To secure the wireless connection between devices with low computational power has been a challenging problem due to heterogeneity in operating devices, device to device communication in Internet of Things (IoTs) and 5G wireless systems. Physical layer key generation (PLKG) tackles this secrecy problem by introducing private keys among two connecting devices through wireless medium. In this paper, relative calibration is used as a method to enhance channel reciprocity which in turn increases the performance of the key generation process. Channel reciprocity based key generation is emerged as better PLKG methodology to obtain secure wireless connection in IoTs and 5G systems. Circulant deconvolution is proposed as a promising technique for relative calibration to ensure channel reciprocity in comparison to existing techniques Total Least Square (TLS) and Structured Total Least Square (STLS). The proposed deconvolution technique replicates the performance of the STLS by exploiting the possibility of higher information reuse and its lesser computational complexity leads to less processing time in comparison to the STLS. The presented idea is validated by observing the relation between signal-to-noise ratio (SNR) and the correlation coefficient of the corresponding channel measurements between communicating parties.

Next generation of wireless systems specifically 5G, introduces a platform for better exploitation of Internet of Things (IoTs). IoTs do not only require the heterogeneity of the operating devices [

The architecture of PLKG is divided into different blocks which collectively work to produce a private key as shown in

According to [

The researchers have implemented relative calibration in terms of channel coefficients which are obtained in both time and frequency domains. From literature we have discovered that schemes like Channel Gain Compliment (CGC) [

The contributions of this paper are included as following:

In order to ensure channel reciprocity, the relative calibration is implemented using state of art deconvolution techniques including the Total Least Square (TLS) and the Structured Total Least Square (STLS).

Circulant deconvolution technique is proposed as an alternative to the existing techniques and is hypothesized as better performing than the TLS and the STLS.

The proposed deconvolution technique replicates the performance of the STLS by exploiting the possibility of higher information reuse and its lesser computational complexity leads to less processing time in comparison to the STLS.

The simulation results of the proposed method also validate that secure communication is possible by adapting the circulant deconvolution within wireless systems having ultra-low latency including 5G and IoTs systems due to its less computational cost.

The paper is organized as follows. Section 2 discusses the system model in hand. Section 3 describes the method of performing the relative calibration. The deconvolution using circulant structure has been introduced in Section 4. Section 5 provides the simulation results. Finally, conclusions are discussed in Section 6. Vectors and matrices are denoted using boldfaced characters. In this paper,

It is assumed that two nodes A and B referring to Alice and Bob, respectively, need to communicate over a wireless Time Division Duplex (TDD) channel within time duration shorter than channel coherence time. The system model is shown in _{A}_{B}_{A}_{B}_{A}_{B}_{A}_{B}_{A}_{B}

where G(t,

where P(

where, g represents vector that contains channel coefficients from forward effective channel, H represents a square matrix of a specific structure covering the channel coefficients of the reverse effective channel and p is a vector that represents the calibration metric. p contains the non-reciprocity part of the channel and that is why it is first learned and then used to rectify erroneous channel measurements as shown in

To compensate the time-invariant filter imperfection, relative calibration can be performed using the deconvolution techniques. In this section, the deconvolution is performed using the TLS and the STLS as discussed in Subsection 3.1 and Subsection 3.2.

Let us assume that the forward and reverse channel coefficients at kth channel measurement are real, finite-valued and defined as

It is assumed that

For a more realistic approach to address the problem of deconvolution, we assume that both

_{k}

As the noise is Gaussian i.i.d (independent and identically distributed),

and _{c}_{c}

Relative calibration is performed in two step fashion as depicted in

In this phase, Alice and Bob learn the channel imperfections by sending pilot signals to each other. The channel coefficients from Alice to Bob and Bob to Alice are stored

In this phase,

The limitations of TLS and STLS depend mainly on the structure of

In the case of

Let us assume we have a vector

The vectors results in

Recalling

While using circulant transformation for

The linear model in

The parameters used for the simulation are shown in

Parameter | Value |
---|---|

Channel coefficients | 30 |

Filter coefficients | 30 |

Implementation probes | 500 |

SNR observed |

In general, the filter responses can be complicated but to keep our assumption simple,

It can be observed that the circulant performs slightly better in low SNR regions and achieves maximum at 0 dB. The decrease in percentage for both methods in

The deployment of relative calibration has introduced as an enhancement in terms of reciprocity in the PLKG architecture which has a major influence in securing communication between nodes. The deconvolution method is proposed in order to implement the relative calibration with less computational cost in comparison to the state-of-the-art methods. Existing deconvolution methods like TLS and STLS are implemented and discussed for comparative purpose. STLS being more efficient than TLS in terms of quality, is used to perform deconvolution however due to its higher computational cost as a trade-off to quality, the circulant deconvolution is proposed as an alternate solution. In this context, a comprehensive comparison between the two methods is also presented, highlighting the reasons and motivation to use circulant deconvolution. It is to be concluded that the circulant deconvolution replicates the performance of STLS even with less computational cost. The simulation results of the proposed method also validate that secure communication is possible by adapting the circulant deconvolution within wireless systems having ultra-low latency including 5G and IoTs systems due to its less computational cost. The proposed circulant deconvolution is recommended as a better scheme in comparison to the state-of-the-art techniques and this is clearly validated by the simulation results. As an immediate succession, the relative calibration is to be implemented over complete PLKG chain and its effect on the created keys should be observed in real time scenarios.