08-04-2016, 07:55 PM
Hi,
Please I need the matlab codes for this paper :
Low-Complexity Polynomial Channel Estimation in Large-Scale MIMO with Arbitrary Statistics
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channel estimation using the polynomials matlab code
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Hi,
Please I need the matlab codes for this paper :
Low-Complexity Polynomial Channel Estimation in Large-Scale MIMO with Arbitrary Statistics
11-04-2016, 12:21 PM
channel estimation using the polynomials matlab code
Abstract
This article is concerned with the problem of superimposed training (ST)-aided channel estimation for orthogonal frequency division multiplexingmodulated amplify-and-forward relay networks in doubly selective environment. A ‘subblockwise’ linear assumption-based channel model is proposed to represent the mobile-to-mobile time- and frequency-selective channels. We then propose a novel ST strategy that allows the destination node to separately obtain the channel information of the source → relay page link and the relay → destination link, from which the optimal ST signals are derived by minimizing the channel mean-square-error. To enhance the performance of channel estimation, a subblock tracking-based low-complexity decision feedback approach is introduced to iteratively mitigate the unknown data interference. Finally, extensive numerical results are provided to corroborate the proposed studies.
Introduction
Cooperative communication systems have attracted much attention due to their ability to exploit spatial diversity by utilizing relays to assist transmission between a source and a destination node[1–3]. Like any other wireless communications systems, channel state information (CSI) at both the relay nodes and the destination nodes are required to optimize certain criterions. For example, in relay beamforming schemes[4, 5] as well as subcarrier pairing schemes[6, 7], the destination needs both the channel knowledge of source → relay and relay → destination links in order to know the relay’s operation.
To obtain the separate CSI from the source node (S) to the relay node ® and the relay node to the destination node (D), time- and/or frequency-multiplexed pilots are employed in amplify-and-forward(AF) relay networks[8–10]. For orthogonal frequency division multiplexing (OFDM)-modulated AF relay networks, the authors of[11] proposed a two-phase training prototype, where the relay superimposes its own training to the received training signal such that separated channels can be estimated at the destination, from which optimal training as well as optimal power allocation factor between R and S are derived based on Bayesian Cramer-Rao bound.
Previous studies in AF relay systems[8–11] mainly focused on the block-fading or slow-fading scenarios (e.g., the normalized Doppler spread over one OFDM block is less than 0.1). However, for practical broadband relay networks where the source and the relay can all be moving nodes, e.g., mobile terminals in moving cars or high-speed trains. Under such transmission environment, one must assume that the wireless channels of S → R and R → D to be time- and frequency-selective fading. To alleviate the number of unknown channel parameters, doubly selective channels are typically represented by two ways: by using the basis expansion model (BEM)[12–14], which decomposes the channel into a superposition of time-varying orthogonal basis functions (e.g., Fourier bases) weighted by time-invariant coefficients, and by using a blockwise linear model[15], which tracks the channel variation as a linear fashion over specific block periods. Previous contributions on channel estimation involving either BEM or blockwise linear channel models have been reported by the authors of[12, 13, 15–18]. Although such channel modeling methods are generally reliable for a relatively high Doppler frequency, more than 30% transmission efficiency is wasted for transmitting known pilots, thus leading to a reduction in transmission efficiency.
To improve valuable transmission efficiency while without entailing unrealistic assumption or highcomplexity, an alternative approach, referred to as superimposed training (ST), has been studied in[17, 19]. In such schemes, channel estimation can be performed without a loss of rate with bearable data interference since the training signals are arithmetically added onto the unknown data.
Motivated by the advantages of ST, this article presents a novel ST-based doubly selective channel estimation for OFDM-modulated AF relay networks. By modeling the doubly selective channel as a ‘subblockwise’ linear model, separated channel estimation of S → R and R → D is estimated straightforwardly by a two-step approach: First, we adopt a time-domain ‘subblock’ tracking scheme whose aim is to model the time-selective channel within one OFDM block as multiple subblock fading structures such that channel estimation over each subblock can be performed by a linear time-invariant structure. Second, we smooth the initial channel estimates over multiple subblocks of one OFDM block by using polynomial fitting. The optimal ST design criterions for both S and R are derived w.r.t. minimizing the mean square error (MSE) of channel estimation. Furthermore, a subblock tracking-based low-complexity decision feedback (DF) approach is provided to enhance the performance of channel estimation by iteratively mitigating the data interference. Finally, simulation results are provided to corroborate our studies.
1.
ST is adopted for channel estimation, and thus offers higher transmission efficiency in comparison with the existing pilot-assisted schemes [10, 13, 16, 20].
2.
A ‘subblockwise’ linear channel model with polynomial fitting is introduced to facilitate the separated channel estimation of S → R and R → D.
3.
Optimal ST signals at both S and R are optimized w.r.t. channel MSE.
4.
A low-complexity DF process with subblock tracking is provided to iteratively enhance the performance of channel estimation.
The rest of the article is organized as follows. The following section presents the system model of OFDM-modulated AF relay networks with ST strategy. The ST-based channel estimation algorithm and optimal training design are then provided in Section “ST-based channel estimation”. Using the analyzed MSE derived in the same section, we optimize the power ratio between ST and data sequence w.r.t. channel capacity in Section “Channel estimation enhancement”. Section “Simulation results and discussion” reports on some simulation experiments to corroborate the validity of our theoretic analysis, and we conclude the article with conclusion.
Abstract
This article is concerned with the problem of superimposed training (ST)-aided channel estimation for orthogonal frequency division multiplexingmodulated amplify-and-forward relay networks in doubly selective environment. A ‘subblockwise’ linear assumption-based channel model is proposed to represent the mobile-to-mobile time- and frequency-selective channels. We then propose a novel ST strategy that allows the destination node to separately obtain the channel information of the source → relay page link and the relay → destination link, from which the optimal ST signals are derived by minimizing the channel mean-square-error. To enhance the performance of channel estimation, a subblock tracking-based low-complexity decision feedback approach is introduced to iteratively mitigate the unknown data interference. Finally, extensive numerical results are provided to corroborate the proposed studies.
Introduction
Cooperative communication systems have attracted much attention due to their ability to exploit spatial diversity by utilizing relays to assist transmission between a source and a destination node[1–3]. Like any other wireless communications systems, channel state information (CSI) at both the relay nodes and the destination nodes are required to optimize certain criterions. For example, in relay beamforming schemes[4, 5] as well as subcarrier pairing schemes[6, 7], the destination needs both the channel knowledge of source → relay and relay → destination links in order to know the relay’s operation.
To obtain the separate CSI from the source node (S) to the relay node ® and the relay node to the destination node (D), time- and/or frequency-multiplexed pilots are employed in amplify-and-forward(AF) relay networks[8–10]. For orthogonal frequency division multiplexing (OFDM)-modulated AF relay networks, the authors of[11] proposed a two-phase training prototype, where the relay superimposes its own training to the received training signal such that separated channels can be estimated at the destination, from which optimal training as well as optimal power allocation factor between R and S are derived based on Bayesian Cramer-Rao bound.
Previous studies in AF relay systems[8–11] mainly focused on the block-fading or slow-fading scenarios (e.g., the normalized Doppler spread over one OFDM block is less than 0.1). However, for practical broadband relay networks where the source and the relay can all be moving nodes, e.g., mobile terminals in moving cars or high-speed trains. Under such transmission environment, one must assume that the wireless channels of S → R and R → D to be time- and frequency-selective fading. To alleviate the number of unknown channel parameters, doubly selective channels are typically represented by two ways: by using the basis expansion model (BEM)[12–14], which decomposes the channel into a superposition of time-varying orthogonal basis functions (e.g., Fourier bases) weighted by time-invariant coefficients, and by using a blockwise linear model[15], which tracks the channel variation as a linear fashion over specific block periods. Previous contributions on channel estimation involving either BEM or blockwise linear channel models have been reported by the authors of[12, 13, 15–18]. Although such channel modeling methods are generally reliable for a relatively high Doppler frequency, more than 30% transmission efficiency is wasted for transmitting known pilots, thus leading to a reduction in transmission efficiency.
To improve valuable transmission efficiency while without entailing unrealistic assumption or highcomplexity, an alternative approach, referred to as superimposed training (ST), has been studied in[17, 19]. In such schemes, channel estimation can be performed without a loss of rate with bearable data interference since the training signals are arithmetically added onto the unknown data.
Motivated by the advantages of ST, this article presents a novel ST-based doubly selective channel estimation for OFDM-modulated AF relay networks. By modeling the doubly selective channel as a ‘subblockwise’ linear model, separated channel estimation of S → R and R → D is estimated straightforwardly by a two-step approach: First, we adopt a time-domain ‘subblock’ tracking scheme whose aim is to model the time-selective channel within one OFDM block as multiple subblock fading structures such that channel estimation over each subblock can be performed by a linear time-invariant structure. Second, we smooth the initial channel estimates over multiple subblocks of one OFDM block by using polynomial fitting. The optimal ST design criterions for both S and R are derived w.r.t. minimizing the mean square error (MSE) of channel estimation. Furthermore, a subblock tracking-based low-complexity decision feedback (DF) approach is provided to enhance the performance of channel estimation by iteratively mitigating the data interference. Finally, simulation results are provided to corroborate our studies.
1.
ST is adopted for channel estimation, and thus offers higher transmission efficiency in comparison with the existing pilot-assisted schemes [10, 13, 16, 20].
2.
A ‘subblockwise’ linear channel model with polynomial fitting is introduced to facilitate the separated channel estimation of S → R and R → D.
3.
Optimal ST signals at both S and R are optimized w.r.t. channel MSE.
4.
A low-complexity DF process with subblock tracking is provided to iteratively enhance the performance of channel estimation.
The rest of the article is organized as follows. The following section presents the system model of OFDM-modulated AF relay networks with ST strategy. The ST-based channel estimation algorithm and optimal training design are then provided in Section “ST-based channel estimation”. Using the analyzed MSE derived in the same section, we optimize the power ratio between ST and data sequence w.r.t. channel capacity in Section “Channel estimation enhancement”. Section “Simulation results and discussion” reports on some simulation experiments to corroborate the validity of our theoretic analysis, and we conclude the article with conclusion.
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