# Why do we ever use low-order modulation schemes?

Many communication standards implement adaptive modulation and coding with modulation and coding scheme (MCS) tables. In these tables, we typically use low order modulation for low spectral efficiency. For example, in the "MCS index table 1 for PDSCH" of 5G NR, QPSK is used to deliver spectral efficiency from 0.2344 to 1.3262 bits; beyond these, we use 16-QAM for spectral efficiency from 1.3281 to 2.5703 bits; and so on, c.f. 3GPP TS 38.214 Table 5.1.3.1-1.

It is, however, well known that to achieve the same data rate, higher-order QAM is always more energy efficient than lower-order QAM, c.f. Figure 2 of Ungerboeck's celebrated paper on TCM. For example, to transmit 1.5 bits with 16-QAM requires ~0.6dB less (SNR) than with 4-QAM (QPSK).

Why do we ever want to use QPSK or BPSK? Why don't we just use 64-QAM (or 256-QAM) together with low rate channel coding? Is it because channel coding/decoding complexity is higher when we use only high-order modulation?

• Could you give an example of "just use 64-QAM (or 256-QAM) together with low rate channel coding"? Oct 25, 2023 at 11:19
• "to achieve the same data rate, higher-order QAM is always more energy efficient" -- Have you considered the error rate? I'd suggest adding equations to your question that quantify the benefits/disadvantages of increasing the modulation order.
– MBaz
Oct 25, 2023 at 13:18
• @AlexTP For example, QPSK with a channel code of R=1/2 delivers spectral efficiency of 1 bit. Alternatively, we can deliver 1 bit with 64QAM and a channel code of R=1/6. Oct 26, 2023 at 2:08
• @MBaz The figure in the question quantifies the difference in energy (SNR) efficiency. It's computed by the channel capacity formula, i.e. $C=I(X; Y)$ where $X$ denotes the channel input (random variable) and $Y$ the channel output (random variable.) Oct 26, 2023 at 2:18
• @syeh_106 by talking about channel capacity, is your question about Shannon random codes (or rate bounds in finite blocklength regime) or practical codes (ie structured codes to reduce the decoding complexity)? Also, do you assume infinite codeword length (eg for system design) or finite length (eg more about point to point communication)? Sorry too many questions, just because this is a very large and subtle subject. Oct 26, 2023 at 10:40

As we go for higher modulation order, detection complexity increases by exponentially , Hypothesis grows and detection becomes computationally intensive task.

Also in use cases where channel condition is poor, bandwidth efficiency has to sacrificed switching to lower modulation schemes as channel becomes susceptible to noise and interference.

One of the Key factor is power consumption too, transmission by lower modulation order has less power consumption. In short, there is a tradeoff always depending upon the requirements and each scheme comes with its pros and cons

• " in use cases where channel condition is poor, bandwidth efficiency has to sacrificed switching to lower modulation schemes..." When the channel condition is poor, e.g. SINR is low, it means we need reduce transmission rate. This can be done with low order modulation or low rate channel coding. So this doesn't necessarily justifies low order modulation. Oct 26, 2023 at 3:31
• "transmission by lower modulation order has less power consumption" This is not true. The amount of power is something we can/should choose to meet our performance goal (e.g. data rate). In fact, information theory (e.g. the paper in the question) tells us that to deliver 1 bit reliably, it takes less (average) power to use 64QAM with a channel code of R=1/6 than to use QPSK with a channel code of R=1/2. Oct 26, 2023 at 3:42
• Detection complexity is indeed higher for higher order modulation. Thanks for pointing this out. This and the complexity in decoding appear to be the main reason for opting for low order modulation, when low spectral efficiency is needed. Oct 26, 2023 at 8:15
• For example, consider (A) QPSK with a rate 1/4 channel code, and (B) 64QAM with a rate 1/12 channel code, both delivering 0.5 bit per channel use. The complexity for detecting 64QAM of Option (B) is clearly much higher. Moreover, the channel decoder of (B) needs to process 3X more coded bits. And what do we really gain with (B)? At this low spectral efficiency of 0.5 bit per channel use, the SNR advantage of (B) is no more than 0.02dB. Oct 26, 2023 at 8:21
• @syeh_106 "At this low spectral efficiency of 0.5 bit per channel use, the SNR advantage of (B) is no more than 0.02dB" how do you come up with this conclusion? Oct 26, 2023 at 8:35

As indicated by the figure quoted by the OP, indeed, Ungerboeck discovered that in AWGN channel, with high-order modulation scheme to transmit lower number of bits per symbol is more power efficient than using the lower order modulation. For instance, while usually we use QPSK modulation for the purpose of transmitting 2 bits per symbol interval, Ungerbock pointed out that for the same purpose, if we use 8PSK (or 16QAM) constellation for modulation, we can get some power gain, that is, we can achieve the same BER under a lower SNR without sacrifice of bandwidth efficiency. From there, in 1980's, Ungerbock officially published his famous paper to propose the new coding technique, so-called "Trellis coding modulation (TCM)". Following his paper, TCM became a very hot research topic in the whole world and soon got many applications, such as in satellite communications, modem designs, wireline data transmission systems, and soon.

It should be noted that the gain indicated by the above figure is a theoretical result. It is not available automatically without extra cost. Instead, in reality it needs some sort of coding techniques with a certain complexity.

Later after turbo coding (TC) (as well LDPC) appeared and getting hot, TCM is eventually cooled down, since the former provides more coding gain with lower complexity.

One major motivator for choosing a low-order modulation scheme such as BPSK or QPSK over 16-QAM or 256-QAM is improved energy efficiency. Different modulation schemes require different Eb/N0 for a given BER. Eb is the RF signal energy per bit, and N0 is the noise power spectral density. Assuming that N0 does not depend on the modulation scheme, this simply means that the schemes require different amounts of received signal energy per bit to achieve a given BER. A lower Eb/N0 requirement thus implies that less signal energy needs to be transmitted per bit.

For better TX energy efficiency, it is thus good to use a modulation scheme that requires as low Eb/N0 as possible for the targeted error probability. From this perspective, it is good to choose BPSK, QPSK or, even better, an orthogonal modulation scheme such as M-PPM or M-FSK with a very high M. The improved energy efficiency, however, often comes at the cost of spectral efficiency.

For a battery-powered wireless device, choosing BPSK over 256-QAM would generally improve the device lifetime. On the contrary, in an application where power and energy consumption are no concern at all, choosing 256-QAM or even 1024-QAM would of course make more sense because of the higher data rate.

In contrast to what the OP says, use of higher-order QAM is generally not more energy-efficient than use of lower-order QAM -- the higher the order, the greater Eb/N0 is required.

One can reach these conclusions by reading communications literature and by performing waveform-level RF signal reception simulations using Matlab or Octave. Particularly performing the simulations is recommended for understanding the differences between modulation schemes.

Additionally note that, compared to the simpler modulation schemes, the generation of QAM signals may require more complex electronic circuitry (i.e. a greater amount of high-power-consuming circuit blocks). It is easier to achieve high TX/RX power-efficiency using OOK/BPSK/BFSK compared to 1024-QAM.

• Here is an example consideration that might help: For BER=10^-5, 16-QAM and 256-QAM with square constellations require Eb/N0 of roughly 13.6 and 22.9 dB, respectively. If you use 256-QAM instead of 16-QAM, you ideally need to transmit approx. 751% more signal energy per bit. Choosing 16-QAM could avoid severe excessive TX energy consumption here. Dec 29, 2023 at 12:06
• Thanks for taking time to write an answer & comments. But you missed something in the comparison: coding. Without channel coding, 16QAM delivers 4 bits, while 256QAM delivers 8 bits. This is not an apple-to-apple comparison. For a fair comparison, we should include channel coding, e.g. 16QAM with R=1/2 code vs 256QAM with R=1/4 code. You may check out Ungerboeck's celebrated paper for more details: ieeexplore.ieee.org/document/1056454 Jan 2 at 8:29
• You are welcome. I have not read much about coding. I took a look at Ungerboeck's masterpiece (it has got a pretty impressive amount of citations!). Jan 8 at 1:42
• I think I understand Ungerboeck's main point there. Anyways, whatever advantages and disadvantages coding may bring, I believe that the main trade-off is still between spectral efficiency and energy efficiency. The low-order modulation schemes tend to require low Eb/N0 and are therefore energy-efficient. If you know a modulation scheme, be it with or without coding, that requires a low Eb/N0 and offers high spectral efficiency, that could be a better choice in some cases (e.g. if it does not increase TX/RX complexity and power consumption excessively). Jan 8 at 2:04
• "For example, to transmit 1.5 bits with 16-QAM requires ~0.6dB less (SNR) than with 4-QAM (QPSK)." <-- As a reply to this: a 0.6-dB reduction in the required Eb/N0 in many cases might not be worth the trouble of designing a 16-QAM TX+RX instead of QPSK TX+RX. The required extra electronic circuitry could consume so much power that even the 0.6-dB improvement is not truly achieved. Also, on consumer market, the higher data rate achievable with the 16-QAM TRX could sell more stuff than the lower-data-rate coded-16-QAM system. Jan 8 at 2:36