In this section, we propose a solution to the issues present in the LTE-eMTC. The new design is specifically optimized for LTE MTC operating on narrow bands, henceforth referred to as “LTE-nMTC” or simply nMTC.
3.2. Simplified Random Access Signaling
The preamble in LTE random access does not contain any kind of device identifier, thereby causing ambiguities among accessing devices. Then, the contention resolution message is used to solve the problem. As noted before, the objectives for the MTC are very different from these of the traditional mobile broadband LTE in that MTC is mainly for the delivery of relatively small datagrams with low cost devices, high energy efficiency (long battery life), and relaxed latency requirements. This is precisely in contrast to the mobile broadband LTE where the emphasis is on high data rates, low latency, and support of streaming data services. That is, only a small amount of application data needs to be transmitted per access. The overhead of the current LTE access method thus becomes significant, and may become a bottleneck in terms of battery life, considering that signaling takes much longer time to close the MTC link than in the legacy mobile broadband LTE due to the reduced capability of an MTC device and the need for coverage extension (we will see more detailed discussions in this regard in
Section 4. Simplification of the random access procedure can potentially save device power as a result of the elimination of the preamble and the contention resolution from the random access procedure.
There are two goals of the random access preamble, one is to indicate the presence of the device and the other is to provide a means of estimating the round-trip propagation delay of the device at the receiver. The information exchange between the base station and the device follows the preamble is to solve the potential collisions. We use a special orthogonal frequency division multiplexing (OFDM) signal to accomplish these goals. This idea is the extension of our previous work [
21]. For ease of comprehension, we first briefly review some of our previous work in this subsection.
Figure 2 shows the proposed random access signal and the corresponding arrive time at the base station. Guard Time (GT) is used to prevent the random access signal from distorting the following data channel due to the round-trip propagation delay. Our proposed random access signal is a modulated signal that contains the random access message
just like the signal in the data channel. Apparently, random access signals from different devices arrive at the receiver at different time due to the round-trip propagation delay. So, we can use a long CP (e.g.,
for a cell size of 5 km) to absorb the round-trip delay. It makes the signal in the DFT window is a full ODFM symbol without the inter-symbol-interference (ISI) and the inter-carrier-interference (ICI) [
20]. After the system acquisition in the downlink, the frequency offset is corrected. The residual frequency offset is small and has less of an effect on decoding an OFDM symbol. Besides this, our proposed random access signal can achieve a good PAPR by using single-carrier frequency division multiple access (SC-FDMA) just like the data channel. It is obvious that long CP will increase the overhead of an OFDM symbol, but it will be compensated by using a longer OFDM symbol (i.e., smaller subcarrier spacing) as will be seen later.
We assume that the random access signal occupies subcarriers in frequency domain and OFDM symbols in time domain, the bandwidth for RACH channel is which consists of subcarriers. Then, the number of random access channels is . Apparently, the subcarrier spacing is and the transmission bandwidth of the access signal is .
The message
contains a 10-bit access ID, 4-bit resource request, and 10-bit CRC, resulting in a message that has
information bits (more details can be found in [
21]). The device sends message
on one of
random access channels which is randomly selected. The access ID in our design is similar to the temporary ID in LTE random access procedure to distinguish the devices within the cell. The device randomly selects an access ID from a pool of
IDs. The 10-bit CRC is using to check the decoding status at the receiver.
The false alarm of decoding access message is caused by the CRC check error which is very small and can be ignored.
Figure 3 shows the simplified random access procedure for LTE-nMTC.
Although the access message decoding does not require the timing information due to the protection of the long CP in the current design, the round-trip propagation delay of the access signal,
, still remains unknown and needs to be estimated from the detected access request signal by the base station. The estimated delay is then attached to the uplink resource assignment message (cf.
Figure 3) so that the device can adjust its transmission time (according to
) to ensure the time alignment of the subsequent uplink transmissions (including data and control channels) from different devices. A smaller CP can then be used only to accommodate the multipath spread on the traffic channel. The propagation delay estimation using the access request signal is described in
Section 3.4.
The probability of an access channel which is selected by more than one device is
This is the random access channel collision probability. Another collision situation is that more than one device select the same access ID. It can be expressed as
where
is the size of the access ID pool. Therefore, the total collision probability can be written as
In general, the number of access channels is smaller than the number of total access IDs. Therefore, . When an access channel is selected by more than one device, there will be a decoding failure at the base station. The device will prepare another random access attempt when there is no uplink resource assignment to itself in a given duration. Apparently, the collision will increase the air time.
Reducing the collision probability requires an increase in the number of access channels,
. However, for a given total random access bandwidth of
, a larger
means a smaller bandwidth (
) per random access channel, a lower data rate that each channel supports, and a longer transmission time for a device. The following question then arises: Given a bandwidth of
, what is the resource configuration scheme for the random access channels (i.e., the bandwidth of a random access channel) that minimizes the overall access request message transmission time? We use the “effective bandwidth” to solve this question [
22].
3.3. Effective Bandwidth and Optimal Resource Configuration
The SNR of an OFDM resource element (RE, i.e., a subcarrier over the duration of an OFDM symbol
) of the random access channel can be represented as
as a result of matched-filtering via DFT, where
is the length of an OFDM symbol in time domain,
is the noise density,
is the noise figure, and
is the coupling loss whose value depends on the MTC coverage class of the device:
155, 150, 145, and 140 dB for channel coverage classes 1, 2, 3, and 4, respectively. Apparently, the total number of REs per OFDM symbol is
per channel, yielding the maximum data rate (bits/OFDM symbol) of
or, the maximum data rate in bits/sec of
Taking into account the imperfection of a realistic system, (9) becomes
where
is a scaling factor to reflect the gap between the Shannon capacity and a realistic system.
is a monotonically increasing function of
. Then the transmission time of the access request message
is given by
It means the larger the
is, the larger the data rate, and the smaller the transmission time. In fact, when
,
which represents the
minimum transmission time for message
, i.e.,
given
or the coverage class.
Figure 4 plots (11) relative to
, i.e.,
for devices belonging to the four coverage classes, which represents the extra transmission time due to the use of a finite transmission bandwidth
(i.e.,
). In
Figure 4,
= 20 dBm is the uplink transmit power,
5 dB, and
−6 dB.
From
Figure 4, we can see that the transmission time is monotonically decreasing with respect to the signal bandwidth as we analyzed before. But the decreasing slope of the transmission time is not linear. There is an effective bandwidth
for every coverage class such that once exceeded, increasing bandwidth has less effect on decreasing the transmission time. If we define
as the effective bandwidth, at which
is equal to, e.g., 10%, the
for coverage classes 4, 3, 2, and 1 are then 94, 30, 9, and 3 kHz, respectively. They are summarized in
Table 1. The lower the coverage class is, the less sensitive it is to bandwidth. Clearly, devices belonging to the class whose bandwidth is less than the effective bandwidth are therefore bandwidth-limited, and those whose bandwidth is greater than the effective bandwidth are power-limited. The effective bandwidth therefore provides a good balance between the spectral efficiency (or the total number of FDM channels that a given
supports) ant the transmission time. Since the effective bandwidth of a low coverage class is less than that of a high coverage class, more FDM channels are available for a low coverage class for a given total bandwidth.
Based on this effective bandwidth concept, the subcarrier spacing of 15 kHz for legacy LTE data channels is too large for MTC, and a finer granularity is needed. The subcarrier spacing is thus reduced by a factor of 5, i.e.,
3 kHz in the new design to match the smallest effective bandwidth (CC1). This idea is consistent with the design of NB-IoT design in which 3.75 kHz subcarrier spacing is used [
23]. The reduction of subcarrier spacing has the following implications: (1) Five times as many FDM channels for CC1 devices; (2) The OFDM symbol in time domain is elongated by a factor of 5, which boots OFDM symbol energy by 7 dB; and (3) The data channel CP length can also be increased by five times, i.e.,
while maintaining the same CP overhead
7% as in the legacy LTE,
7% [
24]. Longer CP allows for not only larger multipath spread but also more tolerance to timing errors which relaxes the uplink timing requirement. This is particularly beneficial since timing estimation is less accurate under narrow band than wideband due to the reduced time resolution. However, narrower subcarrier spacing also means more vulnerability to frequency offsets due to frequency tracking errors and/or Doppler spread but it is justified by a much lower mobility (hence lower Doppler effects) in MTC applications than HTC.
Note that
or
represents the transmission time for a non-contention based transmission in a collision-free environment as for the data transmissions. But the random access transmission is unscheduled or contentious. The actual transmission time is hence
plus the re-transmissions in the case of collisions whose probability is directly related to the number of random access channels,
, as given in (4), and is re-written here,
where
is the number of accessing devices. Therefore, the total transmission time is also a function of the collision probability, and can be derived as follows:
Clearly, due to the fact that in the contention-based random access.
Ultimately, we look for the
that minimizes (16). Alternatively, we search for the
that minimizes the extra time or penalty introduced by the
contention among
accessing devices. That is,
where
The optimal random access channel bandwidth in (17) is hence a function of the number of contending devices per random access opportunity.
Figure plots the time penalty,
in (17), as a function of
, which is a monotonically increasing function of
, for the four coverage classes. In
Figure 5,
denotes the
for CC
i. The transmission power of the device is
20 dBm, receiver noise figure
5 dB, and
dB. At an, e.g., 10% penalty, the devices that can be supported by
kHz is
for CC1 (
155 dB), and 3 for CC2 (
150 dB), whereas for CC3 (
145 dB) and CC4 (
140 dB)
dwindles down to less than two. On the other hand, in order for all high coverage classes to support the same number of devices as CC 1, i.e.,
, they have to live with much higher penalties, i.e.,
(for
150, 145, and 140 dB).
This phenomenon can be better explained using
Figure 6, where we observe that for CC 1 (
155 dB) and at
, the optimal bandwidth equals the effective bandwidth, i.e.,
. The 10% performance penalty is thus purely attributable to collisions. Whereas in order for higher coverage classes to support
, each random access channel of these classes has to settle with an optimal bandwidth
that is much smaller than the effective bandwidth
, i.e.,
(
150, 145, and 140 dB) as shown in
Figure 6, in order to make room for a sufficient number of FDM channels,
. The resultant bandwidth deficit (i.e.,
) gives rise to high performance penalty, i.e.,
.
A solution to maintaining the collision at a reasonable low probability (corresponding to, e.g., 10% penalty) for high coverage classes without incurring high bandwidth deficit penalty is to add more random access channels per random access occasion in a time division multiplexing (TDM) fashion so that the total number of random access channels is increased by
times, i.e.,
, where
is the multiplicity of the TDM random access resources in time domain (cf.
Figure 7). The collision probability becomes
Clearly, (19) is less than (15) for . Nevertheless, more TDM resources are needed to compensate for the shortage in bandwidth.
Referring back to
Figure 5 (dotted lines), we show the values of
needed for high coverage classes, i.e.,
,
12, and
36, such that
can be supported without incurring the bandwidth deficit penalty, i.e.,
for
150, 145, and 140 dB. That is, the penalty due to contention is below 10% as long as the number of concurrent contending devices is less than 7 (cf.
Figure 6). In the following discussion,
is hence assumed to be 7 unless otherwise specified. The implication of
on the overall random access capacity will be discussed in
Section 4.4.
The optimal channel configurations are summarized in
Table 2, whereas
Table 3 is for
1.08 MHz to show the bandwidth scalability of the design. We observe that the confliction between the channel bandwidth and the total number of channels is less severe under a wider bandwidth (
1.08 MHz), in which less deficit exists between
and
, thereby, less performance loss is attributable to the bandwidth deficit.
Figure 7 is a block diagram illustrating the random access channel configuration for
180 kHz, where the number of subcarriers is chosen to be
60 which results in a subcarrier spacing of 3 kHz that matches the optimal bandwidth
(cf.
Table 2) by design. The CP overhead for an OFDM symbol is
9%. TTI is the transmission time interval of each random access channel (see
Figure 2 and
Figure 3), which is related to the link budget of the coverage class, and will be determined in
Section 4.