1-20hit |
Sadayuki ABETA Mamoru SAWAHASHI Fumiyuki ADACHI
This paper compares the BER performance of two types of pilot channel-based coherent Rake combining achievable by the use of weighted multi-slot averaging (WMSA) channel estimation filter in DS-CDMA transmission links. One is for the time-multiplexed pilot channel and the other is for the parallel pilot channel. The WMSA channel estimation filter weights and averages the received pilot over a period of several slots to improve the BER performance. We propose the WMSA channel estimation filters for time-multiplexed pilot and parallel pilot structures. Achievable BER performance under frequency-selective fading environments is computer simulated. The simulation results show that almost same BER performance can be achieved for both pilot channel structures when the same energy is allocated to the pilot.
Noriyuki MAEDA Hiroyuki ATARASHI Sadayuki ABETA Mamoru SAWAHASHI
This paper proposes a pilot channel assisted minimum mean square error (MMSE) combining scheme in orthogonal frequency and code division multiplexing (OFCDM) based on actual signal-to-interference power ratio (SIR) estimation, and investigates the throughput performance in a broadband channel with a near 100-MHz bandwidth. In the proposed MMSE combining scheme, the combining weight of each sub-carrier component is accurately estimated from the channel gain, noise power, and transmission power ratio of all the code-multiplexed channels to the desired one, by exploiting the time-multiplexed common pilot channel in addition to the coded data channel. Simulation results elucidate that the required average received signal energy per bit-to-noise spectrum density ratio (Eb/N0) for the average packet error rate (PER) = 10-2 is improved by 0.6 and 1.2 dB by using the proposed MMSE combining instead of the conventional equal gain combining (EGC) in a 24-path Rayleigh fading channel (exponential decay path model, maximum delay time is approximately 1 µsec) in an isolated cell environment, when the number of multiplexed codes = 8 and 32, respectively, with the spreading factor of 32. Furthermore, when the average received Eb/N0 = 10 dB, the achievable throughput, i.e., the number of simultaneously multiplexed codes for the average PER = 10-2 in the proposed MMSE combining, is increased by approximately 1.3 fold that of the conventional EGC.
Noriyuki MAEDA Hiroyuki ATARASHI Sadayuki ABETA Mamoru SAWAHASHI
This paper presents an optimum antenna diversity combining method associated with despreading that employs Minimum Mean Square Error (MMSE) combining over the frequency domain in a frequency-selective fading channel for forward link Orthogonal Frequency and Code Division Multiplexing (OFCDM) wireless access, in order to achieve the maximum radio link capacity. Simulation results considering various propagation channel conditions elucidate that the antenna diversity combining method with Equal Gain Combining (EGC) subsequent to the despreading employing MMSE combining based on pilot symbol-assisted channel estimation and interference power estimation can decrease the required average received signal energy per bit-to-background noise power spectrum density ratio (Eb/N0) the most, taking into account the impact of the inter-code interference. Furthermore, we clarify that the required average received Eb/N0 for the average packet error rate of 10-2 employing the diversity combining scheme with EGC after despreading with MMSE combining is improved by approximately 0.3 dB compared to the diversity combining scheme with EGC before despreading with MMSE combining at the number of code-multiplexing of 24 for the spreading factor of 32 in a 24-path Rayleigh fading channel.
Yoshiaki OFUJI Sadayuki ABETA Mamoru SAWAHASHI
This paper compares by computer simulation the achievable throughput performance employing fast packet scheduling algorithms focusing on the throughput of each user in High Speed Downlink Packet Access (HSDPA). Three packet scheduling algorithms are employed: the Maximum carrier-to-interference power ratio (CIR), Proportional Fairness (PF), and Round Robin (RR) methods. The simulation results elucidate that although the Maximum CIR method achieves an aggregated user throughput within a cell higher than that using the PF and RR methods, the PF method is advantageous because it enhances the user throughput for a large number of users with a lower received signal-to-interference power ratio (SIR), who are located outside the normalized distance of 0.6-0.7 from a cell site (this corresponds to the area probability of 50-60% within the cell) compared to the Maximum CIR method. It is also shown that when the PF method is employed, the probability of user throughput of greater than 2 Mbps in the vicinity of the cell site becomes approximately 45% (5%) for L = 1-path (2-path) fading channel, while it is almost 80% (50%) when using the Maximum CIR method. Finally, we show that the average user throughput in a 2-path Rayleigh fading channel is reduced by approximately 30% compared to that in a 1-path channel due to severe multipath interference (MPI) and that the average user throughput is strongly affected by the total traffic produced within a cell, which is directly dependent on the number of users within a cell and the data size per packet call.
Nobuhiko MIKI Sadayuki ABETA Hiroyuki ATARASHI Mamoru SAWAHASHI
This paper proposes a multipath interference canceller (MPIC) employing multipath interference (MPI) replica generation (MIG) utilizing previously transmitted packet combining (PTPC), which is well-suited to incremental redundancy, in order to achieve a peak throughput of nearly 8 Mbps in a multipath fading environment in high-speed downlink packet access (HSDPA). In our scheme, more accurate MPI replica generation is possible by generating MPI replicas utilizing the soft-decision symbol sequence of the previously transmitted packets in addition to that of the latest transmitted packet. Computer simulation results elucidate that the achievable throughput of the MPIC employing MIG-PTPC is increased by approximately 100 kbps and 200 kbps and the required average received signal energy per symbol-to-background noise power spectrum density ratio (Es/N0) per antenna at the throughput of 0.8 normalized by the maximum throughput is improved by about 0.3 and 0.7 dB compared to that of the MPIC using the soft-decision symbol sequence after Rake combining of the last transmitted packet both in 2- and 3-path Rayleigh fading channels for QPSK and 16QAM data modulations, respectively. Furthermore, we clarify that the maximum peak throughput using the proposed MPIC with MIG-PTPC coupled with incremental redundancy achieves approximately 7 Mbps and 8 Mbps with 16QAM and 64QAM data modulations in a 2-path Rayleigh fading channel, respectively, within a 5-MHz bandwidth.
Yoshiaki OFUJI Sadayuki ABETA Mamoru SAWAHASHI
This paper proposes a unified packet scheduling method that considers the delay requirement of each traffic data packet whether real time (RT) or non-real time (NRT), the channel conditions of each accessing user, and the packet type in hybrid automatic repeat request (ARQ), i.e., either initially transmitted packet or retransmitted packet, in the forward link for Orthogonal Frequency and Code Division Multiplexing (OFCDM) wireless access. In the proposed packet scheduling method, the overall priority function is decided based on PTotal = αDelayPDelay + αTypePType + αSINRPSINR (PDelay, PType, and PSINR are the priority functions derived from the delay requirement, type of packet, and the received signal-to-interference plus noise power ratio (SINR), respectively, and αDelay, αType, and αSINR are the corresponding weighting factors). The computer simulation results show that the weighting factor of each priority function as αType/αDelay = 0.6, αSINR/αDelay = 0.4 assuming the linear-type function in PDelay and a constant-type function in PType is optimized. Furthermore, we show that the outage probability for achieving the packet loss rate (PLR) of less than 10-3 for non-real time (NRT) traffic users employing the proposed packet scheduling method is reduced by approximately two orders of magnitude compared to that using the Priority Queuing (PQ) method while maintaining the PLR of real-time (RT) traffic users at the same level as that using the PQ method.
Atsushi HARADA Sadayuki ABETA Mamoru SAWAHASHI
This paper proposes an adaptive radio parameter control scheme that utilizes an optimum radio parameter set comprising the maximum number of retransmissions in hybrid automatic repeat request (HARQ) in addition to the data modulation and channel coding scheme (MCS) according to the Quality of Service (QoS) requirements (i.e., the required packet error rate and delay) and propagation conditions such as the delay spread in the forward link of Orthogonal Frequency and Code Division Multiplexing (OFCDM) broadband wireless access. We elucidate by simulation evaluation that most of the optimum MCSs are common regardless of the delay requirement of traffic data, i.e., common between non-real time (NRT) and real-time (RT) class data. Concretely, the three MCSs of QPSK with the coding rate of R=1/2, 16QAM with R=1/2 and 3/4 are optimum ones, although the additional MCS of QPSK with R=1/3 is effective only for the RT class data in the lower received average received signal energy per symbol-to-background noise power density ratio (Es/N0) region. Furthermore, application of a much higher MCS set, 16QAM with R=5/6 and 64QAM with R=3/4, in addition to the three common MCSs improves the throughput under much higher Es/N0 conditions in a small delay spread environment. The simulation results show that the delay requirement, i.e., the maximum number of retransmissions, in HARQ does not affect the key radio parameter such as MCS, because of informative results such as a smaller number of retransmissions associated with a less-efficient MCS achieves a higher throughput than does using a more highly-efficient MCS allowing a larger number of retransmissions. Consequently, it is concluded that the proposed adaptive radio parameter control according to the QoS requirements substantially results in the selection of the optimum MCS irrespective of the delay requirement except for the extreme case where no retransmissions are allowed and for special propagation channel conditions.
Naoto OKUBO Yoshiaki OFUJI Sadayuki ABETA Takehiro NAKAMURA
This paper investigates the uplink throughput performance and the interference power to other cells using an Evolved UTRA (E-UTRA) laboratory and field experimental system. In E-UTRA uplink, the near-far problem is not an issue since the orthgonality among the users within the target cell is maintained. Therefore, the fractional transmission power control (TPC), in which the target level of TPC is adjusted according to the path loss level, can be adopted. Thus, it is expected the high cell throughput and the large coverage area by combining fractional TPC, adaptive modulation and channel coding (AMC), and variable resource block (RB) allocation. The indoor and field experimental results show that the peak throughput of approximately 45 Mbps is achieved by allocating a wider bandwidth and setting higher target level for the UE located near the cell site while keeping the adjacent cell interference level almost the constant. We also showed that the system capacity can be improved by 50% in simple cell model by applying the AMC and the fractional TPC.
Takahiro TAKIGUCHI Kohei KIYOSHIMA Yuta SAGAE Kengo YAGYU Hiroyuki ATARASHI Sadayuki ABETA
This paper evaluates the downlink performance of an LTE-Advanced (LTE-A) heterogeneous network that uses carrier aggregation (CA) between macro and small cells. The concept of utilizing the CA functionalities in LTE-A is effective in increasing the network capacity in a congested area through raising of the base station density using small cells overlaid onto an existing macro cell network. This concept is also effective in maintaining the mobility performance of user equipment (UE) because handover operation is not applied when entering/leaving a small cell, but component carrier addition/removal is only performed through CA while maintaining the connection to a macro cell. In order to present comprehensive performance evaluations in an LTE-A heterogeneous network with CA, this paper evaluates various performance criteria, e.g., downlink cell throughput and downlink user throughput. According to the obtained simulation results, the total downlink cell throughput achieved in an LTE-A heterogeneous network deployment with CA (four small cells overlaid onto a macro cell sector) exhibits a 3.9-fold improvement compared to a conventional-macro-cell-only network deployment using two frequency bands.
Shingo SUWA Hiroyuki ATARASHI Sadayuki ABETA Mamoru SAWAHASHI
This paper elucidates the optimum bandwidth per sub-carrier in the reverse link for multicarrier (MC)/DS-CDMA using a 10 to 80-MHz bandwidth in a multipath fading channel with numerous resolved multipaths, taking into account all major effects, i.e., the improvement in the Rake time diversity effect and the degradation in the path search and the channel estimation due to multipath interference (MPI). In the paper, we assume a broadband channel model with the maximum delay time of up to approximately 1 µsec simulating a microcell with the radius of less than 1 km in an urban area. The simulation results clarify that the improvement in the radio link performance is almost saturated at a bandwidth greater than approximately 40 MHz when the spreading factor of the channel is SF=32, and the best performance is achieved at the bandwidth of approximately 20-40 MHz when SF=4, employing two-branch antenna diversity reception (an average equal power delay profile and an exponential decay power delay profile are assumed, where the number of multipaths is changed from 12 to 48 for both profiles). This is generated by the tradeoff between the improvement in the Rake time diversity effect and the increased MPI in addition to the degradation in accuracy of the path search and channel estimation associated with a lower average received signal-to-interference plus background noise power ratio. Therefore, we conclude that MC/DS-CDMA, where each sub-carrier has the bandwidth of approximately 20-40 MHz, is one of the most promising candidates for broadband packet wireless access in the reverse link.
Sadayuki ABETA Mamoru SAWAHASHI Fumiyuki ADACHI
Adaptive channel estimation filters are presented for coherent DS-CDMA reverse link using time-multiplexed pilot and parallel pilot structures. Fast transmit power control (TPC) is adopted in the reverse link. Fading statistical properties are not preserved when fast TPC is used. When fading is slow, the channel is similar to non-fading channel, but its starts to vary as fading become faster since fast TPC cannot track fading perfectly. A pragmatic approach is used in this paper to derive adaptive channel estimation filter. The filter coefficients are updated based on the measured autocorrelation function of the instantaneous channel estimate. The bit error rate (BER) performance under frequency selective Rayleigh fading is evaluated by computer simulation to show that the adaptive channel estimation filter provides superior performance to the previously proposed non-adaptive WMSA filter.
Hiroyuki ATARASHI Sadayuki ABETA Mamoru SAWAHASHI
This paper proposes Variable Spreading Factor-Orthogonal Frequency and Code Division Multiplexing (VSF-OFCDM) as the most promising forward link wireless access method in broadband packet wireless transmission using an approximate 50 to 100 MHz bandwidth. The proposed OFCDM employing VSF can flexibly realize near optimum wireless access satisfying higher radio link capacity both in isolated cell environments such as hot-spot areas and indoor offices and in multi-cell environments such as cellular systems by adaptively changing the appropriate spreading factor, SF, in the frequency domain based on the cell structure, radio link conditions such as the delay spread, and major radio link parameters such as the data modulation scheme and channel coding rate. Furthermore, by establishing SF=1, i.e., no spreading mode, VSF-OFCDM can be used as orthogonal frequency division multiplexing (OFDM). Computer simulation results demonstrate that, while SF=1 (OFDM) achieves higher link capacity than SF>1 in an isolated-cell environment, OFCDM with the optimized SF value over 1 achieves approximately 1.4 times higher capacity compared with OFDM in a multi-cell environment associated with the advantageous one-cell frequency reuse. Consequently, VSF-OFCDM can provide seamless deployment of broadband packet wireless access with higher radio link capacity, that is, OFDM in an isolated-cell environment, and OFCDM with the adaptively optimized SF value over 1 in a multi-cell environment according to the major radio link conditions and radio link parameters, by only changing the spreading factor.
Sadayuki ABETA Seiichi SAMPEI Norihiko MORINAGA
This paper proposes an adaptive coding rate and process gain control technique with channel activation function to realize a CDMA based radio subsystem for multi-media communication services that include two types of media, i.e., fixed size data such as the computer data and still image, and constant bit rate data such as voice and video. The proposed system achieves high throughput data transmission for the fixed size data by controlling the process gain and coding rate according to the variation of the channel. Moreover, to adopt the constant bit rate data, the proposed system also employs a channel activation technique. Computer simulation confirms that the proposed system is very effective for multi-media communication services.
Sadayuki ABETA Hiroyuki ATARASHI Mamoru SAWAHASHI Fumiyuki ADACHI
This paper compares the packet error rate (PER) performance of three access schemes, i.e., single-carrier (SC)/DS-CDMA, multi-carrier (MC)/DS-CDMA, and MC-CDMA assuming an 80-MHz bandwidth in order to achieve an optimum broadband packet wireless access scheme. In a broadband propagation channel, severe multipath interference degrades the accuracy of timing detection of multipath components (path search) and channel estimation required for coherent detection. Computer simulation results show that, in the reverse link, SC/DS-CDMA achieves better performance than MC/DS-CDMA because the pilot signal power in one sub-carrier required for path search and channel estimation decreases as the number of sub-carriers increases. The superiority of MC-CDMA to MC (SC)/DS-CDMA in the forward link is also demonstrated, because frequency diversity is effectively utilized in association with the mitigation of a much longer symbol duration than the delay spread in MC-CDMA, meanwhile a higher degree of multipath interference offsets the Rake time diversity in MC (SC)/DS-CDMA in a broadband multipath fading channel.
Hiroyuki ATARASHI Sadayuki ABETA Mamoru SAWAHASHI
This paper evaluates high-speed broadband packet wireless access in the forward link using coherent Time Division-Orthogonal Frequency and Code Division Multiplexing (TD-OFCDM) by applying time-multiplexed pilot symbol assisted channel estimation and integrating efficient multi-level modulation, hybrid automatic repeat request (ARQ), and code-multiplexing over a 50-100 MHz bandwidth. Computer simulation results first clarify that the common time-multiplexed pilot symbols with the transmit power of 6 dB higher than that of data symbols should be placed at both the beginning and end of a packet, and that the optimum averaging interval of channel estimates in the frequency domain is different according to the delay spread of a channel. Based on these optimized parameters for packet transmission, we show that the orthogonality among the code-multiplexed channels is destroyed due to severe frequency selective (multipath) fading and the accumulation of spread signals using equal gain combining (EGC) in the frequency domain. This degrades the achievable throughput performance especially when employing multi-level modulation and a high coding rate. Consequently, coherent TD-OFCDM with 8PSK data modulation and the convolutional coding of rate R = 2/3 employing sixteen-code multiplexing (spreading factor (SF) is 16) achieves the highest throughput of approximately 105 Mbps at the average received Eb/N0 (signal energy per bit-to-noise power spectrum density ratio) of approximately 24 dB in a 3-path Rayleigh fading channel (rms delay spread, σ= 0.1 µsec). Furthermore, in coherent TD-OFCDM with QPSK and R = 4/5 or 8PSK and R = 1/2, throughput performance greater than 80 Mbps is achieved at the average received Eb/N0 of approximately 20 dB even in a 24-path Rayleigh fading channel (σ= 0.2 µsec).
Nobuhiko MIKI Hiroyuki ATARASHI Sadayuki ABETA Mamoru SAWAHASHI
This paper elucidates the most appropriate hybrid automatic-repeat-request (ARQ) scheme, i.e., which can achieve the highest throughput, for high-speed packet transmission in the W-CDMA forward link by comparing the throughput performance of three types of hybrid ARQ schemes: type-I hybrid ARQ with packet combining (PC), type-II hybrid ARQ, and basic type-I hybrid ARQ as a reference. Moreover, from the viewpoint of maximum throughput, the respective optimum roles of ARQ and channel coding in hybrid ARQ are also clarified, such as the optimum coding rate and the packet length related to the interleaving effect. The simulation results reveal that the type-II scheme exhibits the best throughput performance, and the required received signal energy per chip-to-background noise spectral density ratio (Ec/N0) at the throughput efficiency of 0.2/0.4/0.6 is improved by 0.7/0.3/0.1 dB and 3.9/1.8/0.5 dB, respectively, compared to the type-I scheme with and without PC in a 2-path Rayleigh fading channel with the average equal power at the maximum Doppler frequency of 5 Hz and the packet length of 4 slots (= 0.667 4 = 2.667 msec). However, the improvement of the type-II scheme compared to the type-I scheme with PC is small or the achievable throughput is almost identical in the high-received Ec/N0 region. On the other hand, the type-I scheme with PC is much less complex and thus preferable, while maintaining almost the same throughput performance or allowing very minor degradation compared to that with type-II. The results also elucidate that, while the optimum coding rate depends on the required throughput in the basic type-I and type-I with PC schemes, it is around between 3/4 and 8/9 in type-II, resulting in a higher throughput efficiency. In addition, for high-speed packet transmission employing a hybrid ARQ scheme, a shorter retransmission unit size is preferable such as 1 slot, and the fast transmit power control is effective only under conditions such as a low maximum Doppler frequency and a high transmit Ec/N0 region.
Nobuhiko MIKI Hiroyuki ATARASHI Sadayuki ABETA Mamoru SAWAHASHI
This paper compares the throughput performance employing hybrid automatic repeat request (ARQ) packet combining, i.e., Chase combining, and Incremental redundancy, considering the frequency diversity effect in the broadband forward-link channel for Orthogonal Frequency and Code Division Multiplexing (OFCDM) packet wireless access achieving a peak throughput above 100 Mbps. Simulation results show that the achievable throughput at the average received signal energy per symbol-to-background noise power spectrum density ratio (Es/N0) of 0 and 6 dB employing Incremental redundancy is increased by approximately 35 and 30% compared to that using Chase combining for QPSK and 16QAM data modulation schemes with the coding rate of R = 1/2, respectively, considering a large frequency diversity effect in a 12-path exponential decayed Rayleigh fading channel, since the reduced variations in the received signal level in a broadband channel bring about a larger coding gain in Incremental redundancy. We also show that when adaptive modulation and channel coding (AMC) is applied, Incremental redundancy is superior to Chase combining since the large coding gain is effective in achieving a large time diversity gain for a low number of retransmissions such as M = 1 or 2 for a maximum Doppler frequency up to fD = 400 Hz. It is demonstrated, nevertheless, that the total throughput when employing Incremental redundancy associated with a near optimum MCS set according to the channel conditions becomes almost identical to that using Chase combining when a large number of retransmissions, M, is allowed, such as M = 10, owing to time diversity along with frequency diversity.
Akihito MORIMOTO Sadayuki ABETA Mamoru SAWAHASHI
This paper investigates the effect of fast cell selection (FCS) associated with fast packet scheduling methods and hybrid automatic repeat request (HARQ) with Chase combining, in which the optimum cell (or sector) transmitting a slot-assigned downlink shared channel (DSCH) is selected based on the received signal-to-interference power ratio (SIR), in high-speed downlink packet access (HSDPA). The Round robin (RR), Proportional fairness (PF) and Maximum carrier-to-interference power ratio (CIR) schedulers are used as the scheduling algorithm. The simulation results elucidate that although almost no additional diversity gain through FCS is obtained for the PF and Maximum CIR schedulers, the improvement in throughput by FCS coupled with the RR scheduler is achieved. Furthermore, we elucidate that the effect of FCS is small when only inter-sector FCS is performed; however, inter-cell FCS is effective in improving the radio link throughput for the access users with a lower received SIR near the cell edge. The radio link throughput at the cumulative distribution of 20% of soft handover users when both inter-sector and inter-cell FCS are performed is increased by approximately 20% and 60% for PF and RR schedulers, respectively, compared to that without FCS, i.e. with hard handover. We also show that when a traffic model such as the modified ETSI WWW browsing model is taken into account, the effect of FCS associated with the decreasing effect of fast packet scheduling is greater than that assuming continuous packet transmission. The user throughput at the cumulative distribution of 20% employing both inter-sector and inter-cell FCS is increased by approximately 60% compared to that without FCS.
Nobuhiko MIKI Hiroyuki ATARASHI Sadayuki ABETA Mamoru SAWAHASHI
This paper presents a comparison of the throughput performance employing hybrid automatic repeat request (HARQ) with packet combining, such as Type-I with packet combining (simply Chase combining hereafter) and Type-II (Incremental redundancy hereafter), using turbo coding in a multipath fading channel in high speed downlink packet access (HSDPA). We apply a multipath interference canceller (MPIC) to remove the influence of severe multipath interference. Link level simulation results show that the maximum throughput using Incremental redundancy with 64QAM is improved by approximately 5-8% compared to that using Chase combining, and that the required average received signal energy of 12 code channels per chip-to-background noise spectrum density (Ec/N0) at the throughput of 4 Mbps with Incremental redundancy is decreased by approximately 1.0 dB rather than that with Chase combining when the vehicular speed is higher than approximately 30 km/h. Furthermore, we elucidate based on the system level simulation that although no improvement is obtained in a slow mobility environment such as the average vehicular speed of 3 km/h, the achieved throughput of Incremental redundancy is increased by approximately 5-6% and 13% for the average vehicular speed of 30 km/h and 120 km/h, respectively, compared to that with Chase combining.
Akihito MORIMOTO Sadayuki ABETA Mamoru SAWAHASHI
This paper proposes cell selection (CS) based on shadowing variation for the forward-link Orthogonal Frequency and Code Division Multiplexing (OFCDM) packet wireless access. We clarify its effects using a broadband propagation channel model in a comparison with fast cell selection (FCS), which tracks the instantaneous fading variation, and with the conventional slow CS, which tracks only the distance-dependent path loss, based on radio link level simulations that take into account time-varying instantaneous fading and shadowing variations. The simulation results show that the achievable throughput with FCS improves slightly in a broadband channel with an increasing number of paths when the average path-loss difference between two cells is greater than 2 dB. Nevertheless, we show that the optimum CS interval becomes approximately 100 msec, because the interval can track the time-varying shadowing variation considering low-to-high mobility up to the maximum Doppler frequency of 200 Hz. Consequently, we show that the throughput by employing the CS based on shadowing variation with the selection interval of 100 msec is increased by approximately 5 and 15% compared to that using the conventional slow CS with the selection interval of 1 sec, for the maximum Doppler frequency of 20 and 200 Hz, respectively.