DE102019200483A1 - Process for the transmission of data - Google Patents

Abstract

A method of data transmission, the method comprising the steps of: transmitting by a transmission device data over a transmission channel with unknown channel coefficients affected by noise, receiving data by a receiving device and estimating the channel coefficients using an estimation algorithm, calculating a decoding metric based on the estimated channel coefficients, characterized by modifying the decoding metric based on an uncertainty in the channel estimate.

Description

The invention relates to a method for transmitting data over a transmission channel with unknown channel coefficients, which are influenced by noise.

It is assumed that the channel coefficient remains constant for n _c channel uses and changes independently along ℓ coherence blocks, which are also called diversity branches. Therefore the packet size is n = ℓn _c . The channel coefficient can be random or predeterminable. The method according to the invention can be used in both cases.

mit $$\begin{array}{ccc}{y}_i=\left(y_{i\mathrm{,1}},y_{i\mathrm{,2}},\dots ,y_{i,n_c}\right)& x_i=\left(x_{i\mathrm{,1}},x_{i\mathrm{,2}},\dots ,x_{i,n_c}\right)& z_i=\left(z_{i\mathrm{,1}},z_{i\mathrm{,2}},\dots ,z_{i,n_c}\right)\end{array}$$

wobei x_i ∈ X^{n c} mit jedem |x_i,j|² = 1 (zum Beispiel binary phase-shift keying BPSK, quadrature phase-shift keying QBPSK, etc.). y_i ∈ ℂ^{n c} bezeichnet die übermittelten und empfangenen Vektoren. h_i ist der Kanalkoeffizient und z_i ist der korrespondierende Term für das AWGN-Rauschen, das verteilt ist gemäß Z_i∼CN(0, 2σ²I_{n c} ), d. h. $$p_z\left(z\right)=\frac{1}{2\pi {\sigma }^2}\text{exp}\left(-\frac{1}{2{\sigma }^2}{\left|z\right|}^2\right).$$

The relationship between input and output data on the channel for the i-th coherence block given by $$\begin{array}{cc}{y}_i=H_i{x}_i+{\mathrm{e.g.}}_i,& i=\mathrm{1,}...,\mathcal{l}\end{array}$$

With $$\begin{array}{ccc}{y}_i=\left(y_{i\mathrm{,1}},y_{i\mathrm{,\; 2nd}},...,y_{i,n_c}\right)& x_i=\left(x_{i\mathrm{,1}},x_{i\mathrm{,\; 2nd}},...,x_{i,n_c}\right)& {\mathrm{e.g.}}_i=\left({\mathrm{e.g.}}_{i\mathrm{,1}},{\mathrm{e.g.}}_{i\mathrm{,\; 2nd}},...,{\mathrm{e.g.}}_{i,n_c}\right)\end{array}$$

where x _i ∈ X ^{n c} with each | x _{i, j} | ² = 1 (e.g. binary phase-shift keying BPSK, quadrature phase-shift keying QBPSK, etc.). y _i ∈ ℂ ^{n c} denotes the transmitted and received vectors. h _i is the channel coefficient and z _i is the corresponding term for the AWGN noise, which is distributed according to Z _i ∼CN (0, 2σ ² I _{n c} ), ie $$p_{\mathrm{e.g.}}\left(\mathrm{e.g.}\right)=\frac{1}{\mathrm{2nd}\pi {\sigma }^{\mathrm{2nd}}}\text{exp}\left(-\frac{1}{\mathrm{2nd}{\sigma }^{\mathrm{2nd}}}{\left|\mathrm{e.g.}\right|}^{\mathrm{2nd}}\right).$$

wobei C das Set von Codewörtern (d. h. das Codebook) bezeichnet und $$p_{Y|HX}\left(y_i|h_i,x_i\right)=\frac{1}{{\left(2\pi {\sigma }^2\right)}^{n_c}}\text{exp}\left(-\frac{1}{2{\sigma }^2}{\Vert y_i-h_i{x}_i\Vert }^2\right).$$

In equation (1), h _{i are} the unknown complex channel coefficients. The recipient has no knowledge of the probability distribution h _i . In order to perform the decoding, the value for h _i must be known. If h _{i is known to} the recipient, optimal decoding (ie maximum likelihood decoding) can be carried out in accordance with $$\begin{array}{ll}\widehat{x}=arGma{x}_{x\in \mathrm{C.}}{p}_{\left\{y|x,H_1,H_{\mathrm{2nd}}...,H_{\mathcal{l}}\right\}}\left(y|x,H_1,H_{\mathrm{2nd}}...,H_{\mathcal{l}}\right)\hfill & \left(\mathrm{2nd}\right)\hfill \\ =arGmi{n}_{x\in \mathrm{C.}}{\displaystyle {\sum }_{i=1}^{\mathcal{l}}{\Vert y_i-H_i{x}_i\Vert }^{\mathrm{2nd}}}\hfill & \left(\mathrm{3rd}\right)\hfill \end{array}$$

where C denotes the set of code words (ie the codebook) and $$p_{Y|HX}\left(y_i|H_i,x_i\right)=\frac{1}{{\left(\mathrm{2nd}\pi {\sigma }^{\mathrm{2nd}}\right)}^{n_c}}\text{exp}\left(-\frac{1}{\mathrm{2nd}{\sigma }^{\mathrm{2nd}}}{\Vert y_i-H_i{x}_i\Vert }^{\mathrm{2nd}}\right).$$

wobei $\langle y_i,h_i,x_i\rangle$

die Korrelation zwischen y_i und h_ix_i sind, gegeben durch $$\langle y_i,h_i,x_i\rangle ={\displaystyle {\sum }_{j=1}^{n_c}{y}_{i,j}{h}_i^{\ast }{h}_{i,j}^{\ast }.}$$

With some algebraic manipulations, equation (2) can be transformed into $$\widehat{x}=arGma{x}_{x\in \mathrm{C.}}{\displaystyle \sum _{i=1}^{\mathcal{l}}\Re \left\{〈y_i,H_i,x_i〉\right\}}$$

in which $〈y_i,H_i,x_i〉$

the correlation between y _i and h _i x _i are given by $$〈y_i,H_i,x_i〉={\displaystyle {\sum }_{j=1}^{n_c}{y}_{i,j}{H}_i^{\ast }{H}_{i,j}^{\ast }.}$$

Here * denotes the complex conjugate.

In order to supply the decoder with an estimate of the channel coefficients h _i , a preamble w _i consisting of m symbols is usually appended to each coherence block in the code word. The preamble is a known sequence of +/- 1 and is used by the recipient to estimate the values for h _i . However, since the preamble is transmitted over the noisy transmission channel, the estimate ĥ _i of h _{i will} be influenced by an error that will increase the probability of decoding errors. The error | ĥ _i - h _i | will be smaller on average if the preamble is long (ie if m is large). However, a long preamble comes at the expense of transmission efficiency, since no user data is transmitted in it. It is therefore advantageous to keep the length of the preamble m short compared to the code word length n.

The estimator that is commonly used is a maximum likelihood estimator that calculates the following estimate: $${\widehat{H}}_i=\frac{1}{m}〈{\tilde{w}}_i,w_i〉.$$

d. h. beim Dekodieren wird davon ausgegangen, dass ĥ_i der tatsächliche Kanalkoeffizient ist.Here w̃ _{i is} the noisy version of w _i . Using the noisy estimate ĥ _i , the decoding takes place according to $$\begin{array}{ll}\widehat{x}=arGma{x}_{x\in \mathrm{C.}}{p}_{\left\{y|x,H_1,H_{\mathrm{2nd}}...,H_{\mathcal{l}}\right\}}\left(y|x,{\widehat{H}}_1,{\widehat{H}}_{\mathrm{2nd}}...,{\widehat{H}}_{\mathcal{l}}\right)\hfill & \left(5\right)\hfill \\ =arGmi{n}_{x\in \mathrm{C.}}{\displaystyle {\sum }_{i=1}^{\mathcal{l}}{\Vert y_i-{\widehat{H}}_i{x}_i\Vert }^{\mathrm{2nd}}}\hfill & \left(6\right)\hfill \end{array}$$

ie when decoding it is assumed that ĥ _{i is} the actual channel coefficient.

In summary, in the prior art, the process at the receiver takes place as follows: an estimate of the channel coefficients h _{i is} determined using a known estimation algorithm (for example maximum likelihood estimate). Then there are two options: the estimated value ĥ _i can be used instead of the value h to calculate the following decoding metric: $$x=arGma{x}_{x\in \mathrm{C.}}p\left\{y|x,H_1,H_{\mathrm{2nd}}...,H_{\mathcal{l}}\right\}\left\{y|x,{\widehat{H}}_1,{\widehat{H}}_{\mathrm{2nd}}...,{\widehat{H}}_{\mathcal{l}}\right\}$$

The disadvantages of the prior art are illustrated below using an example of a transmission with a (24, 12) binary Golay linear block code. The transmission takes place via a parallel AWGN channel with ℓ = 2, n _c = 16 and m = 4. The signal-to-noise voltage ratio is denoted by $$\frac{E_S}{N_0}=\frac{1}{\mathrm{2nd}{\sigma }^{\mathrm{2nd}}}$$

Here it is the symbol energy. N ₀ is the one-sided noise power spectral density. The performance of the code is in 1 represented as a frame error rate (FER), ie as the ratio between decoding errors and the number of transmissions. The performance is shown for the case that the channel coefficients (h ₁ , h ₂ ) are completely known (bottom line) and also for channel estimates (ĥ ₁ , ĥ ₂ ) (middle two courses) with m = 4 preamble symbols. The top course represents the performance in a channel estimation using a hard estimate. The deterioration in performance compared to the ideal case is large and reaches approximately 1.3 dB at FEP≈ 10 ^-2 .

The object of the invention is to provide a method for transmitting data over a noisy transmission channel and in particular a decoding method which reduces the disadvantages mentioned.

According to the invention, the object is achieved by the features of claim 1.

• Übertragen durch eine Übertragungsvorrichtung von Daten über einen Übertragungskanal mit unbekannten Kanalkoeffizienten, die durch Rauschen beeinflusst werden,
• Empfangen von Daten durch eine Empfangsvorrichtung und Schätzen der Kanalkoeffizienten unter Verwendung eines Schätzalgorithmus,
• Berechnen einer Dekodiermetrik basierend auf den geschätzten Kanalkoeffizienten.

The method for data transmission according to the invention comprises the following steps:

• Transmitting by a transmission device data over a transmission channel with unknown channel coefficients affected by noise,
• Receiving data by a receiving device and estimating the channel coefficients using an estimation algorithm,
• Calculate a decoding metric based on the estimated channel coefficients.

According to the invention, the decoding metric is modified based on an uncertainty in the channel estimate. By adapting the decoding metric, it is possible to improve the performance of the decoder compared to the prior art.

It is preferred that the estimation algorithm is a maximum likelihood estimate.

• Bit-weises Berechnen von Log-Likelihood-Ratios basierend auf den geschätzten Kanalkoeffizienten,
• Erstellen einer Liste von möglichen Codewörtern, insbesondere unter Verwendung eines List-Decoding-Verfahrens mit niedriger Komplexität und Auswählen der finalen Codeworte aus der Liste.

It is further preferred that the modification step comprises the following steps:

• Bit-by-bit calculation of log likelihood ratios based on the estimated channel coefficients,
• Creation of a list of possible code words, in particular using a list decoding method with low complexity and selection of the final code words from the list.

It is then preferred that the list complexity with a low complexity is an ordered statistics decoding method or successful-cancellation-list decoding.

wobei

• wobei x̂ das Ergebnis des Dekodierens ist,
• L eine Liste der möglichen Codewörter ist und
• ℓ die Anzahl der Koherenzblöcke ist,
• y_i die empfangenen Vektoren sind,
• ĥ_i die geschätzten Kanalkoeffizienten sind,
• x_i das übermittelte Signal ist,
• a und b zwei Designparameter sind.

It is further preferred that the selection of the final code word is based on the following metric: $$\widehat{x}=arGma{x}_{x\in L}{\displaystyle {\sum }_{i=1}^{\mathcal{l}}\mathrm{2nd}\Re \left\{〈y_i,{\widehat{H}}_i,x_i〉\right\}+\frac{1}{a}}{\left|〈y_i,x_i〉\right|}^b$$

in which

• where x̂ is the result of the decoding,
• L is a list of possible code words and
• ℓ is the number of coherence blocks,
• y _{i are} the received vectors,
• ĥ _{i are} the estimated channel coefficients,
• x _{i is} the transmitted signal,
• a and b are two design parameters.

It is further preferred that the design parameter a is the number of symbols in the preamble or is calculated based on the number of symbols in the preamble.

It is further preferred that the design parameter b is a positive number.

It is further preferred that the design parameter a is the number of symbols in the preamble and the design parameter b = 2.

A specific exemplary embodiment of the invention is explained in more detail below:

mit a und b als Designparameter verwendet, um das finale Codewort aus der Liste auszuwählen, d. h. gemäß $$\widehat{x}=argma{x}_{x\in C}{\displaystyle {\sum }_{i=1}^{\mathcal{l}}2\Re \left\{\langle y_i,{\widehat{h}}_i,x_i\rangle \right\}+\frac{1}{a}}{\left|\langle y_i,x_i\rangle \right|}^b.$$

In the context of the method according to the invention, the channel coefficients h _{i are} preferably used, as is known from the prior art, in order to calculate the log likelihood ratios bit by bit. A low-complexity list decoding method is then used to create a list of the possible code words. Then a modified metric $${\displaystyle {\sum }_{i=1}^{\mathcal{l}}\mathrm{2nd}\Re \left\{〈y_i,{\widehat{H}}_i,x_i〉\right\}+\frac{1}{a}}{\left|〈y_i,x_i〉\right|}^b$$

used with a and b as design parameters to select the final code word from the list, ie according to $$\widehat{x}=arGma{x}_{x\in \mathrm{C.}}{\displaystyle {\sum }_{i=1}^{\mathcal{l}}\mathrm{2nd}\Re \left\{〈y_i,{\widehat{H}}_i,x_i〉\right\}+\frac{1}{a}}{\left|〈y_i,x_i〉\right|}^b.$$

The optimal values for a and b for the case under consideration are a = m (number of symbols in the preamble) and b = 2.

The idea is to use a list decoder to make a list of the possible code words to reduce complexity. When trying to calculate the metric for each codeword in the codebook, the complexity is proportional to the total number of codewords in the list. The reduction in the performance of the decoder can be limited if the list size is large enough. The complexity can be further reduced by increasing the number of pilot symbols.

A list decoder is thus used to generate a list of code words whose size is considerably smaller than the size of the codebook, a hard estimate of the channel coefficients, namely ℓ _i for i = 1, ..., ℓ, determining becomes. Then the above metric is calculated only for the code words in the list, ie $$\widehat{x}=arGma{x}_{x\in \mathrm{C.}}{\displaystyle {\sum }_{i=1}^{\mathcal{l}}\mathrm{2nd}\Re \left\{〈y_i,{\widehat{H}}_i,x_i〉\right\}+\frac{1}{a}}{\left|〈y_i,x_i〉\right|}^b.$$

To check the performance of the method according to the invention, a transmission over an AWGN channel with a (24, 12) Golay code was simulated (with a = m and b = 2). The result is also in 1 shown. The embodiments according to the method according to the invention correspond to the middle two courses. The list decoding method used is an ordered statistics decoding method. With FER ≈ 10 ^-2 , the gain compared to the previously known methods is approximately 0.8 dB with a list size of 299 code words. It should be noted that the improvement in performance is not noticeable when the metric is applied to the entire codebook, as this increases the complexity due to the 4096 code words present. The difference to the perfect CSI performance is about 0.4 dB.

Claims (8)

A method of data transmission, the method comprising the steps of: transmitting by a transmission device data over a transmission channel with unknown channel coefficients affected by noise, receiving data by a receiving device and estimating the channel coefficients using an estimation algorithm, calculating a decoding metric based on the estimated channel coefficients, characterized by modifying the decoding metric based on an uncertainty in the channel estimate. Procedure for data transmission according to Claim 1 , wherein the estimation algorithm is a maximum likelihood estimate. Procedure for data transmission according to Claim 1 or 2nd , characterized in that the modification step comprises: bit-wise calculation of log likelihood ratios based on the estimated channel coefficients, creation of a list of possible code words, in particular using a list decoding method with low complexity and selection of the final code words the list. Procedure for data transmission according to Claim 3 , wherein the list decoding method with low complexity is an ordered statistics decoding method or successful-cancellation-list decoding. Procedure for data transmission according to Claim 3 or 4th , where the selection of the final code word is based on the following metric: $$\widehat{x}=arGma{x}_{x\in L}{\displaystyle {\sum }_{i=1}^{\mathcal{l}}\mathrm{2nd}\Re \left\{〈y_i,{\widehat{H}}_i,x_i〉\right\}+\frac{1}{a}}{\left|〈y_i,x_i〉\right|}^b$$

where x̂ is the result of the decoding, L is a list of the possible code words and ℓ is the number of coherence blocks, y _{i are} the received vectors, ĥ _{i are} the estimated channel coefficients, x _{i is} the transmitted signal, a and b are two design parameters are. Procedure for data transmission according to Claim 5 , where the design parameter a is the number of symbols in the preamble or is calculated based on the number of symbols in the preamble. Procedure for data transmission according to Claim 5 or 6 , where the design parameter b is a positive number. Procedure for data transmission according to the Claims 5 to 7 , where the design parameter a is the number of symbols in the preamble and the design parameter b = 2.

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