Fingerprint Based Codebook for RIS Passive Beamforming Training

Abstract

In this article, we propose a new RIS passive beamforming scheme in two main stages. First, a fingerprint-based codebook (FP-CB) design phase occurs, where the area of interest is divided into a number of points and the optimal reflection patterns (RPs) corresponding to these points are determined and stored alongside the coordinates of these points in the codebook database (DB). Second, there is the searching and learning online stage, in which, based on the receiver (RX) and FP points’ locations, the system determines a group of candidate RPs. Then, it just searches through them instead of examining the entire CB RPs to select the best RP that can be used for configuring RIS during the data transmission period. The proposed mechanism proves that designing a positioning information-based CB can highly reduce the system overhead computational complexity and enhance performance comparable to the conventional CB-based scheme and the full channel estimation (CE)-based scheme. For example, selecting only 10 candidate RPs from the FP-CB can obtain a better effective achievable rate than a CE-based scheme in a rapidly changing channel.

1. Introduction

Networks such as 5G and beyond have become a hot topic in both academia and industry to enable and boost new services such as holographic communication, autonomous driving, tactile internet, and so on [1,2,3]. These applications have several requirements, e.g., massive traffic capacity of up to 10 Gbps/m², a low latency time of 0.1 ms, and low power consumption. Hence, new emerging technologies appear to be key players in providing these needs, e.g., millimeter wave (mmWave) and terahertz (THz). However, the received signal using these bands is highly attenuated and rapidly fluctuates due to the channel’s large and small-scale fading [4,5], respectively. Moreover, they are highly reliable and can be blocked by static and dynamic obstacles such as buildings, furniture, and human bodies. Thus, a new promising technology called reconfigurable intelligent surface (RIS) has been developed to overcome the aforementioned issues [6,7,8]. RIS is a programmable planar surface containing a number of passive elements that can redirect the incident signal based on the amplitudes and phase shifts of their elements. Hence, the RIS can be used to provide alternative paths to the transmitted signal and establish constructive signal superposition to guarantee a more consistent communication channel. Thus, it assists in extending the coverage of the network and enhancing its performance.

For efficient usage of RIS in wireless communication networks, the amplitudes and phase shifts of the RIS elements should be determined and configured to redirect the transmitter (TX) signal into the receiver (RX) direction in a process called passive beamforming (PBF) [6,9]. This procedure is a challenge because of the passive nature of the RIS, as it cannot exchange control signals with the TXs or the RXs, and as a result, the PBF vector determination process is performed at the base station side owing to its abundant resources. This PBF process is categorized into two major classes: channel estimation (CE)-based methods [10] and codebook (CB)-based solutions [11,12]. CE-based schemes need pilot feedback to fully estimate the channels of the TX–RX and TX–RIS–RX links. Then an optimization process, e.g., alternating optimization (AO), should be performed to adjust the RIS elements. The overhead of CE and AO-based schemes significantly delays TX–RX communication and wastes system resources, especially with a high number of RIS elements. Because the CE phase should be performed at the beginning of each link establishment period with overhead, $\mathcal{O}\left(N\right)$, where $N$ refers to the number of RIS elements. Moreover, designing active–passive beamforming (A–PBF) in an optimal and joint manner causes high time consumption and complicated procedures, where the AO method needs $\mathcal{O}\left(N_i{N}^{4.5}\right)$ as a computational complexity, where $N_i$ refers to the number of required iterations to achieve convergence.

Recently, CB-based solutions have been proposed to address these issues and guarantee fair performance. These schemes are divided into three stages: codebook generation, searching, and learning phases. First, the CB design stage aims to construct a suitable CB containing several codewords, i.e., reflection patterns (RPs). In the second stage, each RP is examined and evaluated. Then, in the learning stage, the system selects the optimal codeword for configuring the RIS elements during the data transmission period. The CB-based PBF (CB-PBF) schemes estimate only the end-to-end composite channel and do not need to perform the joint A–PBF optimization process. However, online searching through the CB RPs is required; hence, time slots relevant to CB size shall be used, causing a communication delay. Furthermore, designing an effective and descriptive CB is not an easy procedure. The authors in [11] discussed the stages of CB-based schemes and evaluated the performance of a random CB-based algorithm. However, a random CB cannot cover the entire space and obtain the required performance. In [12], CBs were designed in TX, RIS, and RXs, and then a multi-lobe beamforming (BF) training algorithm was proposed to reduce the needed time for the A–PBF process. However, this scheme suffers an outage if the first layer beam or following beams miss the TX–RIS–RX link. Moreover, both schemes still need high overhead, especially when considering large-sized or multi-layer CBs, respectively. Hence, a more efficient CB design that covers the area of interest is mandatory. Furthermore, the time consumption for searching shall be reduced based on intelligent principles.

Inspired by the availability of positioning information (PI) beyond 5G networks [13,14,15], we propose a new fingerprint-based CB (FP-CB) for the PBF process, where this CB is designed considering the target network environment. Then, depending on the estimated RX location information, the system selects the codeword that can be sub optimally used for configuring the RIS. To the best of our knowledge, passive beamforming based on PI is still an open direction for research to reduce system overhead and enhance its performance. In the proposed fingerprint-based PBF (FP-PBF) scheme, first offline, we divide the area of interest into a number of points, and using the CE and AO-based schemes, an optimal RP corresponding to each point is determined. Subsequently, the FP points’ locations and selected RP pairs are stored in a database to be further used. Second, in the online phase, when a new RX requests to connect with the TX, the system estimates the RX’s location. Then, it calculates the Euclidean distances between the RX and the FP-CB points to select a group of RPs as candidate codewords to handle the localization error. Thereafter, by searching these elected RPs, the system can select the best RP that can provide the RX with the maximum received power to be used in the data transmission period. The proposed PBF scheme reduces the overhead and time consumption in the beam training step by searching within a few RPs instead of the entire codebook. Moreover, it can provide the network with a higher rate compared to the random-based CB, CE, and AO schemes, particularly in rapidly changing channels, even if the RX location estimation has a high error. The novelty of the proposed scheme is that its CB is built based on the environment; hence, it describes it. Moreover, the search algorithm is performed using PI to reduce the required overhead.

The paper structure is as follows: Section 2 presents the system model of the RIS-aided communication system, while a brief discussion about codebook-based schemes is given in Section 3. Then, Section 4 illustrates the procedure of the proposed FP-PBF scheme. Meanwhile, the performance evaluation and the conclusion are presented in Section 5 and Section 6, respectively.

2. System Model

The RIS-aided wireless communication system model is presented in Figure 1. The TX contains M-element antennas, while the RX has a single antenna. Meanwhile, the RIS, which is used to reflect the TX incident signal to the RX, consists of N passive elements. In our study, we used RIS to overcome direct link blockage and extend network coverage. Consequently, the received signal at the RX, $y_r$, will contain the signal of the LOS TX–RX link and the reflected TX–RIS–RX link. This $y_r$ can be presented as:

$$y_r=\left({\mathit{G}}_{\mathbf{2}}\mathsf{\Theta }{\mathit{G}}_{\mathbf{1}}+{\mathit{H}}_{\mathit{o}}\right)\mathit{V}{x}_t+n,$$

(1)

where ${\mathit{H}}_{\mathit{o}}\in {\mathbb{C}}^{1\times M}$ is the channel matrix between the TX and RX, ${\mathit{G}}_{\mathrm{1}}\in {\mathbb{C}}^{N\times M}$ is the channel from the TX to the RIS, while ${\mathit{G}}_{\mathbf{2}}\in {\mathbb{C}}^{1\times N}$ is the channel from the RIS to the RX. Moreover, the RIS diagonal phase shift matrix is expressed by $\mathsf{\Theta }=diag\left\{\mathit{\theta }\right\}$, where $\mathit{\theta }={\left[{\theta }_1,{\theta }_2,\dots ,{\theta }_N\right]}^T$ is the reflecting passive beamforming vector at the RIS and ${\theta }_n=\gamma e^{j{\varphi }_n}$. Here, the ${\varphi }_n\in \left[\left.\mathrm{0,2}\pi \right)\right.$ is the value of the RIS element $n$ phase shift, and $\gamma \in \left[\mathrm{0,1}\right]$ is the amplitude of the reflection coefficient. Moreover, $\mathit{V}\in {\mathbb{C}}^{M\times 1}$ denotes the active TX beamforming vector, $x_t$ is the transmitted symbol by the TX, and $n~\mathcal{C}\mathcal{N}\left(0,{\sigma }^2\right)$ refers to the received additive white Gaussian noise at the receiver, where ${\sigma }^2$ is the noise power. For the efficient performance of the RIS aided beyond the 5G network, the system should design the beamforming vectors for both the TX and RIS, i.e., $\mathit{V}$ and $\mathit{\theta }$, respectively. As an advantage of CB-based solutions, the process of A–PBF can be separated to reduce system complexity [11]. Moreover, because of the fixed TX and RIS positions, the active beamforming vector can be designed once using any convenient BF method in the literature [16]. Hence, in this work, we focus on obtaining the PBF vector $\mathit{\theta }$, which is still under study by researchers in the field.

3. Codebook-Based Solutions

In codebook-based solutions, the passive beamforming schemes are performed in three necessary phases. Firstly, the system designs a codebook of RPs, which is a subset of the entire universal space, e.g., the random RPs codebook and the sum distance maximization codebook (SDM-CB). Second, the system examines and evaluates all RPs. In this stage, every RX sends a feedback signal containing information about its received signal to the TX, which estimates the end-to-end composite channel. Then, the system performs the ABF vector optimization process and evaluates the corresponding objective function (OF). Thirdly, a learning phase is performed to select the optimal RP based on a predefined target metric. For example, the rote learning method stores the observations corresponding to each RP, and the one that maximizes the target metric is utilized to configure the RIS in the data transmission period.

The codebook design phase is a fundamental step because an appropriate CB can guarantee a higher rate with lower system overhead. The original CB is the universal solution set, which contains all possible configuration patterns; however, this CB is very large, especially with a high number of RIS elements. Moreover, it is highly complicated and time-consuming to search within this CB. Hence, codebook generation methods are used to select $Q$ codewords from the universal space, and then the PBF scheme searches these RPs to select the best one for RIS configuration. Hence, the system-required overhead when adapting CB-based schemes is $\mathcal{O}\left(Q\right)$, while the computational complexity in the single-user case is $O\left(QM\right)$. In the literature, different CB generation methods are suggested. Firstly, random CB generation was proposed in [6], where random values of the RIS elements’ phase shifts are chosen without any further enhancement. Figure 2a shows an example of random CB with $Q=6$ and $N=1$. The random CB cannot efficiently cover the search space or use the limited allocated training period. Thus, a sum distance maximization CB (SDM-CB) was suggested in [17] to overcome these issues. The SDM-CB generation method is a heuristic mechanism based on maximizing the summation of the Euclidean distances between all RP pairs. However, it obtains a moderate gain comparable to random CB because it cannot examine all available RPs until convergence. Figure 2b shows an example of SDM-CB with $Q=6$ and $N=1$. It is still uncertain whether these CBs can cover the target area and achieve suboptimal performance after adapting probable learning schemes. Furthermore, searching through a large CB is a time- and resource-wasting process.

4. Proposed Fingerprint-Based PBF Scheme

This section presents the proposed PBF scheme using the FP-based CB. Similar to other CB-based solutions, this scheme is performed in three main stages: first, designing the CB; here we design our codebook based on fingerprint points. Then, the system performs a searching stage through a specific group of selected RPs, i.e., configuring RIS elements only using these RPs. After that, the scheme selects the best codeword for the RIS to obtain the desired performance using the rote learning method due to its simplicity.

To design the fingerprint-based codebook, $\mathit{W}$, the interested area is divided into P points, as shown in Figure 3. The number of points denotes the total number of the designed CB codewords. The space between the points is determined according to the acceptable CB size and complexity. Here, we assume a 3 m horizontal and vertical space, $d_s$, between each point, so the number of points is 200 when considering a network coverage area of $30\times 60$ m². Then, in an offline phase, the beamforming vector corresponding to each point, i.e., the reflection pattern, is determined once using channel estimation and the PBF optimization scheme that was proposed in [18] or any other preferable CE-based scheme. After that, the system stores the x–y coordinates of the P points with their current optimal RPs that are selected for these points in the FP codebook, $\mathit{W}$, as presented in

Table 1. FP codebook.

Point ID	$\mathbf{1}$	$\mathbf{2}$	$\mathbf{3}$	.	.	$\mathit{P}\mathit{-}\mathbf{1}$	$\mathit{P}$
$\mathbf{x} \mathbf{coordinate}\mathbf{,} x_p$	1.5	1.5	1.5	.	.	28.5	28.5
y coordinate,$y_p$	1.5	4.5	7.5	.	.	55.5	58.5
PBF vector	${\mathit{\theta }}_{\mathbf{1}}$	${\mathit{\theta }}_{\mathbf{2}}$	${\mathit{\theta }}_{\mathbf{3}}$			${\mathit{\theta }}_{\mathit{P}\mathit{-}\mathbf{1}}$	${\mathit{\theta }}_{\mathit{P}}$

. These RPs are the optimal ones only in certain channel conditions, i.e., when the system determines them, and for sure, with channel changes, they will not remain optimal. However, they can present possible optimal or sub-optimal RPs in future online stages. Moreover, they are more descriptive than randomly generated RPs.

In the online phase, when a new RX requests to connect to the TX, the system estimates the RX position, $\left(x^{\prime },y^{\prime },z^{\prime }\right)$. Then, using Table 1, the Euclidean distance, $d_p$, between the estimated RX location and each pth FP point is calculated as:

$$d_P=\sqrt{{\left(x^{\prime }-x_p\right)}^2+{\left(y^{\prime }-y_p\right)}^2+{\left(z^{\prime }-z_p\right)}^2}$$

(2)

Here, we assume $z^{\prime }$ and $z_p$ are constant at the RX plane, i.e., $z^{\prime }=z_p=1\mathrm{m}$. By sorting the distances, the nearest $C$ points can be determined. Then, the corresponding $C$ RPs to these points are chosen as the candidate codewords for the searching stage. Because the estimated location comes with an error due to several reasons [16], we consider using these $C$ candidate RPs instead of using the nearest RP, thus obtaining better performance, as will be discussed in the results section, where this $C$ parameter is affected by the localization accuracy. After defining the $C$ candidate RPs, the system examines these RPs, and the RX sends uplink feedback corresponding to each RP. Therefore, the learning stage selects the RP that can maximize the searching OF, where we assume maximizing the RX received power, $y_r$, as OF. Algorithm 1 summarizes this scheme. Using our proposed scheme for the PBF process, the system overhead will be $\mathcal{O}\left(C\right)$, while the computational complexity will be reduced to $O\left(C\mathrm{M}\right)$.

5. Performance Evaluation

In this section, we evaluate the performance of the proposed fingerprint-based passive beamforming scheme. First, we compare its achievable rate, in bits/s/Hz (bps/Hz), that can be provided to the RX with the benchmarks’ schemes: CE-based PBF, random configuration PBF, and random CB-PBF schemes. Using (1), the achievable rate can be expressed as:

$$R={\log }_2\left(1+\frac{{\left|\left({\mathit{G}}_2\mathsf{\Theta }{\mathit{G}}_{\mathbf{1}}+{\mathit{H}}_{\mathit{o}}\right)\mathit{V}\right|}^2}{{\mathsf{\sigma }}_n^2}\right)$$

(3)

where ${\mathsf{\sigma }}_n^2$ donates the average noise power. We consider the CE and AO schemes because they can provide optimal performance, and our FP-CB is built using them, while the random CB-PBF scheme is the conventional CB-PBF method.

For localization accuracy, we consider that the positioning service can estimate RX location with an error following a normal distribution that has a 2.5-m standard deviation. This accuracy can be easily obtained using GPS or Wi-Fi services. Second, we investigate the impact of localization accuracy on our scheme, where varied accuracies are assumed. Then, we study the impact of time-variant channels on the schemes’ performance. Furthermore, this work assumes RIS assists a multi-input, single-output system where the same channel parameters as [18] are considered. Furthermore, the target area is shown in Figure 3, where the fingerprint points are uniformly distributed. Moreover, when a new RX enters the network, its position can be anywhere in the area, following a uniform distribution. Around 100,000 Monte Carlo simulations are considered, and other simulation parameters are summarized in

Table 2. Simulation Parameters.

Parameter	Value
TX signal power	0.001 Watt
TX location	($\mathbf{30}$, $\mathbf{30}$, $\mathbf{50}$)
RIS location	($\mathbf{0}$, $\mathbf{30}$, $\mathbf{50}$)
RXs height	$\mathbf{1}$ m
Number of TX/RIS/RX antennas	16/16/1
Noise power spectrum density	−160 dBm/Hz
System bandwidth	10 MHz

.

Algorithm 1: The proposed FP-PBF scheme.

Inputs$: \mathrm{FP} \mathrm{codebook} \mathit{W}$$\mathrm{with} P$$\mathrm{RPs}, \mathrm{and} \mathrm{the} \mathrm{number} \mathrm{of} \mathrm{candidates} \mathrm{RPs}, C$. for each new RX do  Calculate$\mathrm{the} \mathrm{RX} \mathrm{estimated} \mathrm{location}, \left(x^{\prime },y^{\prime },z^{\prime }\right)$  $\mathbf{Calculate}, d_P$ , for each FP point p, using (2)  Determine$\mathrm{the} C$ nearest points.  Configure$\mathrm{RIS} \mathrm{elements} \mathrm{using} \mathrm{the} \mathrm{candidate} C$ RPs.  Calculate and memorize OF for each cth RP.  $\mathbf{Find} C^{*}=arg\mathit{max}{y}_r$  $\mathit{\theta }=\mathit{W}\left[C^{*}\right]$ end for     Output$: \mathrm{The} \mathrm{passive} \mathrm{BF} \mathrm{vector} \mathit{\theta }$.

Figure 4 shows the achievable rate obtained using the proposed FP-PBF scheme, which is comparable to other PBF schemes. The rates of CE-PBF and random configuration methods are the upper and lower benchmarks. Any increase in the random CB size or the number of candidate RPs for searching in our proposed FP-CB, $C$, enhances the achievable rate because a wider coverage of space can be guaranteed. However, that will also increase the required overhead. The proposed scheme outperforms the random CB-based scheme even if the same number of RPs are used. For example, using 7 RPs, the FP-PBF method obtains an achievable rate of 11 bps/Hz, which is a 23% increase over the random CB-based scheme’s performance. Moreover, at a certain number of RPs, the achievable rate of the proposed scheme nearly saturates using 10 RPs; it achieves 11.07 bps/Hz and obtains near performance to the CE-based method. Moreover, lower complexity and a shorter time can be guaranteed using the proposed scheme. For instance, using 10 candidate RPs for searching achieves a rate of 11.07 bps/Hz, which is lower than that obtained using the complicated CE-based scheme with only 0.4 bps/Hz; however, when considering the required system overhead, results will change as we will further discuss.

First, we study the effect of the localization accuracy in Figure 5, where the proposed FP-PBF scheme achievable rate is presented versus the standard deviation of localization error, ${\sigma }^2$, when the number of candidate RPs is varied from one to 15 RPs. Here, providing localization with low accuracy decreases the achievable rate even though the same number of RPs are used. For instance, using one candidate RP can provide RX with a rate of nearly 10.3 bps/Hz on average if the provided localization comes with a 2 m error, while the rate is decreased to 8.5 bps/Hz if the error reaches 10 m. Moreover, to mitigate the impact of the high localization error and obtain better performance, searching using more RPs from FP-CB is recommended. For example, if the positioning error reaches 10 m, using three RPs guarantees only a 9.42 bps/Hz achievable rate on average, whereas using 10 and 15 candidate RPs can obtain 10.16 and 10.54 bps/Hz rates, respectively. Thus, we will consider using between five and 10 candidate RPs for the searching stage, as a balance between the obtained performance and immunity against positioning error can be achieved.

Figure 6 shows the impact of the time-variant channel on the performance of the proposed FP-CB scheme and the CE and AO schemes. In which we study the obtained effective achievable rate, $R_e=\left(1-\tau /T\right)\times R$, where $\tau$ and $T$ are the searching overhead and the channel coherence time. The proposed scheme outperforms the CE and AO schemes in rapidly changing channels because it needs a lower overhead for searching, $\mathcal{O}\left(C\right)$, comparable to the CE-based scheme, which needs, $\mathcal{O}\left(N\right)$ overhead. For example, assuming $T=100$, using five and 10 candidate RPs, the proposed scheme obtains 10.38 and 9.98 bps/Hz effective rates, respectively, while the CE-based scheme achieves 9.66 bps/Hz effective rates. Furthermore, when considering the system’s required computational complexity (CC), we can see a high reduction in CC when the system uses the proposed scheme over the CE and AO schemes. For instance, assuming FP-CB with $C=16$, the proposed scheme CC will be $16\times 16$, while the CC of the CE and AO schemes will be ${16}^{4.5}$, considering $N_i=1$. Although a random CB-based scheme has the same CC as our proposed scheme in this case, its achievable rate is lower, as presented in Figure 4.

6. Conclusions

In this work, we propose a new CB-based PBF scheme. Firstly, a fingerprint CB is designed by dividing the area of interest into a number of points, and then, in the offline phase, the CE-PBF scheme is adapted to determine the best RP corresponding to each point. Thereafter, using the estimated RX location and the constructed CB, a candidate group of RPs whose points’ positions are near the RX position is determined. Then, the system searches only these RPs to select the suboptimal one to be used in the data transmission period. The proposed scheme proves that constructing PBF codebooks and determining the PBF vector based on positioning information is a promising direction to achieve high network performance and reduce system overhead, especially with rapidly changing channels. For example, using a group of 10 candidate RPs for searching obtains a 9.98 bps/Hz effective rate, which is 0.32 bps/Hz higher than that obtained by CE-PBF. Moreover, even if the localization service has a 10 m error in the estimated RX location, using 10 candidate RPs, the FP-PBF method will obtain a 10.16 bps/Hz achievable rate, which is not a big decrease compared to the 11.07 bps/Hz rate that can be obtained if the error is 2.5 m. As a future extension, dynamic CB based on PI can be designed to mitigate the impact of environmental changes on the fingerprint CB. Furthermore, RIS with a higher number of elements can be considered.