A circulant based space-time coding for multiple input multiple output system in fading channels

Norouzi, Mandana; Wu, Yuteng; Chahande, Pradnya; Macias, Fernando Alonso; Atkin, G.E.

doi:10.1109/eit.2013.6632674

Cited by 4 publications

(6 citation statements)

References 23 publications

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“…The decision metrics are based on the squared Euclidean distance. ML decoder chooses a set of signals

false({\overset{false^}{y}}_{1}, {\overset{false^}{y}}_{2}, {\overset{false^}{y}}_{3}, {\overset{false^}{y}}_{4} false)

from the signal modulation constellation to minimise the Euclidian distance [5, 10] over all possible values of y j , j = 1, 2, 3, 4. Therefore

{\overset{false^}{y}}_{j} = argmin ()(, ()(, {|h_{j}|}^{2} - 1) {|y_{j}|}^{2} + d^{2} false({\tilde{y}}_{j}, y_{j} false))

where

{\overset{false~}{y}}_{j}^{'} s

; j = 1,2,3,4 are the decision statistics built by combining the received signals with CSI.…”

Section: Embedded Space–time Multiplexing Codes Based On Circulant mentioning

confidence: 99%

“…To evaluate the performance of ESTC code, it is necessary to calculate the PEP of error. PEP is defined; transmitting codeword Y and detecting it as

\overset{false^}{Y}

P_{e} = P false(Y false\to \overset{false^}{Y} false)

[5, 9]. The average PEP of error for a MIMO fading channel is [9, 10]

P_{e} = Q ()(, \sqrt{\frac{E_{normals}}{2 N_{0}} \sum_{t = 1}^{L} | | H_{t} (y_{t} - {\overset{false^}{y}}_{t}) | |^{2}})

where E s is the energy per symbol at each transmit antenna, N 0 /2 is the power of the noise, L is the transmitted data frame length, H t is the channel coefficients; the y t ’s and

{\overset{false^}{y}}_{t}

’s are the components of code words Y and

\overset{false^}{Y}

.…”

Section: Embedded Space–time Multiplexing Codes Based On Circulant mentioning

confidence: 99%

“…The average PEP (11) with respect to the distribution of Γ and based on its moment generating function (MGF) is [9, 10]

\begin{matrix} right leftthickmathspace.5em \\ P_{normale} & = \frac{1}{π} \int_{0}^{π / 2} \int_{0}^{normal∞} E ()(, exp ()(, - \frac{{normalΓ}^{2}}{2 si n^{2} false(θ false)})) f_{normalΓ} false(normalΓ false) d θ \\ = \frac{1}{π} \int_{0}^{π / 2} M_{Γ} ()(, - \frac{1}{2 si n^{2} false(θ false)}) d θ \end{matrix}

where M Γ is the MGF. In Rayleigh‐fading channels, the MGF can be represented as [5, 10]

M_{normalΓ} false(s false) = {()(, det (][, I_{N} - s false(Y - \overset{false^}{Y} false) {(bold-italicY - \hat{Y})}^{H} \frac{E_{s}}{2 N_{0}}))}^{- n_{R}}

where n R is the number of receiver antennas. The MGF for Y can be simplified to [5]

M_{normalΓ} false(s false) = {false\prod}_{i = 1}^{N} [1 - \frac{s E_{normals}}{2 N_{0}} <...>]

…”

Section: Embedded Space–time Multiplexing Codes Based On Circulant mentioning

confidence: 99%

“…In Rayleigh‐fading channels, the MGF can be represented as [5, 10]

M_{normalΓ} false(s false) = {()(, det (][, I_{N} - s false(Y - \overset{false^}{Y} false) {(bold-italicY - \hat{Y})}^{H} \frac{E_{s}}{2 N_{0}}))}^{- n_{R}}

where n R is the number of receiver antennas. The MGF for Y can be simplified to [5]

M_{normalΓ} false(s false) = {false\prod}_{i = 1}^{N} {[1 - \frac{s E_{normals}}{2 N_{0}} {(y_{i} - {\overset{false^}{y}}_{i})}^{2}]}^{- n_{R}}

and by substituting (14) in (12) the PEP of Y is equal to [5]

P_{e} = \frac{1}{π} \int_{0}^{π / 2} {{false\prod}_{i = 1}^{N} (][, 1 + \frac{s E_{s}}{4 N_{0} si n^{2} false(θ false)} {false(y_{i} - {\hat{y}}_{i} false)}^{2})}^{- n_{R}} d θ

…”

Section: Embedded Space–time Multiplexing Codes Based On Circulant mentioning

confidence: 99%

“…In this paper, a new embedded STC (ESTC) design is proposed [5]. The main motivation of the proposed codes is to produce embedded diversity and full rate with less interference.…”

Section: Introductionmentioning

confidence: 99%

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Embedded space–time codes for multiple‐input–multiple‐output systems in Rayleigh fading

Norouzi

Attang

et al. 2015

IET Communications

Self Cite

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“…The decision metrics are based on the squared Euclidean distance. ML decoder chooses a set of signals

false({\overset{false^}{y}}_{1}, {\overset{false^}{y}}_{2}, {\overset{false^}{y}}_{3}, {\overset{false^}{y}}_{4} false)

from the signal modulation constellation to minimise the Euclidian distance [5, 10] over all possible values of y j , j = 1, 2, 3, 4. Therefore

{\overset{false^}{y}}_{j} = argmin ()(, ()(, {|h_{j}|}^{2} - 1) {|y_{j}|}^{2} + d^{2} false({\tilde{y}}_{j}, y_{j} false))

where

{\overset{false~}{y}}_{j}^{'} s

; j = 1,2,3,4 are the decision statistics built by combining the received signals with CSI.…”

Section: Embedded Space–time Multiplexing Codes Based On Circulant mentioning

confidence: 99%

“…To evaluate the performance of ESTC code, it is necessary to calculate the PEP of error. PEP is defined; transmitting codeword Y and detecting it as

\overset{false^}{Y}

P_{e} = P false(Y false\to \overset{false^}{Y} false)

[5, 9]. The average PEP of error for a MIMO fading channel is [9, 10]

P_{e} = Q ()(, \sqrt{\frac{E_{normals}}{2 N_{0}} \sum_{t = 1}^{L} | | H_{t} (y_{t} - {\overset{false^}{y}}_{t}) | |^{2}})

where E s is the energy per symbol at each transmit antenna, N 0 /2 is the power of the noise, L is the transmitted data frame length, H t is the channel coefficients; the y t ’s and

{\overset{false^}{y}}_{t}

’s are the components of code words Y and

\overset{false^}{Y}

.…”

Section: Embedded Space–time Multiplexing Codes Based On Circulant mentioning

confidence: 99%

“…The average PEP (11) with respect to the distribution of Γ and based on its moment generating function (MGF) is [9, 10]

\begin{matrix} right leftthickmathspace.5em \\ P_{normale} & = \frac{1}{π} \int_{0}^{π / 2} \int_{0}^{normal∞} E ()(, exp ()(, - \frac{{normalΓ}^{2}}{2 si n^{2} false(θ false)})) f_{normalΓ} false(normalΓ false) d θ \\ = \frac{1}{π} \int_{0}^{π / 2} M_{Γ} ()(, - \frac{1}{2 si n^{2} false(θ false)}) d θ \end{matrix}

where M Γ is the MGF. In Rayleigh‐fading channels, the MGF can be represented as [5, 10]

M_{normalΓ} false(s false) = {()(, det (][, I_{N} - s false(Y - \overset{false^}{Y} false) {(bold-italicY - \hat{Y})}^{H} \frac{E_{s}}{2 N_{0}}))}^{- n_{R}}

where n R is the number of receiver antennas. The MGF for Y can be simplified to [5]

M_{normalΓ} false(s false) = {false\prod}_{i = 1}^{N} [1 - \frac{s E_{normals}}{2 N_{0}} <...>]

…”

Section: Embedded Space–time Multiplexing Codes Based On Circulant mentioning

confidence: 99%

“…In Rayleigh‐fading channels, the MGF can be represented as [5, 10]

M_{normalΓ} false(s false) = {()(, det (][, I_{N} - s false(Y - \overset{false^}{Y} false) {(bold-italicY - \hat{Y})}^{H} \frac{E_{s}}{2 N_{0}}))}^{- n_{R}}

where n R is the number of receiver antennas. The MGF for Y can be simplified to [5]

M_{normalΓ} false(s false) = {false\prod}_{i = 1}^{N} {[1 - \frac{s E_{normals}}{2 N_{0}} {(y_{i} - {\overset{false^}{y}}_{i})}^{2}]}^{- n_{R}}

and by substituting (14) in (12) the PEP of Y is equal to [5]

P_{e} = \frac{1}{π} \int_{0}^{π / 2} {{false\prod}_{i = 1}^{N} (][, 1 + \frac{s E_{s}}{4 N_{0} si n^{2} false(θ false)} {false(y_{i} - {\hat{y}}_{i} false)}^{2})}^{- n_{R}} d θ

…”

Section: Embedded Space–time Multiplexing Codes Based On Circulant mentioning

confidence: 99%

“…In this paper, a new embedded STC (ESTC) design is proposed [5]. The main motivation of the proposed codes is to produce embedded diversity and full rate with less interference.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations