Wideband hybrid precoding techniques for THz massive MIMO in 6G indoor network deployment

Terahertz (THz) communication is becoming an up-and-coming technology for the future 6G networks as it offers an ultra-wide bandwidth. Appropriate channel models and precoding techniques are indispensable to support the desired coverage and to resolve the severe path loss in THz signals. Initially, in this work, the Sub-THz channel (140 GHz) response is investigated by using NYUSIM Channel Simulator for 6G indoor office scenario.The major highlight will be on radio propagation mechanisms, which impact the network performnace in the form of path-loss, received power, time delays, azimuth AoD, Azimuth AoA, Elevation AoD, Elevation AoA and RMS delay in LOS environments. Recent hybrid precoding techniques depending upon frequency-independent phase-shifters not able to cope up with the beam split effect in THz massive MIMO systems, where the directional beams will split into various physical directions at various sub-carrier frequencies. The beam split effect will result in a serious array gain loss across the entire bandwidth, which has not been well investigated in THz massive MIMO systems. Therefore, to address this challenge, delay-phase precoding is proposed in this work. We then extensively investigate its diverse number of time delayers, varying number of antenna elements, and comparison with frequency—mmWave and Sub-THz have been discussed. Finally, the proposed delay-phase precoding techniques outperforms the other existing narrowband and wideband precoding techniques. Therefore,it is an effective technique to implement the future 6G indoor communication network deployment.


Introduction
The International Telecommunication Union (ITU) launched the official research investigation over 6G that helps to design pioneer wireless networks and also to attain self-subsisting networks.To quench out the emerging services and the applications like augmented reality, holographic communications, extremely high definition transmission of videos, the Tera-Hertz (THz) communications acts as a backbone for the future 6G wireless networks.6G also provides the communication with reduced latency for long distance with ultra high reliability.The THz band ranges from 0.1 to 10 THz provides significant bandwidth owing to attain ultra-high data rate.Several interpretations over 6G be has a belief that 6G provides an empowered full-dimensional coverage with unlimited wireless connectivity.For wireless communications, the peak data rate is considered to be an essential indicator to measure its effectiveness and in order to accomplish the above visions of 6G, the peak data rate should be greater than 1 Tbps [1,2].Nevertheless, this peak data rate will not be supported by the existing 5G millimeter wave (mmWave) bandwidth.Comparing THz band, which is in 0.1 THz-10 THz range with the mmWave, the THz band provides the significant bandwidth, for example, the bandwidth greater than 20 GHz is provided to accomplish the extremely high data rate.Therefore, it is extensively believed that the communication through THz band is significant technology for the emerging 6G wireless networks [2].The bandwidth provided should be used effectively in multi-user networks.An autonomous and large dimensional networks are the key features of 6G to provide wide coverage and ubiquitous connectivity.
The bandwidth obtained in the sub 6 GHz of band, and the mmWave band is insubstantial to gratify the exigencies of the users in sixth generation era.The usage of available spectrum is started moving towards the THz band in bandwidth hungry applications [3].In the applications of cellular, biological, molecular and vehicular communications, distinct use cases are encountered [4][5][6].Owing to the bottleneck of large path loss, the THz communication is circumscribed to employ in short range applications.A good number of advanced applications like personal area networks, 6G communication, chip to chip communication uses THz band communication [7].
But the THz signals are often affected by the path loss for example, at 0.6 THz the path loss of 120 dB/100 m will occur.Due to this path loss issue it becomes challenging to accomplish the expected coverage.The precoding approach helps to resolve path loss problem and in this approach there is no need to increase the power at the transmitter.By using this precoding methodology, narrow beams can be generated with large antenna array gain that combats the severe path loss and also the entire optimization process will be simplified into sub rate optimization processes and its complexity is evaluated [8].
The scale of the antenna array is directly proportional to the array gain of the emerging beam.The wavelength of the signal obtained from the THz band is considerably very small, therefore in THz communication, antenna arrays of very large scale is employed.As the optimization of path loss of THz signals can be used by THz precoding, which is a requisite methodology for 6G wireless networks.When compared to the precoding approach used in 5G mmWave systems, the 6G precoding techniques is facing new challenges because of its varied characteristics and these challenges should detected and resolved by an effective 6G system.
The major bottleneck of current wireless communication system is the limitation of available spectrum and because of that the significant quality of service cannot be provided and this can be alleviated by adopting the THz communication.The spectrum gridlock can be removed by applying novel methodologies and new frequency bands.For effective THz communication, the array-of-sub-array architecture is com-pared with the fully connected architecture.The comparison is made in terms of energy efficiency, spectral efficiency, power consumption, channel estimation etc., Highly complex and power consuming hardware is required for THz communication and many new communication strategies are applied owing to the nature of hardware [9].In order to realize a wireless backhaul with an ultra-high speed, it is vital to analyze the bandwidth, transmission distance and the physical properties of the channel.To address these challenges in THz band, the distance can be enhanced by using distance aware bandwidth adaptive methodology.This approach capture all the distinct eccentricities of the channel and uses a full spectrum of resources by enabling several high-speed links.Highly advanced communication methodologies are needed to enhance the distance for transmission and this helps to provide simultaneous operation of ultra high speed links [10].

Related work
Conventionally, various solutions were proposed for hybrid multi-user mmWave systems [11][12][13][14][15].A two-stage hybrid precoding methodology is proposed and it necessitates explicit channel state information (CSI) feedback from users [12].Initially,in the single-user scheme,both MS and BS collectively choose the better combination of RF beamformer and RF combiner for maximizing the channel gain for the particular MS.The interference between the users can be reduced by using a zero-forcing (ZF) baseband precoding algorithm.Here, this algorithm is applied in the BS by inverting the effective channel.A digital ZF baseband precoder estimate a non-iterative non-feedback channel [14].Particularly, the strongest angle of arrivals (AoAs) near the BS and users are computed and it is used at BS and MSs for analog beamforming.After that, the orthogonal pilot symbols are sent by MS to the BS with the strongest AoA directions.This simplifies the equivalent channel estimation utilised in the BS digital ZF precoder.The RF combiner is configured for every independent MS and the RF and baseband precoder is designed at the BS for all the MSs jointly [15].The analog/digital precoder reduces the MSE of the data streams that are received at the MS.Minimum mean square error (MMSE) is also used as a solution for the part of the methodology.
In the traditional hybrid precoding approach, full array gain is achieved by aligning the narrow beam from the analog beamformer in the direction of the intended users [16].Nevertheless, in 5G mmWave massive MIMO systems, the generated beams from various sub-carrier frequencies concentrate on various physical directions because of the usage of phase shifters which is independent of frequency and this leads to loss in array gain [16].Various methods are utilized to tackle this array gain loss which is encountered by the beam squint effect [17][18][19][20][21].An optimized closed form solution is proposed in orthogonal frequency division multiplexing to deal with the hybrid precoding problem in the wide band massive MIMO system [18].To enhance the hybrid precoding approach performance, an optimal solution is proposed to optimize the digital precoder and an analog beamformer iteratively in order to attain the significant performance over the whole bandwidth [1].
Additionally, the design of code books which contains beams of wide bandwidth is made in order to mitigate the beam squint effect which causes loss in array gain [20,21].The design of wide beams having reduced array gain is attained in each sub-carrier where a semi-definite relaxation methodology is used to enhance the overall antenna array gain over the whole bandwidth [20,21].The suggested methods show effectiveness to enhance the rate performance because the beams are squinted slightly and in case of mmWave massive MIMO systems, the loss in array gain is not a major consideration [18][19][20][21].But these methods are not highly effective for THz band massive MIMO communication systems.The generated beams obtained at various sub-carrier frequencies decompose into individual physical directions because of the substantial number of antennas and wide bandwidth of THz signal.
The decomposition of different subcarrier beams in different directions is called beam split, and this is the fundamental difference between THz and mmWave beamforming systems.The beam split effect gives each subcarrier in the signal a different direction, where the subcarriers around the center frequency diverge around the boresight of the beam.It is inferred that the significant array gain will be attained only on the generated beams around the central frequency.And the remaining beams suffer from a high loss in array gain.Consequently, the achievable rate is degraded by the beam split effect [22,23].This can be overcome by using the proposed Geometric Mean Decomposition (GMD) based delay-phase precoding.

Major contributions
-The key contribution of this work is to apply the channel model to evaluate the radio propagation mechanism at THz frequency range for 6G Massive MIMO system performance using NYUSIM Channel Simulator to verify the channel model parameters and antenna properties.-Large scale and Small scale fading have been discussed for 6G indoor office scenario for 140 GHz operating frequency under UMi LOS environment at 0 dBm Transmit power with coverage of 100 m. -The proposed GMD based Delay Phase Precoding with other precoding techniques have been experimented to mitigate the array gain loss due to the beam split effect.
-The proposed GMD based DPP is compared with recent Narrowband and Wideband hybrid precoding techniques in terms of Achievable sum rate per subcarrier (bits/s/Hz).-Finally, by varying the number of time delayers, frequency (mmWave and Sub-THz), and the number of transmitting antennas in the proposed delay-phase precoding technique, the performances have been compared.The paper is structured as Sect. 3 explains network deployment model with the small scale fading, large scale fading, power delay profile analysis.Section 4 illustrates proposed GMD based delay-phase precoding technique.The design approach with flowchart is explained under Sect. 5. Section 6 demonstrates simulation results and discussion with its inferences.Finally, Sect.7 concludes the article.

Network deployment model
Figure 1 depicts the massive MIMO THz network deployment model.In indoor office scenarios, the major focus will be in the downlink, where the single cell access point (AP) is connected to multiple users.The small scale and large scale fading channel models, the structure of an antenna array, and the power delay profile analysis are discussed in the following subsections using NYUSIM [24].

Path loss model
With NYUSIM, the expression for Close In (CI) free-space reference distance path loss model having one meter of reference distance with an additional attenuation caused by diversified atmospheric conditions were applied [25][26][27][28], and the expression is given as: Where 'd' represents the three dimensional (3D) receivertransmitter separation distance, 'f' represents carrier frequency in GHz, where 'n' denotes the path loss exponent and the attenuation term is denoted by AT which is induced by atmosphere, the path loss in free space (dB) is denoted by FSPL(f, 1 m) with one meter of separation between transmitter and receiver at f and χ C I σ represents a Gaussian random variable with zero-mean and standard deviation in dB: (2) where c represents the speed of light in a vacuum and f is the frequency in GHz.The characterisation of AT is given as: The attenuation factor (dB/m) is denoted by 'α' at 1 GHz to 100 GHz of frequency, that constitutes the combined effects of attenuation of haze, rain, dry air and water vapor [26].Here 'd' represents the 3D transmitter-receiver distance of separation in (1).

Channel model
The double-directional channel impulse response (CIR) h dir , in small scale fading, having 'L' multi-path components for every transmission link will be provided as follows: Here G T X & G R X represents antenna gain at transmission and reception.P R X,l , τ l and φ l denotes the magnitude of received power,propagation time delay and phase in the multi-path components.φ represents azimuth angle offset and 't' denotes time.In every multi-path component, φ T X l denotes the angle of departure at the access point and φ R X l represents the angle of arrival for every mobile users (MUs).

Power delay profile analysis
To create a communication link between the APs and MUs and to maintain the desired data rate of a channel, the received power at the MUs should be modified accordingly.The study of the power delay profile is critical for network deployment.
As shown in Table 1, there are a total of 32 input parameters are given as input to the simulator that is categorized into two divisions: antenna properties and channel parameters.
The panel antenna properties are made up of 12 input parameters that are linked to the antenna arrays at transmission and reception, while the panel channel parameter is made up of 20 input parameters that provide information on the propagation channel.The proposed network parameters for urban microcell (UMi) indoor THz communication systems are described in Table 1.The APs use a carrier frequency of 0.14 THz and transmit power of 0 dBm [29].The NYUSIM statistical parameters at 0.14 THz LOS channel path-loss model is given by free space path loss PL 0 = 255.32dB.The power spectrum of 3D Angle of Departure (AOD) is shown in Fig. 2a, and the power spectrum of 3D Angle of Arrival(AOA) is shown in Fig. 2b which have been simulated in NYUSIM.Whereas, the Fig. 3a depicts the corresponding simulated omni-directional Power delay profile.For the 0.14 THz UMi LOS environment, the separation between transmitter and receiver is held at 100 m.The received power is −122.8dBm and the path delay σ is 17.9 ns having a Path Loss Exponent (PLE) of 2.4.The directional power delay profile for a 0.14 THz UMi LOS area with a PLE of 2.7 and transmitter and receiver antenna half power beamwidths (HPBW) of 8 • azimuth and 8 • elevation as shown in Fig. 3b.Both the transmitter and receiver antennas have a gain of 26.5 dBi and the received power is −76.4 dBm with path delay, σ = 0.9 ns. Figure 4a

Delay phase precoding
As the system model is concerned, the system model of DPP will be similar as hybrid precoding, except the design of analog beamformer.In hybrid precoding technique, the design of analog beamformer includes various phase shifters, but in the delay phase precoding method, the precoding approach

Table 2 Simulation parameters for precoding techniques
The number of the AP antennas N t 256 The number of the user antennas N r 1

Number of channel paths L 4
The central frequency f c 0.14 THz The bandwidth B 5 GHz The number of the subcarriers M 128 The number of RF chains N RF 4 The number of TD elements K 4,16 Physical directions of the paths The transmission SNR P t /σ 2 −20 ∼ 15 dB is sub-divided into two parts.The first part will be realized by phase shifters and then the second part will be realized by time delayers.A two stage precoding design is proposed for DPP [22].Initially in the first stage, the frequency indepen-dent beams are generated by phase shifters towards various users which is similar to that of [30].Time delayers provides time delays and it is linked to certain RF chain that are designed using beam direction compensation methodology depending upon the THz signal bandwidth and the physical direction of user and.Consequently, in the whole ultra-wide bandwidth, the frequency dependent beams are aligned with various users.After that in the second stage, a separate zeroforcing precoding will be done for various sub-carriers for reducing the multiple user interference.

System model
A DPP architecture is proposed, where a TD network has been introduced between the PS network and RF Chains, as shown in Fig. 5, in the existing hybrid precoding architecture [18,21] to overcome the beamsplit effect in wideband THz massive MIMO communication and to increase the array gain performance near to optimal [22,23].The AP uses N RF radio-frequency chains and N t -antenna uniform linear array(ULA).By serving an N r -antenna user, the simultaneous transmission of N s data streams is done (N s = N r ≤ N RF N t ).The orthogonal frequency division multiplexing (OFDM) technique is adopted for realizing the reliable wide-band transmission having 'M' sub-carriers.In between the conventional analog beamformer and the digital precoder, a time-delay (TD) network has been introduced .Here the suggested DPP helps to convert the conventional beamformer (phase controlled) into the controlled beamformer with combined delay-phase that is used in the realization of beamforming which is frequency dependent.Every RF chain is linked to 'K' TD elements and every TD element will be linked to 'P t = N t /K ' conventional frequency independent phase shifters in a sub connected fashion.Therefore, at mth subcarrier, the received signal is represented as where ρ represents the average receiver power, H m ∈ C N t ×N r represents the mth sub-carrier channel, the analog beamformer provided by the frequency-independent PSs is denoted as F RF n ∈ C N t ×N RF with the form as where F RF n,l = blkdiag([a l,1 , a l,2 , . . .a l,K ]) represents the analog beamformer that is accomplished by the PSs linked to the lth RF chain through TDs, and A TD m ∈ C K N RF ×N RF represents the frequency-dependent phase shifts that is accomplished by TD network, that satisfies: The baseband precoder is denoted by F BB m ∈ C N RF ×N s at the mth sub-carrier and an additive white Gaussian noise (AWGN) is represented by n u ∈ C N r ×1 at the mth subcarrier [22].

THz channel model
A wide band 'ray-based' channel model is considered for the THz channel [22].By denoting ' f ' as bandwidth and ' f c ' as central frequency, the mth sub-carrier frequency is represented as follows: For mth sub-carrier, the channel is given as The total number of resolvable paths are represented by 'L', τ l and g l denotes the path delay and path gain of the l th path, θ l,m , φ l,m ∈ [−1, 1] represent the spatial direction of the transmitter and the receiver of the lth path and mth subcarrier, respectively, and f t (θ l,m ), f r (φ l,m ) denotes the array responses in the transmitter and the receiver.
For example, f t (θ l,m ) is represented as follows: m , e jπθ 2l,m , . . ., e jπ(N t −1)θ l,m ] T (10) The direction of the paths in the spatial domain is the spatial direction that is determined by the subcarrier frequency and the physical propagation direction.For example, for the transmitter spatial direction, θ l,m = 2d f m c sin γ l , where γ l ∈ [−π/2, π/2] denotes the physical propagation direction of the l th path, 'd' denotes the constant antenna spacing having d = c 2 f c and 'c' represents the speed of the light.

Design approach
To accomplish GMD based proposed DPP precoding techniques, an effective algorithm is proposed.The essence of this proposed algorithm lies in dividing the precoder design into three stages.To maximize the desired signal power, the analog beamformer is designed in stage-1.In the second stage, the design of digital(baseband) precoder using the equivalent channel is done and the time delayers are added to it in stage-3.In this algorithm, the analog precoder for the l th beam F RF u,l is estimated initially in the step 2 for generating the beams in the spatial direction θ l,c .After that the analog beamformer F RF u is generated in step 4. The time delays by 'K' TD elements have been generated in subsequent steps 11-13, where the direction of beams are altered from θ l,c to θ l,m at the frequency f m .Next in step 16, the analog beamformer with the time delay A TD m is generated.Ultimately, in step 5-8, the digital precoder F BB m is estimated depending upon the equivalent channel H m,eq by Geometric Mean Decomposition (GMD) precoding method [31], because the existing Delay Phase Precoding's requires the complex bit allocation to match the different signal-to-noise ratios (SNRs) of various sub-channels.Therefore, geometric mean decomposition (GMD)-based Digital Precoder is proposed in Delay Phase Precoding to avoid the complex bit allocation.From the Algorithm 1, the GMD based DPP achieves near-optimal achievable rate, as every beam is aligned with the spatial Algorithm 1: Proposed GMD based Delay Phase Precoding for Thz Massive MIMO [22] Inputs: Spatial directions θ l,c ,Channel H m ; Outputs: F RFu , F BBm , A T D m ; First stage: Analog Beamformer 1. for l ∈ {1, 2, . . ., N RF } do 2. Generate F RF u,l by [ a l,1 , a l,2 , . . ., a l,K ] T = f t (θ l,c ); 3: end for 4: F RFu = [F RFu,1 , F RFu,2 , . . ., F RF u,N RF ] ; Second stage: GMD Based Digital Precoder 5: H m,eq = H H m F RFu A T D M ; 6: F BBm =μV m,eq,[:,1:NRF] , H m,eq = U m,eq m,eq V H m,eq ; 7: V m,eq is fed into GMD function.;8: Q m,eq R m,eq P H m,eq = U m,eq m,eq V H m,eq , where Q, R, P are outputs of GMD.direction at all the sub-carriers by time delays.Finally the proposed DPP gives two-dimensional analog beamformer from the traditional one-dimensional analog beamformer, i.e., the only control of the phase shifts is extended to the joint control of time delays and phase shifts as shown in Fig. 6.
The DPP approach attains the near optimal array gain in the entire bandwidth whereas the required amount of time delayers are reduced significantly.For example, for 1024 antenna elements having four RF chains, the required amount of time delayers are minimized from 4096 to 128, which obviously leads to reduced power consumption [30].

Simulation results and discussion
We consider the system parameters described in Table 2, with a AP employing an 256 elements of uniform linear array and associated with 128 subcarriers(M) and each having a single antenna.Simulations are performed in MATLAB assuming multi-path channels (L = 4).The performance of the proposed solution is shown in terms of the average achievable sumrate(R) per carrier:  Figure 7 compares the achievable rate per subcarrier of different narrowband precoding methodologies along with the Proposed Delay Phase Precoding, the simulation results are provided.Besides Spatially Sparse Precoding [16], Kalman Hybrid Precoding [11], MMSE Hybrid Precoding [15], ZF Hybrid Precoding [14], Analog Beemsteering are included.The proposed Delay Phase Precoding shows the best performance as per Table 3, along with the Spatially Sparse Precoding, and Kalman Hybrid Precoding, while ZF Hybrid Precoding and Analog Beemsteering achievable rate per subcarrier is lower due to the fact that they are dealing with the beam split effect.
Figure 8 compares the achievable rate per subcarrier of different wideband precoding techniques along with the Proposed Delay Phase Precoding and Optimal Precoding.The Proposed GMD based Delay Phase Precoding shows the best performance (yields 79.64% of optimal precoding) compared to that of SVD based DPP (which yields 78.44% of optimal precoding) as shown in Table 4.The Wideband and Widebeam hybrid precoding's achievable rate per subcarrier are   The proposed Delay-phase precoding network's performance in THz channel and in mmWave channel has been compared in Fig. 10.It can be observed that its performance is much better at frequency, f = 0.14 THz (sub-THz channel) than at f = 28 GHz (mmWave channel).For THz channels, the DPP network is effectively being able to negate the beam split effect caused by the traditional phase-shifters and improve the performance rate substantially whereas in mmWave channel, the proposed DPP network is not able to effectively cancel out the beam squint effect.
In the Fig. 11, the performance of the proposed DPP is compared for various number of AP antennas (N).There is not much difference observed when the value of N changes.Optimal performance is observed at N = 1024.Therefore, the DPP has the capability for solving the achievable rate degradation received by the beam split effect also to achieve more optimal achievable rate performance.

Conclusion
This work verified the downlink single cell AP connected to multiple carrier system for the 6G indoor office network deployment scenario and describes the channel model, the antenna properties, and power delay profile analysis employed using NYUSIM Channel Simulator.After that, we proposed a GMD based DPP technique where a TD network is being introduced to compensate the beam split effect and compared its performance to existing precoding techniques in narrowband and wideband.From the simulation results and the theoretical analysis, it is observed that this DPP technique is capable to eradicate the beam split effect with more optimal (79.64% of optimal) than other DPP methodologie's achievable sum rate per subcarrier performance.Under DPP Technique, the impacts of the carrier frequency of 28 GHz mmWave and 140 GHz, the number of transmitting antennas and the number of time delayers on the achievable sum rate performance for a single cell multi-carrier scenario have been compared.This work will be further broadened for multi-cell scenario in future.

Fig. 2 Fig. 3 Fig. 4 Fig. 5
Fig. 2 Power spectrum depicts a small scale PDP for indoor deployments with a Tx-Rx separation distance of 100 m and a frequency of 0.14 THz.For the Tx and Rx gain of 26.5 dBi, the Path Loss for Omnidirectional, Directional and Directional-best for 0.14 Thz, UMi LOS is shown in Fig. 4b with respect to Tx-Rx Separation distance.Power Delay Profile (PDP) as shown in Fig. 3a, b is represented as a function of time delay which gives the received signal intensity through a multi-path channel.From Fig. 3a, Omnidirectional Power Delay Profile in 140 GHz UMi LOS is presented.This figure shows that in LOS, the received power diminished to zero after about 495 ns.From Fig. 3b, the Directional PDP with Strongest Power in 140 GHz UMi LOS is presented, the received power of PDP diminished to zero after about 495 ns.From Fig. 4b, i.e. the scatter plot, The omnidirectional and directional path loss values are generated for the 140 GHz UMi LOS, with about 100 m T-R distance for LOS.The path loss scattered between 90-180 dB for LOS.Throughout this article, the following notations are used: A represents a matrix, 'a' denotes a vector and a is a scalar.A(i) illustrates the ith column of A, (•) * denotes conjugate transpose, (•) T denotes transpose and tr(A) is its trace.||A|| is the Frobenius norm of A, and |A| is its determinant; [A|B] represents the horizontal concatenation; The p-norm of a is represented as ||a|| p ; diag(A) is a vector generated by the diagonal elements of the matrix A; I N is the N × N identity matrix; 0 M * N is the M × N all-zeros matrix; n ∼ N (μ, σ 2 ) is the complex Gaussian vector of covariance σ 2 and mean 0. E[•] denotes the expectation and R{•} denotes the real part of the variable.

Fig. 10 Table 5
Fig. 10 The rate performance comparison for THz channel and mmWave channel

Fig. 11
Fig. 11 Comparison of rate performance for different number of antennas

Table 1
Input parameters settings

Table 3
Comparison of various Narrowband precoding algorithms with the GMD-Proposed DPP (K = 4) at SNR = 15 dB for N t = 256, N r = 1, and N RF = 4

Table 4
Comparison of various Wideband precoding algorithms and GMD-Proposed DPP (K = 16) with the Optimal precoding at SNR = 15 dB for N t = 256, N r = 1, and N RF = 4