of η, that is, The root-finding problem is solved by Newton's iterative method.

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