A Robust Data Transmission Method for MIMO Systems

Abstract

The present invention discloses a robust data transmission method for a MIMO system, comprising the following steps: Step 1: Obtain the noise power of the channel, the channel estimation value, and the uncertainty of the channel information at the transmitter; Step 2: Initialize the iteration index, the iteration step size, and the precoding matrix; Step 3: Given the current precoding matrix, calculate the worst channel error matrix; Step 4: Calculate the current precoding direction matrix and update the precoding matrix; Step 5: Update the iteration index; Step 6: Repeat Steps 2-5 until the algorithm converges, and output the precoding matrix; Step 7: Multiply the precoding matrix by the data at the transmitter and send the result. The method of the present invention designs an algorithm with an inner and outer two-layer iteration structure, and this method has excellent system performance in a relatively wide signal-to-noise ratio region. Compared with some existing data transmission schemes, it can achieve a larger worst transmission rate of the system, that is, it is optimal in terms of the worst transmission rate performance.

Description

Technical Field

[0001] The present invention relates to the field of digital communication technologies, and particularly to a robust data transmission method for a MIMO system. Background Art

[0002] Multi-antenna communication systems are equipped with multiple antennas at the transmitter and receiver, making full use of spatial resources. Compared with single-antenna systems, they can improve the communication rate or reduce the bit error rate, and have received attention from the academic and industrial communities in recent years. This system has many advantages and has been adopted as a key technology in 4G and 5G communication systems.

[0003] Channel state information (CSI) is very important for communication systems. It can be used for decoding at the receiving end or fed back to the transmitting end for preprocessing to improve communication performance. When the transmitting end knows the complete instantaneous CSI, a special covariance matrix or precoding can be designed to optimize the system performance. However, due to factors such as noise or feedback link delay, the CSI obtained by the transmitting end may be incomplete. This is divided into two cases: one is that the transmitting end obtains the statistical characteristics of the channel, such as the channel covariance matrix, channel mean, etc.; the other is that the transmitting end obtains incorrect instantaneous CSI - obviously, the worse the channel environment, the greater the error and uncertainty of the obtained CSI.

[0004] For the former, the system optimization objective is usually to design the optimal transmit covariance matrix to maximize the average communication rate. However, for the latter, we usually consider the robust design of the system, that is, for the worst system transmission rate / capacity, design the transmit covariance matrix or precoding to maximize the worst system capacity. In this way, it can be ensured that the working performance of the system is not lower than a certain preset level. The American "IEEE Transactions on Signal Processing" ("Worst-caserobust MIMO transmission with imperfect channel knowledge", IEEE Transactionson Signal Processing, 2007, 57(8): 3086-3100) studied the robust transmit strategy. In the case of imperfect instantaneous CSI, a low signal-to-noise ratio approximation was used for the channel capacity, and the optimal transmit covariance matrix was given, improving the robustness of the system. The American "IEEE Signal Processing Letters" ("Joint Optimization of theWorst-Case Robust MMSE MIMO Transceiver", IEEE Signal Processing Letters, 2011, 18(5): 295-298) studied the robust transceiver design of the multi-antenna system. Under the condition that the system only has imperfect instantaneous CSI, the transmit precoding and receive equalizer were designed to minimize the worst data detection error.

[0005] The present invention considers the latter case and designs the optimal precoding matrix to maximize the worst capacity of the system when the transmit end only has incorrect instantaneous CSI. Summary of the Invention

[0006] The purpose of the present invention is to provide a robust data transmission method for a MIMO system to solve the problems proposed in the above background technology.

[0007] To solve the above technical problems, the present invention provides a robust data transmission method for a MIMO system, including the following steps:

[0008] Step 1: Obtain the noise power of the channel, the channel estimation value, and the uncertainty of the channel information at the transmit end; through measurement, the transmit end obtains this information to prepare for the subsequent optimization algorithm.

[0009] Step 2: Initialize the iteration index, the iteration step size, and the precoding matrix; obtain the initial point of the algorithm to start continuous loop iteration.

[0010] Step 3: Given the current precoding matrix, calculate the worst channel error matrix; the purpose of Step 3 is to find the worst channel error under the current precoding matrix, at which time the system rate is the lowest.

[0011] Step 4: Calculate the current precoding direction matrix and update the precoding matrix; when Step 3 gives the worst information error matrix, calculating the current precoding matrix is to maximize the system rate. That is to say, under the given channel error matrix, the system rate is maximized.

[0012] Step 5: Update the iteration index;

[0013] Step 6: Repeat Steps 2 - 5 until the algorithm converges, and output the precoding matrix; by repeatedly performing the interactive iteration of Steps 3 and 4, the worst channel error matrix and the corresponding precoding matrix can be found, and these two values finally obtained are at least locally optimal.

[0014] Step 7: Multiply the precoding matrix by the data at the transmitter and send the result. When the optimal precoding matrix is found and multiplied by the original data, the normal transmission of the data can be carried out. At this time, the system can maximize the worst rate and achieve the purpose of robust transmission.

[0015] Preferably, the specific method of Step 2 is: Initialize the iteration index \(l = 0\), the iteration step size \(t_0\) and the precoding matrix where: \(P\) T is the transmit power, \(N\) T is the number of transmit antennas, and \(I\) is the identity matrix.

[0016] Preferably, the specific method of Step 3 includes:

[0017] Step 3 - 1: Input \(W\) l ;

[0018] Step 3 - 2: Initialize the iteration index \(k = 0\), the iteration step size \(s_0\), and generate the channel error matrix \(\Delta_0\) such that \(\|\Delta_0\|\) F \(\leq\varepsilon\), where \(\varepsilon\) is the uncertainty of the transmitter channel information, and the symbol \(\|\cdot\|\) F is the Frobenius norm;

[0019] Step 3 - 3: Calculate the channel error direction matrix:

[0020] where,

[0021] is the noise power, is the channel estimate value, and the symbol \((\cdot)\) H represents the Hermitian transpose of the matrix;

[0022] Step 3-4: Update the channel error matrix, Δ k+1 := Δ k - s0 / (k + 1)F Δ ;

[0023] Step 3-5: If ||Δ k+1 || F > ε, then correct Δ k+1 := εΔ k+1 / ||Δ k+1 || F ;

[0024] Step 3-6: Repeat Steps 3-3 to 3-5 until the channel error matrix converges.

[0025] Preferably, the current precoding direction matrix in Step 4 is expressed as:

[0026]

[0027] where is the worst channel error matrix in the l-th iteration calculated in Step 3.

[0028] Preferably, in Step 4, the algorithm for updating the precoding matrix is: W l+1 := W l + t0 / (l + 1)F W ; If then correct

[0029] Compared with the prior art, the beneficial effects achieved by the present invention are:

[0030] 1. The present invention designs an algorithm with an inner and outer two-layer iterative structure, and this method has excellent system performance in a relatively wide signal-to-noise ratio region. Compared with some existing data transmission schemes, it can achieve a larger system worst transmission rate, that is, it is optimal in terms of the worst transmission rate performance.

[0031] 2. The present invention repeatedly performs interactive iterations, can find the worst channel error matrix and the corresponding precoding matrix, and finally obtains two local optimal values. The system can achieve the maximization of the worst rate and achieve the purpose of robust transmission. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 is the flowchart of the precoding algorithm of the present invention.

[0033] Figure 2 is the flowchart of the sub-algorithm of the precoding algorithm of the present invention.

[0034] Figure 3 is the performance comparison diagram between the present invention and other methods. Detailed implementation mode

[0035] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0036] Please refer to Figure 1 and Figure 2 As shown, the present invention provides a robust data transmission method for a MIMO system, including the following steps:

[0037] Step 1: Obtain the noise power of the channel, the channel estimation value, and the uncertainty of the channel information at the transmitter end;

[0038] Step 2: Initialize the iteration index, the iteration step size, and the precoding matrix;

[0039] Step 3: Given the current precoding matrix, calculate the worst channel error matrix;

[0040] Step 4: Calculate the current precoding direction matrix and update the precoding matrix;

[0041] Step 5: Update the iteration index;

[0042] Step 6: Repeat steps 2-5 until the algorithm converges, and output the precoding matrix;

[0043] Step 7: Multiply the precoding matrix by the data at the transmitter end and send the result.

[0044] Preferably, the specific method of step 2 is: initialize the iteration index l = 0, the iteration step size t0, and the precoding matrix where: P T is the transmission power, N T is the number of transmit antennas, and I is the identity matrix.

[0045] The specific method of step 3 includes:

[0046] Step 3-1: Input W l ;

[0047] Step 3-2: Initialize the iteration index k = 0, the iteration step size s0, and generate the channel error matrix Δ0, such that ||Δ0|| F ≤ ε, where ε is the uncertainty of the channel information at the transmitter end, and the symbol ||.|| F is the Frobenius norm;

[0048] Step 3-3: Calculate the channel error direction matrix:

[0049] Among them,

[0050] is the noise power, is the channel estimate value, and the symbol (.) H represents the Hermitian transpose of the matrix;

[0051] Step 3-4: Update the channel error matrix, Δ k+1 := Δ k - s0 / (k + 1)F Δ ;

[0052] Step 3-5: If ||Δ k+1 || F > ε, then correct Δ k+1 := εΔ k+1 / ||Δ k+1 || F ;

[0053] Step 3-6: Repeat Step 3-3 to Step 3-5 until the channel error matrix converges.

[0054] The current precoding direction matrix in Step 4 is expressed as:

[0055]

[0056] Among them, is the worst channel error matrix in the l-th iteration calculated in Step 3.

[0057] In Step 4, the algorithm for updating the precoding matrix is: W l+1 := W l + t0 / (l + 1)F W ; If then correct

[0058] The present invention is applicable to a point-to-point MIMO transmission system, that is, a multiple-input multiple-output transmission system, where both the transmitter and the receiver are equipped with multiple antennas. The input-output relationship of the MIMO system can be expressed as

[0059] y = HWx + n,

[0060] Among them, x is the transmitted data, and its autocorrelation matrix is the N T × N T identity matrix; y is the received data; H is the N R × N T dimensional channel matrix; W is the N T × N T precoding matrix; n is Gaussian white noise, and the noise power is The system signal-to-noise ratio is defined as

[0061]

[0062] where P T is the transmission power. Due to the influence of factors such as noise, the instantaneous channel information obtained at the transmitter is incomplete and is described as:

[0063]

[0064] where is the channel estimate value obtained by the transmitter, and the channel error Δ satisfies ||Δ|| F ≤ ε, where ε is the channel uncertainty, and the symbol ||.|| F represents the Frobenius norm. Then the information transmission rate or system capacity of the MIMO system is expressed as

[0065]

[0066] The transmitter obtains the channel estimate through measurement the noise power and the channel uncertainty ε. The present invention then designs a precoding matrix W to maximize the minimum / worst system capacity, that is

[0067] The following combines specific embodiments to calculate and give a detailed explanation of the method of the present invention:

[0068] In this embodiment, both the transmitter and the receiver of the MIMO system are equipped with 5 antennas, and the elements of the channel estimate are independently and identically distributed and follow a complex Gaussian distribution with zero mean and unit variance. The channel uncertainty parameter is further modeled as: where ε r is the relative uncertainty, and we set ε r = 0.25. In addition, the noise power is set to

[0069] A total of 500 samples are generated in the simulation. For each sample, the precoding matrix W is obtained according to the following steps, then the worst capacity value at this time is obtained according to formula (2), and finally the average of the 500 worst capacity values is calculated. For each channel realization, the precoding operation process is as Figure 1 shown and mainly includes:

[0070] S1: The system obtains the noise power of the channel through measurement the channel estimate value the transmitter channel information uncertainty ε.

[0071] S2: Initialize the iteration index, iteration step size, and precoding matrix.

[0072] The specific initialization operations mentioned in this step are as follows:

[0073] The iteration index l = 0; the iteration step size t0 = 5; the precoding matrix where: P T is the transmission power, P T The specific value is obtained according to formula (1), in combination with the given signal-to-noise ratio and calculated.

[0074] S3: Given the current precoding matrix W l , calculate the worst channel error matrix according to the sub-algorithm, denoted as

[0075] For the sub-algorithm mentioned in step S3, refer to Figure 2 shown as follows, and specifically includes:

[0076] S301: Input W l ;

[0077] S302: Initialize the iteration index k = 0; the iteration step size s0 = 1; the channel error matrix

[0078] S303: Calculate the channel error direction matrix:

[0079]

[0080] S304: Update the channel error matrix: Δ k+1 := Δ k - F Δ / (k + 1).

[0081] S305: If ||Δ k+1 || F > ε, then correct Δ k+1 := εΔ k+1 / ||Δ k+1 || F .

[0082] S306: Repeat steps S302 - S305 until convergence.

[0083] S4: Calculate the current precoding direction matrix and update the precoding matrix.

[0084] S401 The current precoding direction matrix is:

[0085]

[0086] S402 The precoding matrix is updated to W l+1:= W l + 5F W / (l + 1);

[0087] Then judge: If then correct

[0088] S5: Update the iteration index l := l + 1, and repeat steps S2 - S4 until the algorithm converges.

[0089] When the above steps are calculated, the precoding matrix W and the corresponding Δ can be obtained. Substituting them into formula (2) can calculate the channel capacity at this time.

[0090] Please refer to Figure 3 shown in the performance comparison between the method of the present invention and other methods in a MIMO system where both the transmitter and the receiver are equipped with 5 antennas. Figure 3 The traditional method in [reference] can be found in "Worst - case robust MIMO transmission with imperfect channel knowledge", IEEE Transactions on Signal Processing, 2007, 57(8): 3086 - 3100. It can be seen that in the low signal - to - noise ratio region (-6dB to 0dB), the performance of the method of the present invention is close to that of the traditional method, and they are both better than the equal - power method. As the signal - to - noise ratio increases, the performance gap between the method of the present invention and the traditional method gradually increases. The average worst - case system capacity of the method of the present invention has a greater gap with the average worst - case system capacity of the other two methods and is significantly higher than the average worst - case system capacity of the other two methods. Compared with the other two methods, in the entire signal - to - noise ratio region, the system average worst - case capacity performance achieved by the method of the present invention is the best. The present invention designs an algorithm with an inner and outer two - layer iterative structure, and this method has excellent system performance in a relatively wide signal - to - noise ratio region.

[0091] It should be noted that in this article, relational terms such as first and second are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations. Moreover, the term "comprising", "including" or any other variant thereof is intended to cover non - exclusive inclusion, so that a process, method, article or device including a series of elements not only includes those elements, but also includes other elements not expressly listed, or also includes elements inherent to such process, method, article or device.

[0092] Finally, it should be noted that the above are only preferred embodiments of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or perform equivalent replacements for some of the technical features. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. A robust data transmission method for a MIMO system, characterized in that It includes the following steps: Step 1: Obtain the noise power of the channel, the channel estimation value, and the uncertainty of the channel information at the transmitter; Step 2: Initialize the iteration index, the iteration step size, and the precoding matrix; Step 3: Given the current precoding matrix, calculate the worst channel error matrix; Step 4: Calculate the current precoding direction matrix and update the precoding matrix; Step 5: Update the iteration index; Step 6: Repeat Steps 2 - 5 until the algorithm converges, and output the precoding matrix; Step 7: Multiply the precoding matrix by the data at the transmitter and send the result; The specific method of the said step 2 is: initialize the iteration index = 0, the iteration step size t0 and the precoding matrix , where: is the transmit power, is the number of transmit antennas, and I is the identity matrix; The specific method of Step 3 includes: Step 3-1: Input , is the precoding matrix in the th loop in Step 2; Step 3-2: Initialize the iteration index \(k = 0\) and the iteration step size \(s_0\), and generate the initial channel error matrix , such that it satisfies , where is the uncertainty of the channel information at the transmitter, and the symbol is the Frobenius norm; Step 3 - 3: Calculate the channel error direction matrix: Among them, is the noise power, is the channel estimate value, and the symbol represents the Hermitian transpose of a matrix; Step 3-4: Update the channel error matrix, ; Step 3-5: If , then correct ; Step 3 - 6: Repeat Steps 3 - 3 to 3 - 5 until the channel error matrix converges; The current precoding direction matrix in Step 4 is expressed as: Among them, is the worst channel error matrix in the th loop calculated in step 3; In the said step 4, the algorithm for updating the precoding matrix is as follows: ; If , then correct .

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