Mm-Wave Ofdm Uplink Transmission Using Sparse Frequency Selective Channel Model

Mm-Wave 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 millimeter-wave 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 (FSCM-SF) can enhance the analysis of the system's spectral efficiency. In terms of spectral efficiency, simulation results show that FSCM-SF implementation outperforms Spatial-Frequency- Wideband implementation. Furthermore, the FSCM-SF 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- To-Noise Ratio (SNR), Bandwidth, Subcarriers.

1. 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 non-orthogonality of the OFDM subcarriers. We provide some summaries in the study's conclusion section.

   Fig. 1. mmWave uplink system

2. 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 phase-shift network connected to the BS

   antennas. The radio frequency (RF) circuits are linked to

   the phase shift network. The t-th time slot's base station signal

   () = () () + () ×1

   (1)

   is represented as

   Vol. 12 Issue 05, May-2023

   (6)

   here () denotes transmitted signal,

   () ×1 denotes channel among BS and UE,

   () ×1 is noise received. Since the system operates in

   wide bandwidth and millimeter waveband, the channel has

   [()] = 2(1) =1 × (( ( 1)/ ))

   (2)

   many channels and frequencies. Considering the double broadband effect, the notation for the m-th component of the channel vector is

   () = () = () () + ()

   ×1

   where (5) is obtained by substituting (1) into (4), and

   () = () ×1 , () = () ×1

   (7)

   [()] 1 = 2(1)(()) =1 =1 × [( ( 1)/ )]

   (8)

   Substituting equation (2) and (3) into (6) gives,

   The l-th 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 l-th 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 l-th

   path's DOA (direction of arrival), -wavelength, and d

   where = 1,2, , ,

   Fourier-transform of () as ()

   0 {()()} = ( ) 2

   (9)

   Assuming that,

   ×1.

   denotes the distance among two BS antennas. The station chose a hybrid architecture using mm-wave 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 l-th path, which is denoted as =

   / ().

   In this situation, represents the DOA for the l-th 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 ()

   ×1 is the Fourier transform of () , and ()

   ×1 is Fourier transform of (). According to (8), we

   [ ()] = 1 2(1)(()) =1 =1 × [( ( 1)/ )]2 1 = 2(1)(()())2 =1 =1 1 = 2 (() ()) =1 × (1)(()())

   (11)

   have

   Where

   1

   1 1 = ( 1 2 )

   (4)

   [()] =

   2(1) (3)

   (() ()) ((() ())) = (() ())

   (12)

   where () = (/ + 1),

   Vectors with = 1,2, , form into × in

   [] = ().

   (5)

   which

   The system chooses beams, which translates to selecting

   columns of U and creating a new matrix, × .

   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).

3. CHANNEL MODELLING

   A. OFDM Symbols

   To modulate the signals for transmission, OFDM symbols are utilized

   R() r×1 and T() t×V1 odl.e1n2oItsesuteh0e5,aMntaeyn-n20a23

   array response vectors of receiver and transmitter,

   respectively.

   = R T

   (20)

   Following is condensed channel model presented in (4):

   where × is diagonal with non-zero complex entries, and R r× and T t× 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.

   1. Beam Selection

      Consider that we have a channel (), according to (11), we have the frequency domain as () ×1 & the channel

      1 [()] = 2 (() =1 ) × (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 non-zero

      = [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.

   2. Frequency-Selective Channel Model

   Consider a geometric channel model based on L scattering clusters for the frequency-selective mmWave channel [12,18]. The d-th 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 inter-frame 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.

   Vol. 12 Issue 05, May-2023

   vec (0) = ( () () ) vec (1) R F R F [vec (c1)] +

   (25)

4. SIMULATION RESULTS

   We conducted computer simulations and determined that an appropriate signal-to-noise 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 Spatial-Frequency-wideband and FSCM- SF implementations at various SNR values. Our results show that FSCM-SF-based 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 (FSCM-SF) 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 Spatial-Frequency-wideband model and Frequency Selective Channel – Sparse Formulation Model

   Fig 3. Comparison between Spectral Efficiency and The

   Bandwidth Factor () between the Spatial-Frequency- wideband model and Frequency Selective Channel – Sparse

   Formulation Model

   Fig 4. Comparison between the Spectral Efficiency vs The Number of Subcarriers (N) between the Spatial-Frequency- wideband model and Frequency Selective Channel – Sparse Formulation Model

5. 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 (FSCM-SF) has improved the system's spectral efficiency analysis. Simulations revealed that the FSCM-SF based implementation resulted in improved spectral efficiency compared to the Spatial-Frequency-wideband based implementation, as shown in Figure 2. Additionally, Figure 4 showed that the FSCM-SF 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, May-2023

performance, this technique needs to be researched further.

REFERENCES

[1] Y. Li and A. Hu, "Wideband Millimeter-wave OFDM Uplink with Hybrid Receiving," 2021 IEEE 4th International Conference on Electronic Information and Communication Technology (ICEICT), Xi'an, China, 2021, pp. 735-739, doi: 10.1109/ICEICT53123.2021.9531323.

[2] K. -Y. Chen, H. -Y. Chang, R. Y. Chang and W. -H. Chung, "Hybrid Beamforming in mmWave MIMO-OFDM Systems via Deep Unfolding," 2022 IEEE 95th Vehicular Technology Conference: (VTC2022-Spring), Helsinki, Finland, 2022, pp. 1-7, doi: 10.1109/VTC2022-Spring 54318.2022.9860467.

[3] P. K. Korrai and D. Sen, "Performance analysis of OFDM mmWave communications with compressive sensing-based channel estimation and impulse noise suppression," 2016 IEEE International Conference on Advanced Networks and Telecommunications Systems (ANTS), Bangalore, India, 2016, pp. 1-6, doi: 10.1109/ANTS.2016.7947867.

[4] Lv, Changwei & Lin, Jia-Chin & Yang, Zhaocheng. (2019). Channel Prediction for Millimeter Wave MIMO-OFDM Communications in Rapidly Time-Varying Frequency-Selective Fading Channels. IEEE Access. PP. 1-1. 10.1109/ACCESS.2019.2893619.

[5] F. Boccardi et al, "Five disruptive technology directions for 5G," IEEE Commun. Mag., vol. 52, pp. 74-80, Feb. 2014.

[6] J. Andrews et al, "What will 5G be?," IEEE J. Sel. Areas Commun., vol. 32, pp. 1065-1082, June 2014.

[7] Z. Pi and F. Khan, "An introduction to millimeter-wave mobile broadband systems," IEEE Commun. Mag., vol. 49, pp. 101-107, June 2011.

[8] T. Rappaport et al, "Millimeter wave mobile communications for 5G cellular: It will work!," IEEE Access, vol. 1, pp. 335-349, May 2013.

[9] W. Roh et al, "Millimeter-wave beamforming as an enabling technology for 5G cellular communications: theoretical feasibility and prototype results," IEEE Commun. Mag., vol. 52, pp. 106-113, Feb 2014.

[10] A. Alkhateeb, G. Leus, and R. W. Heath, "Compressed sensing based multi-user millimeter wave systems: How many measurements are needed?,' in Proc. IEEE Int. Conf. Acoustics, Speech and Sig. Process. (ICASSP), pp. 2909-2913, April 2015.

[11] Z. Gao, L. Dai, and Z. Wang, "Channel estimation for mmwave massive MIMO based access and backhaul in ultra-dense network," in Proc. IEEE Int. Conf. on Commun. (ICC), pp. 1-6, May 2016.

[12] T. E. Bogale and L. B. Le, "Massive MIMO and mmwave for 5G wireless hetnet: Potential benefits and challenges," IEEE Veh. Technol. Mag., vol. 11, pp. 6475, March 2016.

[13] R. W. Heath, N. Gonzlez-Prelcic, S. Rangan, W. Roh, and A. M. Sayeed, "An overview of signal processing techniques for millimeter wave MIMO systems," IEEE J. Sel. Areas Commun., vol. 10, pp. 436- 453, April

[14] J. Wang, "Beam codebook based beamforming protocol for multi-Gbps millimeter-wave WPAN systems," IEEE J. Sel. Areas Commun., vol. 27, pp. 1390-1399, Oct 2009.

[15] S. Hur, T. Kim, D. J. Love, J. V. Krogmeier, T. A. Thomas, and A. Ghosh, "Millimeter wave beamforming for wireless backhaul and access in small cell networks," IEEE Trans. Commun., vol. 61, pp. 4391-4403, October 2013.

estimation and hybrid precoding for millimeter wave cellular systems," IEEE J. Sel. Topics Signal Process., vol. 8, pp. 831-846, Oct 2014.

[17] R. M. Rial, C. Rusu, A. Alkhateeb, N. G. Prelcic, and R. W. Heath Jr., "Hybrid MIMO architectures for millimeter wave communications: Phase shifters or switches?," IEEE Access, Jan 2016.

[18] S. Kashyap, C. Mollen, E. Bjornson, and E. G. Larsson, "Frequency- domain interpolation of the zeroforcing matrix in massive MIMO- OFDM," in IEEE Int. Workshop Signal Process. Advances Wireless Commun. (SPAWC), pp. 1-5, July 2016.

[19] A. Alkhateeb and R. W. Heath Jr., "Frequency selective hybrid precoding for limited feedback millimeter wave systems," IEEE Trans. Commun., vol. 64, pp. 18011818 , May 2016.

[20] A. Ghosh et al, "Millimeter-wave enhanced local area systems: A high- data-rate approach for future wireless networks," IEEE J. Sel. Areas Commun., vol. 32, pp. 1152-1163, June 2014.

[21] O. E. Ayach, S. Rajagopal, S. Abu-Surra, Z. Pi, and R. W. Heath Jr., "Spatially sparse precoding in millimeter wave MIMO systems," IEEE Trans. Commun., vol. 13, pp. 1499-1513, Mar. 2014.

[22] P. Schniter and A. Sayeed, "Channel estimation and precoder design for millimeter-wave communications: The sparse way," in Proc. Asilomar Conf. Signals, Syst., Comput., pp. 273-277, Nov 2014.

[23] K. Venugopal, A. Alkhateeb, N. G. Prelcic, and R. W. Heath Jr., "Channel estimation for hybrid architecture based wideband millimeter wave systems," CoRR, vol. abs/1611.03046, 2016. http://arxiv.org/ abs/1611.03046.

[24] J. Rodr´guez-Fern´andez and N. Gonz´alez-Prelcic, Channel estimation for frequency-selective mmWave MIMO systems with beam-squint, in Proc.2018 IEEE Global Commun. Conf. (GLOBECOM), Abu Dhabi, United Arab Emirates, Dec. 2018, pp. 1 6,

[25] X. Gao, L. Dai, S. Zhou, A. M. Sayeed, and L. Hanzo, Wideband beamspace channel estimation for millimeter-wave MIMO systems relying on lens antenna arrays, IEEE Trans. Signal Process., vol. 67, no. 18, pp.48094824, Sep. 2019.

[26] B. Wang, F. Gao, S. Jin, H. Lin, and G. Y. Li, Spatial- and frequency wideband effects in millimeter-wave massive MIMO systems, IEEE Trans. Signal Process., vol. 66, no. 13, pp. 33933406, Jul. 2018.

[27] B. Wang, F. Gao, S. Jin, H. Lin, G. Y. Li, S. Sun, and T. S. Rappaport, Spatial-wideband effect in massive MIMO with application in mmWave systems, IEEE Commun. Mag., vol. 56, no. 12, pp. 134 141, Dec. 2018.

[28] J. H. Brady and A. M. Sayeed, Wideband communication with highdimensional arrays: New results and transceiver architectures, in Proc. 2015 IEEE Int. Conf. Commun. orkshop (ICCW), London, UK, Jun. 2015, pp. 10421047.

[29] A. Alkhateeb, G. Leus, and R. W. Heath, Jr., Limited feedback hybrid precoding for multi-user millimeter wave systems, IEEE Trans. Commun., vol. 14, no. 11, pp. 64816494, Nov. 2015.

[30] K. Venugopal, N. Gonz´alez-Prelcic, and R. W. Heath, Jr., Optimality of frequency flat precoding in frequency selective millimeter wave channels, IEEE Wireless Commun. Lett., vol. 6, no. 3, pp. 330333, Jun. 2017.

[31] G. C. Ferrante, T. Q. S. Quek, and M. Z. Win, Revisiting the capacity of noncoherent fading channels in mmWave system, IEEE Trans. Commun., vol. 65, no. 8, pp. 32593275, Aug. 2017.

[32] D. Zhang, Z. Zhou, C. Xu, Y. Zhang, J. Rodriguez, and T. Sato, Capacity analysis of NOMA with mmWave massive MIMO systems, IEEE J. Sel. Areas Commun., vol. 35, no. 7, pp. 16061618, Jul. 2017