GA Based Estimation of Sparse MIMO Channels with Superimposed Training

Abstract

LTE-Advanced. Massive MIMO, which employs a large number of antennas at the base station (BS), is a prospective technology for emerging cellular networks due to its magnificent gains in spectral and energy efficiency as compared to conventional MIMO systems [3], [4]. However, the acquisition of an accurate estimate of the channel state information (CSI) is of vital importance for harvesting the substantial advantages of Massive MIMO.
Various empirical studies in the existing literature have established the fact that certain propagation environments lead to a channel impulse response (CIR) that exhibits a sparse structure in spatial, angular or delay domain. A sparse CIR is characterized by few dominant channel taps relative to the length of the channel. A sparse structured CIR is observed in communication environments such as aeronautical communications [5], underwater acoustic communications [6], and wideband high frequency communications [7]. It is established in [8] that MIMO communication channels tend to exhibit a joint sparsity and possess a common support. It is demonstrated in [9] that mmWave based communication systems also tend to have a sparse structured CIR. A prior available knowledge about the sparse nature of a communications channel can be effectively utilized for obtaining the estimate of CSI.
In the existing literature, several blind, semiblind and training based channel estimation techniques have been proposed for MIMO communication systemssee e.g., [10]- [12]. However, recently channel estimation techniques which are based on the approach of superimposed training (SiT) have gained significant attention due to their certain advantages over the counterparts [13]- [16]. SiT based channel estimation techniques achieve enhanced spectral efficiency by evading the need for dedicated time/frequency slots allocation to the training sequence. In SiT based channel estimation techniques, a low power and periodic training sequence is mathematically added over the information sequence at the transmitter side. The periodic structure of the training sequence is exploited by the receiver to estimate CSI. A user sum-rate based comparison of time multiplexed and superimposed arrangement of pilots is conducted in a multi-cell scenario in [17], where it is demonstrated that SiT based pilot arrangement schemes are superior with inherent capability of mitigating pilot contamination in large-scale MIMO systems.
Genetic algorithms (GA) based optimization methods use stochastic search algorithms to efficiently reach an optimized solution which is in a big solution space. GAs model nature's biological evolution, crossover and mutation processes to achieve a complex optimization objective function. When sufficient number of chromosomes are used, the GA has the advantage of not getting stuck in local minimas. GA based optimization algorithms are used in a variety of fields including channel estimation in wireless communications [20]. This paper utilises GA for channel estimation using SiT technique for a MIMO sparse multipath channels, which, to our knowledge, has not been done before. The main contributions of this paper are stated as under: 1. An SiT based estimation technique is proposed for the frequency-selective sparse MIMO channels. 2. GAs are exploited for the purpose of channel estimation and the impact of variations in population size of GAs on the performance of channel estimation is studied.
3. Impact of variations in channels' sparsity level and training to information power ratio on normalized channel mean square error (NCMSE) is thoroughly studied. 4. A comprehensive comparison of the proposed technique with the existing least squares (LS) and linear minimum mean square error (LMMSE) estimation techniques is conducted. The rest of the paper is organized as follows: the multiuser MIMO communication system model is presented in Section II. The details of the proposed channel estimation technique, for sparse MIMO channels that utilizes GA, are presented in Section III. Section IV explains the LMMSE equalizer incorporated in the system model. Section V describes the performance analysis using the performed simulations. Section VI presents the conclusion of the paper.

II. SYSTEM MODEL
The details of the proposed system model are illustrated in Fig. 1 such that N denotes the mobile user terminals and M denotes the elements in receiving antenna array. The signals as transmitted by M users travels through the sparse MIMO channel. L denotes the number of resolvable multipaths in such channel, out of which Q are non-zero paths. The Section III details the channel estimator (CE) block that uses the first order statistics [13], as well as GA based superimposed training sequence estimation. Once an estimate of the CIR is obtained, the training sequence's contribution is removed from the resulting signal using training effect remover (TER) and then it is fed to equalizer. Subsequently, the transmitted information sequence is estimated using LMMSE equalizer. The transmitted information sequence for n th user, denoted by n b , is zero mean and mutually independent for each of the n users. The vector form of the information sequence is where l H is the channel matrix for l th delay tap with dimensions MN  11 12 1 x After temporal sampling of the signal, vector representation is given by can be represented as The convolution matrix H of MIMO channels can be represented as

III. PROPOSED GA BASED METHOD FOR SPARSE MIMO CHANNEL ESTIMATION
An overview of received signals' first-order statistics, exploited in the proposed work, is discussed in Section III-A and Section III-B. The conventional least squares based channel estimation is discussed in Section III-C while our proposed GA based channel estimation is detailed in the Section III-D.

A. Superimposed Training Sequence Design
where n C is given as follows  (22) In case of noise with non-zero mean, the channel can be calculated using the condition 1 PL , and removing

D. Proposed GA Based Channel Estimation
GAs are evolutionary search based techniques that have been frequently utilized to solve channel equalization and estimation problems in challenging wireless environments. This section presents a novel GA assisted algorithm that has been used for sparse multipath MIMO channels' estimation. It uses the first order statistics calculated from the received signal as well as the a priori information about channel's sparsity. The estimation error ξ of the cost function is reduced using the compensation factor . GAs use stochastic search to find the near optimal solution in the entire solution space while at the same time minimizing the objective function given as:

IV. LMMSE EQUALIZER WITH THE PROPOSED TECHNIQUE
The receiver knows the superimposed training sequence transmitted by each mobile user. At the receiver, CIR is convolved with the superimposed training sequence. So, before estimation of information sequence, the contamination caused by training sequence in the information sequence needs to be normalized. This elimination of training sequences' effect at each receiver element is performed by training sequence effect remover block (Fig. 1), which can be expressed as follows       where l nm h denotes the channel's l th tap, as seen from n th mobile user towards the receiver's m th antenna element. The GA based channel estimation technique has been detailed in the previous section. After removing training sequence's effect, the resulting signal is then provided to the equalizer 78 ELEKTRONIKA IR ELEKTROTECHNIKA, ISSN 1392-1215, VOL. 24, NO. 6,2018 for computing the estimate of information sequence. Let n w be the optimal equalizer weight corresponding to the m th antenna element, and is estimated as [22]: subtraction        The estimate of additive noise variance 2 n  can be obtained as given in [13]. Finally, the transmitted sequence of n th transmitter is calculated as      , and are generated independently for each user (transmitter) and for each Monte Carlo run. At each receive antennas element, the signal-to-noise ratio (SNR) is specified as the ratio of power of received signal to the power of AWGN; where it is assumed that received SNR at each antenna is equal. The impact of population size on the MSE and BER performance of proposed method can be seen in Fig. 2(a) and Fig. 2(b), respectively. It is evident that increasing the population size results in an improvement in both MSE and BER performance; however, the rate of increase in marginal for population size higher than 4 L . The effect of channels' sparsity level on MSE performance is plotted in Fig. 3(a). The performance of proposed method is observed to improve with an increase in channels' sparsity. The impact of increase in training to information power ratio in MSE performance of the proposed method is plotted in Fig. 3(b). An increase in power of the training sequence compared to the information sequence results in an improvement in the accuracy of channel estimate calculated at the receiver. However, relative decrease in the power of information sequence beyond 22 / 0.6 cb   leads to a decrease in BER performance of the system. The usefulness of proposed method is demonstrated through the comparison of the proposed SiT-GA method with notable channel estimation methods named as SiT-LS and SiT-LMMSE. The NCMSE and BER are the performance metrics used for this comparison in Fig. 4. For an SNR of 10dB and channels' sparsity level of / 6 /14 QL  , an improvement of 7.93 dB and 5 dB in MSE performance by the proposed SiT-GA method compared to SiT-LS and SiT-LMMSE, respectively, as can be observed in Fig. 4(a). For a BER of 1 10  and channels' sparsity level of / 6 /14 QL  , the proposed method provides an approximate SNR gain of 3 dB and 2 dB as compared to It is also evident that the gain offered by the proposed method in MSE and BER performance, further increases for high degree of channel sparsity. It is thus established that the proposed method promises an improved quality of service (QoS) by offering significant improvement in accuracy of channels' estimate and retrieved information.

VI. CONCLUSIONS
A GA based method for estimation of sparse MIMO channels using superimposed training sequence has been proposed. It has been established that for a channels' sparsity level of Q/L = 6/14 and training-to-information power ratio of 22 / 0.25 cb   , the proposed channel estimation method outperforms the existing SiT-LS and SiT-LMMSE techniques with a gain of about 7.93 dB and 5 dB in NCMSE at an SNR of 10 dB. Similarly, for a BER of 10 -1 , a performance gain of 3 dB and 2 dB in SNR has been observed over the existing SiT-LS and SiT-LMMSE techniques, respectively. Moreover, it has been also established that the increased sparsity level of the MIMO channels leads to a further improvement in NCMSE of the proposed technique. Furthermore, it is observed that increasing the training-to-information power ratio results in an improvement in the channel estimate. However, allocating more power to the training sequence causes reduction in SINR at the receiver. Therefore, an optimal value of the training power needs to be chosen.