# A Deep Learning-Assisted Cooperative Diversity Method under Channel Aging

TL;DR: A deep learning-based cooperative diversity method coined predictive relay selection (PRS) that chooses a single relay with the largest predicted CSI, which can alleviate the effect of channel aging while avoiding MTO and MCFO.

Abstract: Single-relay selection is a simple but efﬁcient scheme for cooperative diversity among multiple user devices. However, the wrong selection of the best relay due to aged channel state information (CSI) remarkably degrades its performance, overwhelming this cooperative gain. Multi-relay selection is robust against channel aging but multiple timing offset (MTO) and multiple carrier frequency offset (MCFO) among spatially-distributed relays hinder its implementation in practical systems. In this paper, therefore, we propose a deep learning-based cooperative diversity method coined predictive relay selection (PRS) that chooses a single relay with the largest predicted CSI, which can alleviate the effect of channel aging while avoiding MTO and MCFO. Performance is evaluated analytically and numerically, revealing that PRS clearly outperforms the existing schemes with a negligible complexity burden.

## Summary (3 min read)

### Introduction

- In contrast, a single-relay selection approach called opportunistic relay selection (ORS) has been extensively recognized as a simple but efficient way to achieve cooperative diversity [6].
- Aged CSI substantially deteriorates the performance of ORS [7]–[9].
- By far, to the best knowledge of the authors, OSTC can achieve the best result under channel aging, but its gap to the optimal performance is still large, which motivates the work in this paper.
- Section III and IV present the proposed scheme and analyze its outage probability, respectively.

### A. Model of Cooperative Networks

- Consider a two-hop decode-and-forward (DF) cooperative network where a source s communicates with a destination d with the help of K relays, neglecting the direct link due to lineof-sight blockage.
- Without loss of generality, time-division multiplexing is applied for analysis hereinafter and therefore the signal transmission is organized into two phases.
- In comparison, the proposed PRS scheme replaces the aged CSI with the predicted CSI ȟ, and determines k̇ in terms of k̇ = argmaxk∈DS γ̌k,d, where γ̌k,d=|ȟk,d| 2Pk/σ 2 n.
- In the first phase, the source broadcasts a pair of symbols (x1, x2) to all relays on two consecutive symbol durations.

### B. Model of Aged CSI

- From a practical point of view, the CSI ĥ used to select relay(s) may remarkably differ from the actual CSI h at the instant of using the selected relay(s) to forward regenerated signals, leading to performance deterioration.
- Under the assumption of a Jakes’ model, the correlation coefficient takes the value ρo = J0(2πfdτ), where fd is the maximal Doppler frequency, τ stands for the delay between the outdated and actual CSI, and J0(·) denotes the zeroth order Bessel function of the first kind.

### C. Model of Predicted CSI

- To train a deep learning (DL) predictor, the applied objective is to generate predicted CSI ȟ that approximates to the actual CSI (zero-mean complex Gaussian random variable) as close as possible.
- Hence, the authors can assume that ȟ also follows zeromean complex Gaussian distribution, i.e., ȟ∼CN (0, σ2 ȟ ).
- Like (2), the correlation coefficient between ȟ and h can be obtained.

### A. DL-based Channel Predictor

- Unlike feed-forward neural networks, recurrent neural networks (RNNs) can memorize historical information in its internal state, exhibiting great power in time-series prediction.
- But back-propagated error signals in RNN tend to infinity (gradient exploding), resulting in oscillating weights, or apt to zero (gradient vanishing) that implies a prohibitively-long training time.
- Each LSTM memory cell contains three gates: an input gate protecting the memory contents from perturbation by irrelevant interference, a forget gate to filter out useless memory, and an output gate that controls the extent to which the memory information applied to generate an output activation.
- At time t, the instantaneous CSI h[t] is acquired at the receiver through estimating a pilot symbol.
- Along with the recurrent unit from the previous time step, d (2) t is generated and then forwarded to the second hidden layer.

### B. Computational Complexity

- The computational complexity brought by deep learning is a general concern.
- Here, let’s assess the predictor’s complexity through calculating the number of complex multiplications.
- The complexity per time step in the training phase is measured by O(NDL).
- During the predicting phase, each weight requires one complex-valued multiplication, amounting to the complexity of O(NDL) per prediction.

### C. Predictive Relay Selection

- The implementation of cooperative relaying schemes can be mainly divided into two categories: distributed [6] and centralized.
- By introducing channel prediction, the CSI got at the current frame is applied to generate predicted CSI that will be used at the next frame, such a prediction horizon provides a new degree of freedom to design a relaying protocol.
- The channel gain hs,k[t] is acquired at relay k by estimating RTS and is used for detecting the data symbols.
- This operation starts once the arrival of CTS, parallel with step 2.
- 6) Once receive the best relay’s packet of its presence, other relays terminate their timers and keep silent.

### IV. OUTAGE PROBABILITY ANALYSIS

- In information theory, outage is defined as the event that instantaneous channel capacity falls below a target rate R, where reliable communication cannot be realized whatever coding used.
- In the case that no relay can decode the source’s signal, the relaying will definitely fail, i.e., P(R||DS| = 0) = 1 (17) b) L=1: Only a unique relay successfully decodes the signal, it becomes k̇ directly and a process of relay selection is skipped.
- Now, the closed-form expression for the first term in (14) is available.

### V. NUMERICAL RESULTS

- The authors make use of Monte-Carlo simulations to validate the correctness of analytical analyses and evaluate performance.
- As the benchmark, the curve of ORS when the knowledge of CSI is prefect, i.e., ρo=1, is plotted as the optimal performance that achieves the diversity of d=4 and its outage probability decays at a rate of 1/γ̄4 in high SNR.
- Its gap to the optimal performance is still large, amounting to around 3dB at the level of 10−2.
- Last but not least, the complexity of the predictor is investigated.
- In comparison with the capability of current digital signal processor, e.g., TI 66AK2x, which provides more than 104 Million Instructions executed Per Second (MIPS), the required computing resource is negligible (< 0.001).

### VI. CONCLUSIONS

- The authors proposed a deep learning-based relaying method to achieve cooperative diversity.
- Taking advantage of time-series prediction of deep recurrent neural network, a channel predictor was built as a new degree of freedom for realizing predictive relay selection.
- The proposed scheme opportunistically selects a single relay with the largest predicted CSI to retransmit, which alleviates the effect of aged CSI while avoiding the problem of multi-relay synchronization.
- Also, computational complexity was analyzed, revealing that its required computing resource is negligible in comparison with off-the-shelf hardware.
- From the perspective of both performance and complexity, it is a good candidate for practical implementation.

Did you find this useful? Give us your feedback

...read more

##### References

49,735 citations

4,347 citations

3,119 citations

412 citations

250 citations