 Open Access
 Authors : Pragnya Sudipta Tripathy, Bijay Kumar Ekka
 Paper ID : IJERTV12IS050308
 Volume & Issue : Volume 12, Issue 05 (May 2023)
 Published (First Online): 06052023
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
MmWave Ofdm Uplink Transmission Using Sparse Frequency Selective Channel Model
Pragnya Sudipta Tripathy Electronics & Instrumentation Engineering
OUTR, BBSR
Odisha, India
Bijay Kumar Ekka Electronics & Instrmentation Engineering
OUTR, BBSR
Odisha, India
Abstract This research paper investigates the impact of wideband and hybrid receiving on the spectral efficiency of millimeterwave OFDM uplink transmission, specifically using a frequency selective channel with sparse formulation model. The study reveals that an increase in bandwidth can cause the beam squint effect, leading to a decrease in spectral efficiency. However, use of the Sparse Formulation of Frequency Selective Channel Model (FSCMSF) can enhance the analysis of the system's spectral efficiency. In terms of spectral efficiency, simulation results show that FSCMSF implementation outperforms SpatialFrequency Wideband implementation. Furthermore, the FSCMSF output is more responsive than the traditional form. The study shows that, regardless of system bandwidth, the sparse formulation of the Frequency Selective Channel Model can improve the spectral efficiency of millimeter wave OFDM uplink transmission. More research is needed to improve the system's efficiency.
Keywords Hybrid Receiving, OFDM, Uplink Transmission, Sparse Frequency Selective Channel Model, Beam Squint Effect, System's Spectral Efficiency, Signal ToNoise Ratio (SNR), Bandwidth, Subcarriers.

INTRODUCTION
Because of its ability to transmit data at high speeds with minimal delay between transmissions, millimetre wave (mmWave) communication has a lot of potential for use in wireless communication systems. However, mmWave communication is plagued with issues such as high blockage, limited coverage, and path loss. In response to these difficulties, orthogonal frequency division multiplexing, also known as OFDM, has seen widespread application in mmWave systems. This allows for improved spectral efficiency as well as mitigation of the effects of frequency selective fading. It has been suggested that using hybrid receiving, which combines analogue and digital processing, can be an efficient method for overcoming the limitations that are posed by conventional receivers in mmWave OFDM systems. Hybrid receiving is a technique that combines analogue beamforming and digital signal processing in order to take advantage of the high directionality of mmWave channels. Because of the reduced complexity of digital signal processing, hybrid reception is becoming more popular. In contrast, the precision of the channel state information (CSI) and the beam alignment of the transmitter and receiver
determine hybrid reception performance. The wideband
effects of mmWave channels can cause beam squinting, which reduces spectral efficiency significantly. This paper investigates the impact of wideband and hybrid receiving on the spectral efficiency of mmWave OFDM uplink transmission, taking into account the channel model's spatial and frequency wideband implications. To improve the precision of our research, we use a sparsely constructed Frequency Selective Channel Model and provide simulation data to back up our findings. Section II introduces the system model after an analysis of the channel model in Section III, and Section IV presents simulation results. Section IV investigates the effectiveness of the spectrum in relation to the number of subcarriers, bandwidth, and nonorthogonality of the OFDM subcarriers. We provide some summaries in the study's conclusion section.
Fig. 1. mmWave uplink system

SYSTEM MODELLING
The decision is shown in Figure 1. In this configuration, a user equipment (UE) with an antenna transmits a signal to a base station (BS), which receives it. M antennas are installed on the BS in a parallel linear array. Analogue reception is possible thanks to a phaseshift network connected to the BS
antennas. The radio frequency (RF) circuits are linked to
the phase shift network. The tth time slot's base station signal
() = () () + () Ã—1
(1)
is represented as
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(6)
here () denotes transmitted signal,
() Ã—1 denotes channel among BS and UE,
() Ã—1 is noise received. Since the system operates in
wide bandwidth and millimeter waveband, the channel has
[()] = 2(1) =1
Ã— (( (
1)/ ))
(2)
many channels and frequencies. Considering the double broadband effect, the notation for the mth component of the channel vector is
() = () = () () + ()
Ã—1
where (5) is obtained by substituting (1) into (4), and
() = () Ã—1 ,
() = () Ã—1
(7)
[()] 1
= 2(1)(())
=1 =1
Ã— [( ( 1)/ )]
(8)
Substituting equation (2) and (3) into (6) gives,
The lth path's complex path gain has a complex Gaussian distribution with a zero mean and variance2 . W is the bandwidth, and is the delay in the time of the lth path. The
number of paths is represented by L, and the frequency of the
carrier is represented by . Because of the array's linearity, we can state that = / () , where is the lth
path's DOA (direction of arrival), wavelength, and d
where = 1,2, , ,
Fouriertransform of () as ()
0
{()()} = ( )
2
(9)
Assuming that,
Ã—1.
denotes the distance among two BS antennas. The station chose a hybrid architecture using mmwave technology and an optimized base station architecture. Analogue beamforming is applied to the received signal prior to passing through the RF chain and transitioning to digital recording.
The complex path gain, which is indicated by the symbol
and corresponds to the lth path, is distributed according to a
complex Gaussian model with a mean of zero and a variance
equal to 2. Within the scope of this discussion, W stands for the bandwidth, and denotes the amount of delay in time associated with the path of the I. L is the total paths, and
denoting the frequency of the carrier. As we know that the
array is linear, we are able to express the angle of arrival
(AOA) for the lth path, which is denoted as =
/ ().
In this situation, represents the DOA for the lth path,
represents the wavelength, and d represents the distance
between adjacent BS (base station) antennas. The station has implemented a hybrid architecture, which combines mm wave technology with an optimized base station architecture, in order to improve the overall performance of the system. Before going through the RF chain and then making the switch to digital recording, the signal that was received goes through the process of analogue beamforming.
The expression for received signal () in frequency
domain can be written as:
() = () () + ()
(10)
p/>
where () is Fourier transform of () , and ()
Ã—1 is the Fourier transform of () , and ()
Ã—1 is Fourier transform of (). According to (8), we
[ ()] = 1 2(1)(())
=1 =1
Ã— [( ( 1)/
)]2
1
= 2(1)(()())2
=1 =1
1
= 2 (() ())
=1
Ã— (1)(()())
(11)
have
Where
1
1 1
= ( 1 2 )
(4)
[()] =
2(1) (3)
(() ())
((() ()))
=
(() ())
(12)
where () = (/ + 1),
Vectors with = 1,2, , form into Ã— in
[] = (). (5)
which
The system chooses beams, which translates to selecting
columns of U and creating a new matrix, Ã— .
According to (7), we have
.
It's worth noting that = , =
{()()}
= {()()}
0
= ( ) , 2
(13)
By using , received signal can be transformed into the
beamspace.
We utilize equations (9) and (3)'s orthogonality property to derive equation (13).

CHANNEL MODELLING
A. OFDM Symbols
To modulate the signals for transmission, OFDM symbols are utilized
R() rÃ—1 and T() tÃ—V1 odl.e1n2oItsesuteh0e5,aMntaeynn20a23
array response vectors of receiver and transmitter,
respectively.
= R
T
(20)
Following is condensed channel model presented in (4):
where Ã— is diagonal with nonzero complex entries, and R rÃ— and T tÃ— contains columns R() and T(), respectively. Under this notation, vectorizing the
1rc(s 1) vec ( ) = ( ) [2rc(s 2) .
T R ]
rc(s )
(21)
channel matrix in (5) gives
1
() = ()
=0
(14)
where , = 0,1, , 1 are random symbols which are independent as well, with {2} = , (), = 0,1, , 1 are the orthogonal waveforms given as
1
() = 2 , 0
(15)
2() 1
(, ) =
2( )
, = ,
(16)
N is the total number of subcarriers, and T is the period of the waveform. As a result, subcarriers are defined in the frequency domain as follows:
where
The channel from equation (6) is chosen in vector form for
the subsequent sparse formulation. Important: the th column of T R is formatted as T() R().
D. Sparse Formulation
Frame gearbox is improved by combining block gearbox and zero padding (ZP). To address the sparse recovery problem, we will assume that both the transmitter and receiver use a single RF chain. Nonetheless, the same strategy can be extended to include more RF chains at both ends. During the training phase, the digital precoder and combiner can be represented by the same matrices. The transmitter employs a
()
2 2
KF precoder for the th training frame, denoted by fRF ,
W () bandwidth , center frequency. Thus, the inter subcarrier difference is = /( + 1), and = /2 +
1
() = (, )
=0
(17)
. So,
which can be implemented with quantized angles at the analogue phase shifters. The next step is to obtain the nth
symbol of the th received frame.

Beam Selection
Consider that we have a channel (), according to (11), we have the frequency domain as () Ã—1 & the channel
1
[()] = 2 (()=1
)
Ã— (1)(())
(18)
in the beamspace, where
1
r [] = H f () [ ] + v []
RF
=0
(22)
where [] represents the th symbol in th training frame that is nonzero
= [0 0 [1] []]
1
(23)
To transmit the combined signal during the th training
()
= 1,2, , . Then, beams having largest values of
[(0)]  are selected.

FrequencySelective Channel Model
Consider a geometric channel model based on L scattering clusters for the frequencyselective mmWave channel [12,18]. The dth delay touch is described in this section.
phase, an RF combiner wRF
[1] [ [2]] = ()[ () RF 0 1] ( RF )
[]+()
(24)
the post combining signal is
Where
is used at the receiver. So that
= rc( )R() ( )
T
=1
(19)
[1] 0 0
where rc() denotes raised cosine pulse signal evaluated at
= [
[2] [1] ]., is the complex gain of the th cluster, is the delay of the th cluster, and are angles of arrival and departure (AoA/AoD), respectively of the th cluster, and
[] [ c + 1]In this scenario, block transmission with c 1 zero padding
is required because it allows for RF circuit reconfiguration
between frames. It also reduces interframe interference and protects against training data loss during reconfiguration. It is impossible to use multiple precoders and combiners for a variety of mmWave symbols at high symbol rates. Equation
(9) is the result of vectorization.
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vec (0)
= ( () () ) vec (1)
R F R F
[vec (c1)]
+
(25)


SIMULATION RESULTS
We conducted computer simulations and determined that an appropriate signaltonoise ratio (SNR) for system is 10 decibels. The system consists of 256 subcarriers and has a bandwidth of 0.02 times the frequency of the carrier band, which is 60 GHz. The time delays and direction of arrivals (DOAs), or arrival angles, have a uniform distribution within the ranges [0, 2] and [0, 256/W], respectively, where W is the number of subcarriers. There are 61 antennas distributed across the base station, and the path gain variation has been set to 1. Figure 2 compares the output response of the spectral efficiency for the SpatialFrequencywideband and FSCM SF implementations at various SNR values. Our results show that FSCMSFbased tuning yields better spectral efficiency for several reasons. Figure 3 compares the output response of the spectral efficiency and bandwidth factor, showing that the two implementations do not significantly differ in the generation of the output response. Finally, Figure 4 compares the system's spectral efficiency againt the number of subcarriers. Our graph demonstrates, the Sparse Formulation of Frequency Selective Channel Model (FSCMSF) results in an improved output response compared to the graph shown. This conclusion is supported by comparing the graphs.
Fig 2. Comparing The Spectral Efficiency vs SNR (dB) between the SpatialFrequencywideband model and Frequency Selective Channel – Sparse Formulation Model
Fig 3. Comparison between Spectral Efficiency and The
Bandwidth Factor () between the SpatialFrequency wideband model and Frequency Selective Channel – Sparse
Formulation Model
Fig 4. Comparison between the Spectral Efficiency vs The Number of Subcarriers (N) between the SpatialFrequency wideband model and Frequency Selective Channel – Sparse Formulation Model

CONCLUSION
In conclusion, the study explored the impact of wideband and hybrid receiving on the spectral efficiency of millimeter wave OFDM uplink transmission using a frequency selective channel with sparse formulation model. The simulations showed that increasing bandwidth causes the beam squint effect to increase, which lowers spectral efficiency. The sparse formulation of the Frequency Selective Channel Model (FSCMSF) has improved the system's spectral efficiency analysis. Simulations revealed that the FSCMSF based implementation resulted in improved spectral efficiency compared to the SpatialFrequencywideband based implementation, as shown in Figure 2. Additionally, Figure 4 showed that the FSCMSF has an improvised output response compared to the standard model. However, the system's bandwidth did not significantly affect the spectral efficiency, as shown in Figure 3. According to these findings, using a sparse formulation of the frequency selective channel model may improve the spectral efficiency of millimeter
nd R. W. Heath Jr., "Channel
wave OFDM uplink transmission. In order to improve system [16] A. Alkhateeb, O. E. Ayach, G. Leus, a Vol. 12 Issue 05, May2023
performance, this technique needs to be researched further.
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