LTE explained… to people like me! — Part 2: modulating the pipes

LTE explained… to people like me! — Part 2: modulating the pipes

In Part 1, we examined the fundamentals around how LTE uses increasing amounts of radio bandwidth in order to transmit more data. In this second part, we will dig into how data is modulated on an LTE carrier, how power levels and interference between cells limit service availability, and why this is important in order to understand how can LTE service be provided from a ballon in the stratosphere.

Modulating data bits onto a carrier

We can change three properties of a carrier in order to superimpose logical 1s and 0s over it — frequency, phase, and amplitude. These methods can be described in a very simplified manner:

In FSK, we indicate the presence of a 1 or a 0 by a change of the frequency within the bit period. In this example, we are aligning a logical 0 to a full sine cycle at the low frequency, and a logical 1 to two and a half sine cycles at the high frequency.

In PSK, instead of changing frequency, we change the phase when we want to transition from a 1 to a 0 or vice-versa.

Finally, in ASK, we change the amplitude of the carrier to indicate a logical 1 or 0.

Scotty, we need more bits!

Using these simple methods, the amount of data we can encode onto a carrier is quite limited, resulting in low throughput. The upside is that the communication is extremely reliable, detectable below the noise floor in some extreme cases such as Lentus, which takes five minutes to transmit a 75-bit message!

As a general rule, the faster & more complexly we modulate a carrier, the more data we can transmit in a given slice of time, but also, the more vulnerable it becomes to noise, interference, and fading.

This can be visualized by how a 1-second-long noise event affects two different carriers, modulated at different rates (sine waves are just illustrative, not to scale!):

In the top signal, only one bit of information is lost. Depending on the error correction algorithms in use, such as FEC, a single bit or more can be recovered without re-transmission of the entire message. In the bottom signal, however, the same noise event causes the loss of 10 bits, which could be unrecoverable and require a re-transmission, significantly lowering the effective throughput in noisy channels.

But Scotty, we need even MORE bits!!

In order to get even more bits through the same channel, we need to introduce the concept of symbols. In simple terms, a symbol can be described as a discrete state change in the transmitted signal in a unit of time, which can be translated to one or more bits per symbol. In our examples so far, a symbol has equated a single bit, as the changes to the carrier have been one of two discrete states (high/low frequency, large/small amplitude, etc.).

By introducing more than two possible states per unit of time, we can “cram” more than one single bit in said unit of time.

If we re-visit PSK, we have so far modulated our carrier with BPSK, or binary phase shift keying. The two phases are separated by 180º, and are mapped to a 1 or a 0. The constellation diagram on the left shows the two states in a graphical way.

The first increase in modulation order is found in QPSK, or quadrature phase shift keying. We now use four phases, 90º apart, to represent four discrete states. Two bits can then be mapped onto each state or symbol, as shown again in the constellation diagram.

If we want to go one step further, 8-PSK allows eight different phase shifts, resulting in three bits per symbol. Higher orders of phase shifting are prone to large error rates, and are not implemented in live systems.

We may have reached the end of the road as far as pure phase shifting is concerned, but what if we combine phase and amplitude shifts? We get into the territory of amplitude or asymmetric shift keying, which leads us to quadrature amplitude modulation (QAM). On the left, the 16QAM constellation with four bits per symbol is shown.

How far can we take this?

Spock, go check on Scotty — I think he can’t carry so many bits…

At this point, we are in the realms of esoteric concepts such as the I (in-phase) and Q (quadrature) components of the carrier, and complex mathematical equations to integrate phase, amplitude and frequency into an even more complex RF signal. This is the formula that represents the I/Q components of a narrowband signal:

Yeah. Me neither. It’s all the brackets that confuse me…

Modulation schemes in LTE

LTE has a number of modulation schemes to choose from, and it can apply them liberally, as required by the combination of reliability and throughput for each specific message that needs to be sent, and the conditions of the channel, in terms of noise and interference. From a slow but reliable QPSK at 2 bits per symbol, Release 12 of the LTE standard caters for 256QAM, which provides 8 bits per symbol. We can see 256QAM graphically, through the capture of the real-time constellation of an AirFiber 5X HD point-to-point link in operation:

Interestingly, there are moments when the link conditions improve for one of the radios, and it decides to jump onto an even higher order modulation, 512QAM, which provides 16 bits per symbol! Newer LTE releases specify up to 1024QAM in the downlink, only possible as the processing capabilities of networks and user devices increase over time.

Resource blocks, resource elements, frames, subframes…

We are going to peel this onion in reverse, and see how data is organized and overlaid across subcarriers and time elements.

The smallest data carrying element in LTE is the Resource Element (RE). This is defined as one subcarrier by one symbol, or 15 kHz in bandwidth by ~71 nanoseconds in time. We then add REs in both time and frequency domains, and we end up with this structure:

7 REs in time domain, combined with 12 REs in frequency domain, make up a Resource Block (RB), which is 0.5ms “long” and takes up 180 kHz of bandwidth. A resource block is defined as a slot in the time domain, two RBs make up for a subframe, and ten subframes make up for a full LTE frame. A frame then takes up however many subcarriers are available in the frequency domain, in the above diagram, 72 in a 1.4 MHz wide LTE channel. In the 10 MHz channels on Band 20 we have been studying, we have 50 RBs in the frequency domain. It is my understanding, but have not been able to verify this, that the same modulation scheme is applied to a whole RB, thus, we cannot modulate one RE with QPSK and another RE in the same RB with 64QAM. If you know for sure, please do let me know in a comment!

LTE channel structure

As with any system where a central entity controls access to resources, marshals client entities, and needs to keep everything in sync, the LTE standard specifies a large number of different physical channels, dedicated to different tasks, such as providing timing sync and initial information required for cell selection, broadcasting specific details about the network (such as the MCC and MNC), or sending traffic to UEs. The main physical channels defined in the downlink are depicted below:

We can see that within a 10ms frame, an LTE cell uses a few symbols in the six central RBs to send synchronization information, which is modulated at QPSK to increase robustness, while some slots such as #19 is fully dedicated for traffic data, at whatever modulation order has been determined to be viable.

The physical channels seen in the figure are:

• Physical Downlink Control Channel (PDCCH): It allows UEs to get resource allocations for uplink and downlink, and uses QPSK modulation.
• Physical Control Format Indicator Channel (PCFICH): This channel indicates the number of symbols used to transmit the PDCCH, uses QPSK modulation, and can take a value of 1, 2, or 3.
• Physical Downlink Shared Channel (PDSCH): UE traffic data is carried by this channel, and it can use the higher-order modulations available, plus spatial multiplexing via MIMO.
• Primary Synchronization Signal (P-SS): During cell search, a UE uses the P-SS to acquire slot-level timing, and frequency information. Part of the cell ID is carried by the P-SS.
• Secondary Synchronization Signal (S-SS): The S-SS is also used by UEs during cell search, and provides frame-level timing, plus the rest of the cell ID not carried in the P-SS. This signal uses BPSK for even greater robustness, and carries two 31-bit binary sequences.
• Physical Broadcast Channel (PBCH): Information specific to the cell, and parameters governing access control are sent on this channel, using QPSK.

Enough theory, let’s see some real action

The way an LTE cell, in cooperation with the UE (the fancy acronym for your smartphone…), picks the most adequate modulation scheme in real time, can be seen in this short video of a real test against speedtest.net on Vodafone’s LTE network in Band 20:

Initially, the UE is idling, with modulation scheme set at QPSK, the lowest available, and the one that consumes the least amount of resources. Once the test begins, first in the download channel, the modulation changes to constant 16QAM, the highest that can be achieved, while we see error rates in the region of 10–15% tops. Download speed is OK at 7–8 Mbps. Once the upload test starts, we see the uplink modulation vary between 16QAM and QPSK, and an error rate close to 30% at times.

The reason for this delta is that the cell transmits at up to 46 dBm, into an antenna that could have an extra 15 dB of gain, whereas the UE is only capable of transmitting at 23 dB, and suffers from a loss in the antenna and feeder subsystem, that can be as high as 3 dB (effectively halving the power!). Thus, whilst the UE can hear the cell quite well, and suffer from few errors, the cell is not able to make out the UE too much above the noise floor, and as a result, large error volumes cause re-transmits and a drop in modulation scheme to compensate.

When a UE is in this situation, it will also need to use high transmit power levels in order to reach the cell, resulting in severe impact on battery life.

If you have traveled to a different region or country, and ever wondered “hmmm, my battery seems to deplete awfully fast here, but back home it’s fine!”, it could be due to poor planning, or use of larger cells, by the local operator, resulting in a higher average transmit power required by your smartphone to reach the network. The problem is compounded by the increased error rates and worse modulation schemes, as we have seen in the video, both of which result in longer transfer times of the same volume of data, and in turn, the higher transmit power levels get used for longer periods of time.

Back to basics — or why you can’t beat physics with math

Remember from Part 1, when I showed a DTMF tone, and in the spectrum graph, two very distinct peaks? They are so clearly discernible, that very simple filters could tell the two tones apart, and decode the key that was pressed. Now, look at this spectrum graph, which shows two 10 MHz LTE carriers from two of my local operators (Vodafone and Orange):

The Orange cell is literally 150m from my house, whereas the nearest Vodafone cell capable of giving me service is about 1.5 km away. This is clearly visible in the spectrum, with clean, defined subcarrier peaks on the Orange carrier, against diffused and garbled subcarriers on Vodafone. Here is capture of three Band 20 LTE carriers, from Vodafone, Movistar and Orange, at 796, 806, and 816 MHz center frequencies:

It is really clear how the modulated REs are visible and discernible to the naked eye on the 796 and 816 MHz carriers, whereas the 806 MHz carrier, being the Vodafone distant cell, still has modulation elements visible, but they are confused and garbled with the background noise. A UE has the same level of trouble as your eyes, when it has to decode the information transmitted by each of these three cells.

What this means, in practice, is that whilst you can use techniques to discern signals from noise that lean heavily on math, such as Kalman interpolation filters, there are limits imposed by physics, such as signal-to-interference-plus-noise ratio (SINR), interference, multipath, destructive fading, poor electronics and RF path design in low-cost devices, and so on. No matter how hard you try, you won’t be able to achieve 64QAM or 256QAM on the Vodafone signal, given the basics: poor signal strength, and thus poor SINR. The LTE cell will need to use lower modulation orders in order to allow your UE’s receiver to successfully decode the 1s and 0s being sent to you.

One big strength of LTE, however, is that it can use QPSK towards your distant UE, and 256QAM on the next RB towards another user that’s right next to the cell, switching between schemes on the fly as determined by the measured channel conditions.

Summary

In this second part of my series on LTE, we saw how binary bitstreams are modulated onto physical radio carriers, and how increasing bandwidth and complex modulation schemes combined can greatly increase the achievable data rate, and the relationship between SINR and channel capacity. We also examined some real-world spectrum traces, and how a distant serving LTE cell causes a smartphone to use higher power levels in order to be heard, while reducing the effective data rates it can achieve.

In Part 3, we will get out on the field, check practical LTE coverage, examine the effects of interference between subcarriers and between cells, and tie it all into how a high-altitude platform such as Loon interoperates with a terrestrial LTE network.