# Talk:Spectral efficiency

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I added D-AMPS to comparison table. some notes:

• D-AMPS (formal standards IS-54 and later IS-136) is actually 6 time slots, not 3 slots. but in real world installations 2 slots were always paired to achieve 13kbps, since 6.5kbps vocoders were not good enough at the time. so i wrote 13kbps * 3 slots in the table.
• technically, 13kbps is the data rate used for voice. for data transmission, the theoretical maximum data rate is 16kbps. since it was rarely achieved in practice, i kept the widely-known 13kbps figure.
• mentioned 1/7 reuse factor comes from the common hexagonal tile configuration. this is widely known fact - you'll find a hexagonal tile diagram & explanation in virtually any book about cellular communications.
• common literature mentions reuse factor of 1/4 or 1/5 when using sector antennas, but this is true for most other communication systems and not just D-AMPS. i kept with the conservative 1/7 reuse factor here, so that we'll have a apples-to-apples comparison with other standards. keep in mind that if you change reuse factors in other standards, you might want to change the factor for D-AMPS. it all depends on the antenna configurations... —Preceding unsigned comment added by 85.250.43.101 (talk) 16:21, 10 May 2008 (UTC)
• D-AMPS is a common name in the US only. in other parts of the world, it is referred to IS-54 and then later IS-136, not D-AMPS. —Preceding unsigned comment added by 85.250.43.101 (talk) 16:15, 10 May 2008 (UTC)

## Review

The definition could be a bit more general as it applies to more than digital. It could apply to analogue. It could apply to how spectrum is allocated by regulatory agencies.

What units of measurement do you have in mind? I mentioned system spectral efficiency in Erlangs/MHz/cell in the article, which also can be applied to analogue. Mange01 (talk) 22:16, 21 February 2008 (UTC)

The Shannon theorem formula should be here so that you can calculate bits per Hertz.

Telephone modem example is not strictly correct. If the bandwidth is filtered to the 3100 Hertz you will not get the 56000 bit rate through. To get that rate there will have to be less filtering. The channel will be quantized to 8 bits and so can only carry 16 bits per Hertz at the most.

correction: channel is quantized (on both sides) at 13 to 14 bits, and then u-law or a-law companded to 8 bits. 89.138.246.240 (talk) 00:12, 16 February 2008 (UTC)
I somewhat doubt that the baseband waveform used for digital modulation undergoes A/mu-law companding. Oli Filth(talk) 02:02, 16 February 2008 (UTC)
The modem compensates for the A/mu-law companding, meaning that it expands the 8 bit signal to a 13 bit signal before it sends it. So the modem can only use 8 bits per sample. (In Europe. Is it 7 or 8 bit in the U.S.?)Mange01 (talk) 22:16, 21 February 2008 (UTC)

"In wireless networks, the system spectral efficiency in bit/s/Hz/area unit, bit/s/Hz/cell or bit/s/Hz/site is a measure of the quantity of users or services that can be simultaneously supported by a limited radio frequency bandwidth in a defined geographic area."

This sentence packs in too many units - probably better to break it into two sentences with one unit in the first, and then an extension to the variations. Otherwise it is too confusing to read.

It would be good to add some analogue systems eg single sideband instead of AM or FM. We could have a bit of regulatory requirements. We could also have the tradeoffs, eg more power to get more signal to noise ratio, but more spectrum can reduce the power required.

In the comparason table it would be good to add some more, for example those landline modems, and some amateur digital radio schemes, some satellite transmission systems.

We could have a section on how efficiency can be improved, some techniques are mentioned in passing already.

Wouldn't that be the same as the article radio resource management? Mange01 (talk) 22:16, 21 February 2008 (UTC)

If I can find the time I may get around to some improvements over the next few months.

GB 22:47, 24 January 2007 (UTC) --

I see that Mehwoot has had a go at recalculating the spectral efficiency of a V.92 modem. However the raw bandwidth at the exchange is 0-4000 Hertz sampled at 8 bits at 8000 samples per second. An antialias filter will reduce this bandwidth somewhat below the 4000 Hertz limit. I will confirm what the rates are for what bandwidths. The maximum data throughput that could happen would be 64000 bits per second or 16 bits per Hertz. GB 06:30, 28 January 2007 (UTC)

Mehwoot was being an idiot and just changing random numbers, I'm pretty sure. It was probably correct the way it was.58.106.7.5 12:35, 27 April 2007 (UTC)

Good section. I like the take on bits/hz per area. This is particulary important for wireless broadband and converged wired-wireless networks.

Robert Syputa

## Bit/s/Hz

Huh? Hz = s-1, therefore Hz-1 = s. Hence, bits * s-1 * Hz-1 = bits * s-1 * s Hence, bits/s/Hz = bits.

So, why use units of bits/s/Hz for spectral efficiency, when "bits/s/Hz" is just a confusing way of saying "bits"? —The preceding unsigned comment was added by 124.189.8.183 (talk) 03:46, 3 March 2007 (UTC).

Because to say, for example, that GSM has a spectral efficiency of 0.52 bits would sound more confusing (although dimensionally correct). bits/s/Hz is the standard unit. Oli Filth 02:10, 10 March 2007 (UTC)
Actually, bit/s/Hz is even more common according to google. Just like bit/s is much more common than bits/s. Mange01 22:37, 30 April 2007 (UTC)
bits/s is incorrect, you can't add English "s" to a unit and make a unit plural, just like meters per second is not ms/s

By the way bits/s/Hz is not a unit, it violates at least two of metric system rules. If we want to keep Hz and s (which is allowed in metric system and makes sense here), it should be written as bit/Hz·s (or bit/s·Hz).

actually, the article correctly says "bit" not "bits", just the heading here doesn't —The preceding unsigned comment was added by 203.173.44.87 (talk) 01:15, 7 May 2007 (UTC).

No, bits/s/Hz = bits is incorrect. Hz is cycles per second, so Hz-1 is seconds per cycle, so bit/s/Hz is bits per cycle. But s and Hz are SI units, and cycle is not, so we say bit/s/Hz or some appropriate variant. Dicklyon (talk) 02:57, 16 February 2008 (UTC)

(ec) I'm not convinced this logic is correct, or if it is, we tend to ignore the issue in everyday usage. Take another example, Eb/No. We know that
$\frac{E_b}{N_0} = \frac{P_s T_b}{P_n / B}$
where Ps and Pn are signal and noise power, Tb is bit period, and B is bandwidth. Therefore, the units according to the above logic are
$\frac{\mathrm{W}.\mathrm{s}.\mathrm{bit}^{-1}}{\mathrm{W}.\mathrm{Hz}^{-1}} = \frac{\mathrm{W}.\mathrm{s}.\mathrm{bit}^{-1}}{\mathrm{W}.\mathrm{s}.\mathrm{cycle}^{-1}}$
or "cycles per bit". But we always refer to Eb/No as "dimensionless". Oli Filth(talk) 11:50, 16 February 2008 (UTC)

Well, at least it is established in literature and publications. A Google search and Google Book Search gives:

• bit/s/Hz — 42.900 web hits, 453 books [1]
• bits/s/Hz — 30.400 web hits, 360 books [2]
• b/s/Hz — 9.610 web hits, 291 books
• bits/sec/Hz — 4.760 web hits, 234 books
• system spectral efficiency — 2.440 web hits, 98 books [3]
• bit/sec/Hz — 1.830 web hits, 141 books
• bits per second per Hertz — 959 web hits, 198 books
• system spectrum efficiency — 904 web hits, 37 books [4]
• area spectral efficiency — 703 web hits, 41 books [5]
• bit/s/Hz/site — 411 web hits, 1 book
• bit per second per Hertz — 357 web hits, 24 books
• bits/s/Hz/cell — 250 web hits, 8 books [6]
• b/s/Hz/sector — 181 web hits, 5 books [7]
• bit/s/Hz/sector — 155 web hits
• b/s/Hz/m^2 — 89 web hits
• bits/s/Hz/m^2 — 58 web hits
• bit/s/Hz/m^2 — 36 web hits
• bit/s/Hz/km^2 — 31 web hits
• bits/s/Hz/km^2 — 9 web hits

Mange01 (talk) 11:47, 16 February 2008 (UTC)

Revised by Mange01 (talk) 22:47, 13 April 2008 (UTC)

• bits per cycle – 14 book hits [8] + 7 more singular [9]
• bits/cycle – 90 book hits [10] + 66 more singular [11]

Cycle measures added. Dicklyon (talk) 08:10, 27 December 2009 (UTC)

### bit/s•Hz

I reverted the addition of this new variant unit. This discussion followed: Dicklyon (talk) 08:10, 27 December 2009 (UTC)

WP:MOS#units gives clear guidance on how to format units. Reverting. 80.65.242.187 (talk) 05:41, 26 December 2009 (UTC)
WP:MOS#units does not seem to be a section. Can you provide a working link? I'm sorry about my edit summary on reverting your undo of my revert, as I didn't look in the right place here for your comments. If you want to propose a change to bit/s·Hz, I think you need to bring that up here, explain why, and point out at least a few dozen reliable sources that do it that way. Dicklyon (talk) 06:44, 26 December 2009 (UTC)
See the survey below. As you can see from links given there, 6/2/3 = 1 while 6/2·3=9. So bit/s/Hz = (bit/s)/Hz = bps/Hz is not equal to your suggestion bit/s·Hz. A horizontal division line has higher priority than multiplication, while the / division operator has the same priority as multiplication. Also note that a/b·c is not equal to a/bc. Theoretically bit/(s·Hz) would be the same thing, but the unit should indicate that we divide the bit rate in bit/s by the channel bandwidth in Hz.
We have a conflict between two WP principles here. (1) Wikipedia should not establish new standards and correct "great wrongs". (2) Wikipedia should use units that avoid confusion. Bit/s/Hz is the established unit in the literature in this field, while some people find it confusing and prefer (bit/s)/Hz. I think the current version of the article is a good compromise since it reflects both views. Regarding section 2 of the article - the system spectral efficiency - I think we have to use the established unit bit/s/Hz/site, since less confusing units would be really complicated. Mange01 (talk) 18:24, 26 December 2009 (UTC)
This is irrelevant, it is merely a matter of formatting; the unit is exactly the same. The Manual of Style specifies perfectly good practice for this case, and I see no reason to deviate from it. The relevant section is WP:Manual of Style (dates and numbers)#Unit symbols. However, I suggest you should have a passing familiarity with all of it before getting in the way of perfectly reasonable edits. 80.65.242.187 (talk) 07:35, 27 December 2009 (UTC)
Dismissing another editor's explanations and concerns as irrelevant is not likely to advance your position. And the section you reference says "There should be no more than one slash per compound unit symbol (e.g., kg/(m·s), not kg/m/s or kg/m·s)" which in any case is not consistent with your ambiguous or incorrect notation "bit/s·Hz". Let's respect the convention in reliable sources until we come up with a consensus to do otherwise. Also please note at the top of that MOS page where it says "This guideline is a part of the English Wikipedia's Manual of Style. Use common sense in applying it; it will have occasional exceptions." Dicklyon (talk) 07:51, 27 December 2009 (UTC)
@80.65.242.187: As explained earlier above, Hz is cycles/s, so bit/s/Hz would be bit/cycles and is NOT equivalent to bit as a unit. And bit/s·Hz does not even make sense at all, because multiplication does not take precedence over the division symbol. Finally, as Mange01 has pointed out, bit/s/Hz is the established unit denotation for spectral efficiency (and not e.g. bit/cycles). Nageh (talk) 09:46, 27 December 2009 (UTC)

## Survey: bit/s/Hz, (bit/s)/Hz or bit·s−1·Hz−1 as Spectral efficiency unit?

Please vote at Talk:Eb/N0#Survey on which unit that should be used at Wikipedia for measuring Spectral efficiency. For a background discussion, see Talk:Spectral_efficiency#Bit/s/Hz and Talk:Eb/N0#Bit/s/Hz. Mange01 (talk) 07:21, 16 April 2008 (UTC)

## Vandalized

There was a very nasty picture that made my stomach sick when I opened this page, but it vanished before I could do anything. Did any good soul remove it, or we have a hole in Wikipedia?

There was no image link in page source. Probably reverted between the time I downloaded vandalized version and the time it was fixed. There are some very ill people out there. You have my continuing support in fighting them.

P.S.

Anyone thought of AI software that would try to establish whether the image submitted is something vulgar and notify administrators? I have a few clues to start with. Thx. -- Mtodorov 69 13:47, 7 May 2007 (UTC)

## Spectral effiency of analog transmission modes

What is the spectral effiency of analog transmission modes as AM ( A3), SSB, FM, analogue TV, etc.? —Preceding unsigned comment added by 91.46.209.184 (talk) 20:00, 15 April 2008 (UTC)

I have found one article that seems to be measuring number of simultaneous calls per bandwidth unit in Erlang/Hz. [doi.wiley.com/10.1002/0470020121.ch7] However, I don't have access to the full text version, only the Google search result, so I might have misunderstood it. There are several articles measuring the area capacity in Erlang/MHz/area unit or Erlang/MHz/cell, as I mentioned in the System spectral efficiency section. Mange01 (talk) 18:45, 16 April 2008 (UTC)

## WiMAX spectral efficiency?

Not sure if this is the right place to put this but there is a misleading inconsistency in this page and the main wimax page [12] with regards to the spectral efficiency of wimax (802.16d), this page states an efficiency of (4.8 bit/s)/Hz but the main wimax page states for 802.16d a spectral efficiency of 3.7 (bit/s)/Hz

Spectral efficiency for any adaptive scheme (like WiMAX or LTE) is a bit tricky to nail down, since Marketing wants to quote the maximum value while Engineering cringes and generally talks in terms of averages. Also, many efficiency calculations depend on the exact overhead structure used, etc., so it's not at all unusual to have different authoritative sources quote figures that vary by even that much. NX7U (talk) 04:49, 10 June 2008 (UTC)

195.59.43.240 (talk) 13:01, 7 May 2008 (UTC)Rob

I split the table entry for CDMA2000 1x into separate entries for voice and PD (packet data), and made some corrections to the frequency reuse and resultant calculations. Also added a new entry for CDMA2000 1x EV-DO. NX7U (talk) 04:44, 10 June 2008 (UTC)

## Definition of Spectral Efficiency

I'd like to add that the definition of spectral efficiency assumed on this page is not the only one in use. Another, older and still pretty common definition is the ratio between the capacity of the modulation method used and the Shannon capacity. Under this definition, BPSK has more spectral efficiency than 64-QAM, since the mutual information limit for 64-QAM is so far away from capacity. Whereas this page's definition would simply say that 64-QAM has more "efficiency" because it is sending more bits.

I think at minimum this page should specifically give a literature reference as to where the definition being used came from. —Preceding unsigned comment added by Spope3 (talkcontribs) 22:04, 2 March 2009 (UTC)

The existing intro states "Spectral efficiency, spectrum efficiency or bandwidth efficiency refers to the amount of information that can be transmitted over a given bandwidth in a specific communication system". I don't think this definition contradicts what you're saying. Oli Filth(talk|contribs) 22:09, 2 March 2009 (UTC)
Several different definitions occur in the literature, see [13], but the unit is almost always "something per hertz". Otherwize it should not be called "spectral" i.m.h.o. I have searched on Google books, but i have not found your definition Spope3 in the literature. To my understanding, your definition would result in a unitless measure, for example a percentage measure. It resembles channel efficiency (missing article) or channel utilization, which is a normalized throughput, related to the maximum possible throughput. Mange01 (talk) 10:04, 3 March 2009 (UTC)

## Example numbers

Not sure if that is intentional, but example numbers are not consistent. Example 7 is followed by examples 6 and 7.93.159.77.200 (talk) 08:34, 16 July 2009 (UTC)

## V.92 efficiency

Maybe this is a naive question: if V.92 is so extremely efficient with spectral bandwidth (14 (bit/s)/Hz ), why is not every system exploiting V.92's modulation scheme? -Abdull (talk) 13:16, 6 February 2010 (UTC)

For the full spectral bandwidth (i.e. for peak bit rate) the V.92 modem requires a signal-to-noise ratio of about 37 dB. That may be achieve over a rather short phone line if only the lowest 4 kHz of the spectrum is utilized (which is the case in V.92 modems but not in broadband modems such as ADSL). The signal-to-noise ratio is typically much lower in wireless communication systems, or in broadband modems.
It would be nice if the table had a column for SNR requirement for full bit spectral efficiency. Or if we could procue a plot showing the relationship between SNR requirement and spectral efficiency of some common systems- one system per curve. A simple AWGN channel might be suffiecient to make the results comparable. Mange01 (talk) 01:43, 7 February 2010 (UTC)
This sounds like a very good idea. I'm not sure where I could find this data, but I would be happy to add it to the table if someone point me in the right direction. Haakoo (talk) 14:42, 18 January 2011 (UTC)

## Move the table to a template that can be embedded in many articles?

Would it be a good idea to move the comparison to a template that is embedded in the end of articles about all compared systems? For example template:spectral efficiency comparison table. The table should be collapsible.

Can it be done? Mange01 (talk) 21:08, 7 May 2010 (UTC)

## New column to the able: Energy per bit

We need to add one new column to the table, with Energy per bit, from were we can compare the different Carrier/Noise needed to each modulation. —Preceding unsigned comment added by 85.138.250.13 (talk) 10:54, 22 October 2010 (UTC)

## Missing reference

The reference to: Kolbrun Johanna Runarsdottir (2008). "Comparison of Mobile WiMAX and HSDPA" (PDF). Master of Science Thesis, Stockholm, Sweden. is a dead link now. I've tried to find it on-line, but I can't. If anyone know where to find it, please update the link.

The numbers for 3G WCDMA seems a bit strange, at least without mentioning the number of "mobiles" that can simultaneously access the system. I'd appreciate it anyone have more information about WCDMA. Haakoo (talk) 15:27, 19 January 2011 (UTC)

How do they seem strange? Could you elaborate as I might be able to help if I knew where the "strangeness" is. WCDMA doesn't really have a hard limit as to how many users can use a cell. Especially with CS voice over HSPA, signalling on HSPA and F-DPCH and other recent advancements have come to play. Practical limits naturally do exist, but as power control can be done with 10 users on a single SF256 code, theoretical values in the downlink could be over 1000. But that's just one limiting factor. Noise from multiple users etc. come into play far sooner. Nasula (talk) 15:53, 19 January 2011 (UTC)

For me the values seem very low if you compare them with the other techniques. Does WCDMA realy have a spectral efficiency of only 0.077 (bit/s)/Hz? I do understand that you can have several transmission at the same time. My understanding might be wrong, but shouldn't spectral efficiency reflect the "total" amount of (bit/s)/Hz? It might also be something related to CDMA I haven't quite understood that would explain why it is like it is. Haakoo (talk) 10:50, 20 January 2011 (UTC)
A very low value is correct for a spread-spectrum signal, and no it shouldn't reflect the total. The overall bad usage efficiency comes from other mechanisms, not from spectral efficiency. Dicklyon (talk) 15:39, 20 January 2011 (UTC)