Copyright 2018 Thomas Schwengler.

Chapter 8

This chapter introduces OFDM concepts, starting with signal transmission and orthogonal subcarrier properties. It then illustrates how standards like Wi-Fi, WiMAX, and LTE make use of OFDM properties. We present a cursory overview that allows the reader to understand the fundamentals of OFDM and OFDMA, for further reading, see for instance [4], [121], [140].

8.1 OFDM basics

We present here the fundamentals of Orthogonal Frequency Division Multiplex (OFDM), which is used in standards like Wi-Fi, WiMAX, and LTE.

8.1.1 OFDM Basics

OFDM techniques consist in splitting a user data stream into several sub-streams, which are sent in parallel on several subcarriers. These sub-streams and subcarriers benefit from a number of properties that we now review in details.

Recall the classic example of continuous wave to encode information: the carrier frequency in itself in not capable of encoding information. The quantity of information s(t) is encoded by changes or modulation of the wave, and affects the amount of spectrum required Δfc as shown on figure 8.1.


Figure 8.1: Duality time-frequency. Information is encoded by changes (modulation) of a wave, which broadens its spectrum occupied in the frequency domain.

One can of course use several carriers fi,i ∈{1,2,,Nc}, and filter them separately. That is a common approach and is used extensively in FDMA systems: in particular multiple network operators who own licenses over a same area must take care not to exceed allowed levels of adjacent channel interference into one-another’s bands.

OFDM improves on the idea by using orthogonal properties of functions to increase spectral efficiency by choosing a specific interval Δf = fi+1 -fi between subcarriers. Multiple parallel signal streams are used: si(t) = exp(it) (where ωi = 2πfi), and in frequency domain: Si(f) = δ(f - fi).

In fact time signals are limited in a time window, and a user information symbol has a time interval for transmission: [0, Ts], so

si(t) = ui ⋅1[0,Ts] ⋅exp(jωit)

(where ui is a user information symbol) and the frequency domain representation of the signal is modified from a perfect Dirac function δ(f - fi) to a sinc function1:

Si(f) = ui ⋅exp(πjf Ts)⋅Ts ⋅sinc(πfTs)

This last expression is derived from Fourier transform, using definitions from the next section.


Figure 8.2: Subcarrier spacing is determined by a condition of orthogonality between the subcarriers, which allows to decode each one without interference form its neighbors.

8.1.2 Fourier Transform

Now recall the duality between time domain and frequency domain, with Fourier transform (and inverse Fourier transform) to switch from one domain to the other. Several definitions exist; let us the following definition of Fourier transform

       ∫  ∞
U (f) =     u(t)⋅ej2πftdt

and inverse Fourier transform

       ∫ ∞
u(t) =     U (f)⋅e-j2πftdf

(Other definitions exist, with different signs under the exponent and different 2π factors, so it is important to always specify what definitions are used.) With this definition, the reader can readily derive formula (8.2):

           ∫ Ts j2πft                        sin(πf Ts)
Si(f ) = ui ⋅   e    dt = ui ⋅exp(jπfTs )⋅Ts ⋅-πfT----
            0                                    s

8.1.3 Orthogonality

OFDM is a multicarrier modulation in which a user bit stream (of rate Ru) is transmitted over Nc subcarriers, each having a symbol rate Rs = R
Ncu, or a symbol duration Ts = R1
 s = NRc-
 u. The advantage of that parallel transmission is that the symbol time may be increased, which mitigates inter-symbol interference.

Each symbol stream is multiplied by a function ϕk from a family of orthogonal functions {ϕk},k ∈{0,,Nc - 1}. In CDMA, these functions were Walsh codes, in OFDM, they are windowed complex exponentials (or possibly cosine functions):

        {  jω t
ϕk (t) =   e  k  if t ∈ [0,Ts]
          0     elsewhere

So in a similar manner to the CDMA forward link presented in section 7.1, multiple channels are multiplexed and combined, using exponential functions instead of Walsh code sequences:

S   (t) = ∑   s g ϕ (t)
  tot          k k k

(where ui = sigi; si represents the information symbol (+1 or -1), gi is the individual channel gain) or for many successive bits m = 0,1,2,..., etc.

         ∞∑  Nc∑-1
S′ (t) =         sk,m ⋅gk,m ⋅ϕk (t - mTs )
 tot    m=0  k=0

That sequence is manipulated further and sent over the air; on the receiver side, that sequence may decoded by using orthogonal properties of {ϕk}.

-1-  Ts        *
Ts  0  ϕk(t)⋅ϕ l(t)dt = δk- l

where δk-l is the Kronecker symbol (i.e. 0 if k = l, 1 otherwise), and the asterisk (*) denotes the complex conjugate of the expression. Equations (8.6) and (8.9) gives us the orthogonal condition for subcarriers’ spacing: the right hand side equals zero if and only if (ωk -ωl)Ts = 2πn, for n non-zero integer. This leads to the condition Δf = n∕Ts, and 1∕Ts is the smallest separation between two subcarriers.

On the receiving side, the sequence may be decoded by simply integrating for each channel; for channel k, the information bit is retrieved from the sign of the integral:

∫                  Nc-1    ∫
  TsS  (t)ϕ (t)dt = ∑   s g   Tsϕ (t)ϕ  (t)dt = s g T
 0   tot    k            i i 0   i    k        k k s

Although in this case an additional trick is used, and direct and inverse Fourier transforms are used for decoding.

8.1.4 Discrete Fourier Transform

If we then examine the Fourier transform of our functions given in equation (8.6), we obtain a sinc function of pseudo-period Ts, which means that in the frequency domain subcarriers are spaced exactly such that the peak of the next one corresponds to the previous one’s first zero – see figure 8.3.


Figure 8.3: OFDM subcarrier spacing.

The overall envelope looks a bit like a spread spectrum signal, and may be tapered further to reduce out of band spectral power density.

The above choice of orthogonal basis functions has another useful property, relating to Fourier transform. Indeed sampling Stot turns the above expressions into the usual discrete Fourier Transform (DFT), and therefore, instead of multiplying, summing, and then integrating for decoding, OFDM allows to simply carry out a DFT and its inverse (IFT), which are very efficient operations.

Looking back at the Fourier transform (8.3), and sampling the time function and its Fourier transform (with N samples), one may define the following notations: uk = u(tk),tk = kτ,k   {0,1,,N - 1}, and Un = U(fn),fn = n--
Nτ,n   {-N∕2,,N∕2}. And one obtains the discrete Fourier transform

               N∑-1               N∑-1
Un = U (fn ) = τ   uk ⋅ej2πfntk = τ    uk ⋅ej2π knN-
               k=0                k=0

and the inverse discrete Fourier transform

u  = u(t ) = -1-- ∑    U  ⋅e-j2πkNn
 k      k    τN          n
                n= -N∕2

Now comparing these discrete transforms to above Stot with the particular OFDM orthogonal functions, one sees that the sk,m gk,m coefficients are Fourier transforms 2 of the complex amplitude of the subcarriers.

Consequently, encoding-decoding of an OFDM signal is practically not done with integration like (8.10), but by simple FFT. The transmitter builds: {S(ωn)} = DFT{sk,m gk,m}. And the receiver decodes the received spectral signal: Stot = IDFT{S(ωn)}.

If sampling is made as a power of 2 (N = 2p), DFT (and IFT) algorithms are in O(Nlog2N), referred to as fast Fourier transform (FFT) and very efficient to implement. OFDM schemes are therefore based on the nearest power of two, and when fewer subcarriers are users, the same order N = 2p is used for the FFT algorithms, but with zero entries for a subset Nz = N - Nc.

8.1.5 Number of Subcarriers

Note that increasing the number of subcarriers in a given band of spectrum does not increase capacity but provides a useful parameter to optimize: there is an interesting tradeoff between number of subcarriers Nc and subcarriers symbol time Tc. The more subcarriers are used, the longer their symbol rate is, which means that the overall rate of information remains the same, but a longer symbol rate is useful for multipath mitigation (recall conditions when equalizers are required). Consequently subcarrier spacing is a fundamental parameter to chose for an OFDM standard like Wi-Fi vs. WiMAX.3

8.1.6 Other Techniques

A few more standard techniques are used in combination with the above OFDM definition in practical radio systems. [121]

A guard time or interval limits inter symbol interference (ISI): the added guard time allows for larger delay spread and limits multipath interference from one symbol to the next.
Cyclic prefix.
A cyclic repetition of the prefix at the end of the transmission improves frequency orthogonality between sub-carriers and so limits inter carrier interference (ICI).

Copyright 2018 Thomas Schwengler.


Figure 8.4: OFDM guard, cyclic prefix, and windowing: the symbol OFDM symbol time contains useful information over TFFT , and is extended by TGI guard interval, which contains redundant data. A windowing function (such as a raised cosine) is added to improve spectral profile; that windowing erases some (redundant) information over a short time TTR < TGI.

The combination of guard interval and cyclic prefix is interesting: an empty guard interval is typical in non-OFDM systems, and is better to limit ICI, but here it would cause such ICI, that instead the guard interval is filled with some redundant data; the interesting problem is that the data causes ISI, but the redundancy allows some of that to be lost.

One serious drawback of the OFDM signal, is that it contains abrupt transitions from symbol to symbol, which as the disturbing effect of occupying too much of its adjacent spectrum. Unfortunately that cannot simply be filtered as it would affect the time-domain wave front and degrade signal (recall fig. 8.1). But since part of the signal is redundant (by cyclic prefix), OFDM systems can make use of windowing functions to smoothly transition between symbols (raised cosine families of functions are often used).
FEC, interleaving, etc.
In addition, data scrambling, FEC encoding, interleaving, puncturing, even MIMO are techniques also used with OFDM, as in other modern radio systems. OFDM systems are therefore well suited to resolve rich multipath situations and slow time varying channels, which explains their popularity for standards like Wi-Fi. Their drawbacks are typically 1) that they are not ideal for Doppler shift and phase noise, and 2) the OFDM wave front has high peak to average power ratio (fig. 8.8), and 3) its spectrum does not decay sufficiently fast in adjacent bands.

8.2 IEEE 802 and Wi-Fi

Wi-Fi is a standard for interoperable equipment, certified by the Wi-Fi alliance, and based on various iterations of IEEE 802.11, which uses OFDM for its highest throughput profiles. Wi-Fi has been the most successful local area network standard, and it is worth spending some time examining some of its OFDM parameters.

Details of the 802.11 air interface can be found in a number of references, and recent books have good overview of the latest efforts [123], [124]. We only examine here some aspects of 802.11 as they relate to OFDM in order to provide some insight on performance goals and limitations.

8.2.1 802.11a & g

General Parameters: 802.11a/g uses an N = 64 point FFT in a 20MHz channel, δf = 1∕Ts = 312.5kHz, Ts = 3.2μs, 4 μs time block is used, with cyclic prefix, 52 of the 64 subcarriers are populated, 4 are pilots (for phase and frequency training and tracking), 48 actually carry data.

The 802.11g packet structure includes the following:

Short training field (STF):
8 μs; 10x repetition of 0.8 μs symbol. Uses 12 subcarriers; good autocorrelation property and low peak to average ratio; also used for automatic gain control (AGC)
Long training field (LTF):
8 μs, composed of two 3.2μs training symbols and prepended by a 1.6μs cyclic prefix. Used for time acquisition and channel estimation.
Signal field (SiG):
4 μs (3.2 + 0.8 cyclic prefix), contains 24 bits BPSK describing transmit rate, modulation, coding, length. Forms together with the training field the preamble (totaling 20 μs).
Data Field:
includes service field (16 bits: 7 used to synchronize descrambler, 9 reserved for future use), data bits, and tail bits, and optionally padding bits. The Data field consists of a stream of symbols, each 4 μs (3.2 + 0.8 cyclic prefix), transmitted over 48 subcarriers, and 4 pilots.

8.2.2 802.11n

802.11n is a high throughput amendment to 802.11 containing improvements over 802.11a/g. Major throughput improvements in the physical (PHY) and MAC layers are explained in this section.

Physical layer

A number of improvements in the physical (PHY) layer were designed to increase throughput in some situations, although these improvements may come at a cost, which will be pointed out. Actual data rates are lower than these maximum rates, and are detailed further in section 10.1.1.


bits/ Hz

bits/ subcx


11g PHY

11n PHY 40MHz 800ns GI

11n PHY 40MHz 400ns GI




























































Table 8.1: Throughput rates (in Mbps) of a single stream 802.11a/g/n physical layer, for different modulations, given the number of data subcarriers used (48 for 11g, and 52 for 11n, 108 in 40MHz). Symbol time is 3.2μs. When the classic (long) guard interval of 800ns is used, only 3.2 of 4μs carry actual data, therefore data rate per subcarrier is 312.5kbps ×3.24 = 250kbps. When short guard interval is used (400ns GI), a subcarrier carries 312.5kbps ×3.23.6 = 277.8kbps (recall fig. 8.4). Multiple MIMO streams can multiply the 802.11n results by up to 4.

OFDM carriers:
48 data subcarriers (+4 pilots) for 11g, 52 (+4 pilots) for 11n, and 108 (+6 pilots) for 40MHz operations. That increase in data subcarriers brings the maximum throughput up from 54Mbps to 58.5Mbps. Tradeoff: higher cost of mitigating interference in adjacent channel.
Maximum FEC rate is increased from 3/4 to 5/6, hence reaching maximum data rate of 65Mbps, or 135Mbps in 40MHz channels. Tradeoff: more errors may occur, in which case the system can revert to lower modulation.
Guard interval:
The guard interval, containing cyclic prefix may be shortened from 0.8μs to 0.4μs, thus increasing actual data rate to 72.25Mbps, or 150Mbps in 40MHz. Tradeoff: more ISI.
Multiple spatial streams:
MIMO offers 2, 3, or even 4 times the above rates, reaching 300 to 600Mbps rates. Tradeoff: system complexity and cost.
Greenfield Preamble:
The 802.11n preamble is modified for higher throughput, adding a high throughput training field (series of 4 μs fields). A legacy mode appends this new preamble to the 11g preamble for backward compatibility, whereas the shorter “greenfield” 802.11n only preamble increase throughput by 10 to 15 percent, at the cost of backward compatibility.
Low density parity check (LDPC):
increases FEC efficiency and throughput in some cases.
MAC layer

The media access control (MAC) layer deals with multiple element addressing, channel access prioritization, and control. It transmits among other things beacons with regulatory and management information (such as country code, allowed channels, max power), and scans channels for beacons. Scanning is usually done passively but when regulations allow it, active probe requests can be sent for specific SSIDs or BSSIDs. MAC improvements for 802.11n include:

large frame may see considerable channel variations over time (especially in poor condition, thus low bitrates). Consequently frames can be fragmented, and only an erred fragment needs to be resent. MAC service data units (MSDU) above a certain settable threshold are broken into several fragments sent over different MAC protocol data units (MPDU).
Aggregated MSDU or MPDU: A-MSDU is an efficient MAC frame format that aggregates multiple MSDUs in a single MPDU which maximum size is extended to 4 KBytes and optionally 8 KBytes. A-MPDU is another form of aggregation that aggregates multiple MPDUs in a single MPDU, which maximum size is extended to 64 KBytes.
Enhanced Block Ack:
a new scheme in which the sender requests to enter block acknowledgement (BA) request session, in which BA are requested periodically instead of having ongoing BA.
Optional features:
Other optional features are standardized as part of the 802.11n MAC:

8.2.3 802.11ac

802.11ac is another high throughput amendment to 802.11 containing improvements over 802.11a/g/n. It leaves the 2.4 GHz band unchanged but provides very high throughput at 5 GHz. Its improvements are similar those already standardized in 802.11n, but taken even further.

Physical layer

Preamble and cyclic prefix is left as in 802.11n, but the following parameters are increased further:

Modulation schemes:
up to 256 QAM, 5/6 FEC, for further spectral efficiency at close proximity (and excellent SNR conditions),
Channel bonding:
20, 40, 80MHz, and optionally 160MHz (802.11ac specifies that an 80MHz channel consists of two adjacent 40MHz channels, and a 160MHz channel is defined as two 80MHz channels, contiguous or not)
up to 8 spatial steam (8x8 MIMO), and multi-user MIMO (MU-MIMO), in which an access point can transmit multiple spatial streams to multiple client devices simultanously.

The standard reaches for each spatial stream: 200 Mbps at 256 QAM (5/6) with 400 ns cyclic prefix in 40MHz, 866.7 Mbps in 160MHz. The maximum throughput in 8 spatial stream reaches 6.92 Gbps throughput.


bits/ subcx

20MHz 52cx

40MHz 108cx

80MHz 234cx

160MHz 468cx





























































Table 8.2: Throughput rates (in Mbps) of the 802.11ac physical layer calculated for different modulations, given the channel bandwidth, which determines the number of data subcarriers used. We assume a short guard interval of 400ns, so a symbol time of 3.6μs hence a data rate per subcarrier of 312.5kbps ×3.23.6 = 278kbps.

MAC layer

The improvements follow the general 802.11n ideas. RTS/CTS is improved to deal with secondary channels efficiently. A-MPDU aggregation size is further increased to 1MBytes. Other concepts, like reduced inter-frame space (RIFS) is deemed less efficient than aggregation and becomes obsolete (except for backward compatibility).

Copyright 2018 Thomas Schwengler.

8.2.4 Other 802.11 groups

A number of further development are in the work for 802.11. They produce new amendments to the specification with the following goals:

is another high throughput amendment to 802.11, 60GHz rather that the 2.4 GHz and 5 GHz of 802.11a/g/n. 802.11ad uses higher modulation schemes, wider channels and multi user MIMO techniques, much like 802.11ac, and also reaches multi Gbps throughput. Given the higher frequency, it aims at providing a solution for very high throughput over short distances such as uncompressed video delivery for entertainment systems. [126] (An 802.11ad access point can theoretically reach 7Gbps in a wide channel, and 28Gbps in 4x4 MIMO).
is the TVWS version of Wi-Fi, based on the 802.11ac physical layer. It is designed for use in several contiguous channels of TV White Space spectrum (TVWS), 5, 10, 20, 40MHz channels. It uses 8-16μs symbol time, well suited for LAN application, unlike for instance the longer symbol times of 802.22, which are well suited for wider area applications (see 8.2.5). [127]
focuses on frequency bands below 1 GHz (excluding the TV White Space bands above), including 900MHz. It also deals with coexistence with other systems in the bands such as IEEE 802.15.4 and IEEE P802.15.4g. 4 It allows transmissions up to 1km, by improving link budget with a couple of parameters: lower frequency of course improves propagation and penetration, lower modulation allows data rate down to 100kbps , and smaller channel width (1, 2, 4, 8, 16MHz) improve spectral power density. [128]

Conveniently, these channel widths are exactly 10 times narrower than 802.11ac’s (20, 40, 80, 160MHz); so the standard judiciously chose to use the same number of FFT subcarriers, to increase subcarrier spacing 10 times (31.25kHz, compared to 312.5kHz of Wi-Fi), hence gaining an order of magnitude for symbol time, and therefore acceptable delay-spreads without risk of inter-symbol interference. For example the 2MHz channel still uses 64 FFT (and 52 of these subcarriers carry data), and has the two guard band option (now 4 or 8μs). Recalling 802.11ac rates from table 8.2, 802.11ah rates are one tenth these rates in the 2-16MHz channels.

The 1MHz profile is slightly different: it maintains the same subcarrier spacing of 31.25 kHz, resulting in 32 FFT, 24 of which carry data (similar to half the number of 802.11g subcarriers). Finally an additional profile is created with a simple 2x symbol repetition thus gaining more link budget, and lowering the data rate to 150kbps.

The MAC layer also has a number of improvements to: associate many more devices, save power, improve channel access. Other techniques such as MIMO are similar (though MIMO is restricted to 4 streams).

the High Efficiency WLAN (HEW) study group [129] studies higher efficiency possibilities, including channel models, interferences, and physical layers; it considers in particular the use of an LTE physical layer in unlicensed bands (like 2.4GHz).

8.2.5 802.22

A different 802 standard, 802.22 addresses Wireless Regional Area Networks (WRAN); it defines PHY, MAC, policies and procedures for operations in TV white spaces (TVWS); the standard was published in 2011, and was widely reported on in the press, nicknamed super Wi-Fi. Given the TVWS spectrum landscape, 802.22 defines 6, 7, or 8MHz channels, it uses OFDMA, 2048FFT, QPSK, 16QAM to 64QAM, code rates 1/2, 3/4, 5/6, and 200-300μs symbol time (with cyclic prefix of 1/4 to 1/32 of OFDMA symbol), which adapts well to wider area delay spreads. 5 The standard is therefore analogous to 802.16e in some respects.

8.3 3GPP and LTE

The increasingly inaccurately named third generation partnership project (3GPP) is standardizing 4G around a long-term evolution (LTE) standard and architecture, aiming to:

LTE’s air interface, like other 4G standards, revolves around OFDMA. MIMO is used to either enhance data rates or increase data integrity (diversity and MRC). And the other usual tools are used as well: convolutional and turbo codes, and adaptive modulation (QPSK to 256QAM). LTE offers a flexible range of channel bandwidth (1.4 to 20MHz, and aggregation of multiple channels), both in FDD and TDD bands.

8.3.1 LTE Physical Layer

LTE uses OFDMA for the downlink, with a fairly simple frame structure, and SC-FDMA for the uplink.


LTE FDD uses 10ms frames, divided into 20 sub-frames or slots (of 0.5ms each). Each sub-frame uses 7 OFDM symbols, each with a cyclic prefix. Subchannels separation is Δf =15kHz. (For multimedia broadcast multicast service MBMS dedicated cell, reduced carrier spacing can be used in the downlink Δf=7.5kHz). A cyclic prefix (CP) is used to duplicate part of the symbol: total symbol duration Ts = Tu + Tcp. For normal 15kHz subcarrier spacing, the normal CP is 7 OFDM symbols per slot, which works well in typical urban multipath (Tu = 66.7μs, and Tcp = 5.21μs for first symbol, 4.7μs for the following symbols). An extended CP for larger cells or heavy multipath is available: Tcp = 16.67μs.

This splits radio resources into time and frequency elements, called resource blocks. On the frequency scale a resource block is 12 subcarriers wide (180kHz), on the time scale it is one slot (0.5ms).


OFDMA symbols


CP symbols

CP (μs)

Δf=15kHz, normal



160 first

5.2 first

144 after

4.7 after

Δf=15kHz, extended





Table 8.3: LTE cyclic prefix lengths in number of symbols, subcarriers, and time.

There are three downlink channels in the physical layer, shared, control, and common control. And there are two uplink channels, the shared and the control channel. Modulation techniques used for uplink and downlink are QPSK, 16 QAM, 64 QAM while the broadcast channel uses only QPSK.


Figure 8.5: LTE physical layer uses multiple OFDMA subcarriers and symbols separated by guard intervals.


Figure 8.6: LTE OFDMA Physical layer structure.


Figure 8.7: LTE resource blocks and resource elements (from the 3GPP standard).


The uplink standard is departing from the usual OFDMA approach: it uses single carrier FDMA (SC-FDMA). SC-FDMA is a type of frequency domain equalization (FDE). In SC-FDMA, a bit stream is converted into single carrier symbols, then a Discrete Fourier transform (DFT) is applied to it, subcarriers are mapped to these DFT tones and an inverse DFT (IDFT) is performed to convert back for transmission. Much like in OFDMA, the signal has a cyclic prefix to limit ICI, and pulse shaping is used to limit ISI.

Similar parameters are used as for downlink: subcarrier spacing 15kHz, CP normal or extended (Note that CP is the same for all UE in cell, and the same as downlink). The uplink uses the same symbol period and resource elements as in the downlink. Resource blocks are defined in the same manner, with NSCRB = 12 subcarriers and NRB depends on bandwidth: 6, 15, 25, 50, 75, or 100.

The reasons for preferring SC-FDMA over OFDMA are mainly that transmitting mobile units have strict limitations on the transmit power, and that peak-to-average power ratios (PAPR) are high for OFDMA. [139]


Figure 8.8: CDF PAPR comparison for OFDMA used in the LTE downlink, and SC-FDMA localized mode (LFDMA) used in the LTE uplink – 256 total subcarriers, 64 subcarrier per user, 0.5 roll-off factor, (a) QPSK, (b) 16QAM.

8.3.2 LTE Throughput

LTE physical layer throughput calculations are easily derived from the 3GPP specifications: 1 Radio Frame has 10 sub-frames, each sub-frame has 2 time-slots, each time-slot is 0.5 ms long, 1 time-slot has 7 modulation symbols or OFDMA symbols (when normal CP length is used). Each modulation symbol = 6 bits at 64 QAM (note that these are physical layer bits, not actual user information).

A Resource Block (RB) uses 12 Sub-carriers. Assume 20MHz channel bandwidth (100 RBs), normal CP. The number of bits in a 1ms sub-frame is 100RBs x 12 sub-carriers x 2 slots x 7 modulation symbols x 6bits=100800 bits. So the data rate is 100.8 Mbps. For 4x4 MIMO the peak data rate is simply four time that, or 403Mbps. (Of course, a more robust FEC coding, lowers the bitrate to 336Mbps at 64QAM 5/6, or 302Mbps at 64QAM 3/4.)

Note that the above accounts for every resource block, which has to carry overhead signaling, reference signals, etc. Practically, looking at resource elements in a resource block for one (1ms) subframe, some resource elements are reserved (for instance with control frame indicator CFI=2).


Figure 8.9: Some LTE resource elements are reserved for control channel and reference signals only a subset are used for user data, thus lowering actual throughput.

Out of the 12x14 RE, 36 are used for control (PDCCH) and reference signals, so only 132 can carry data. (See figure 8.9). So 20% of the physical layer data rate is reserved. So the maximum physical layer data rate is 80.64Mbps (or 322.56Mbps in 4x4 MIMO).

Commonly cited numbers are 75Mbps uplink, and 300Mbps downlink for LTE, this because layer 2 has additional transport block size (TBS) restrictions and frame overhead – typically around 9-10%, leading to 75Mbps and 300Mbps rates (for 4x4 MIMO in 20MHz).

8.3.3 LTE QoS

A difficult aspect of wireless systems is quality of service (QoS). LTE systems use different service definitions to provide different quality of services, some have guaranteed rates (GBR), others not (non-GBR). LTE uses several QoS parameters, and sorts them in different QoS Class Identifiers (QCI), which are treated with different requirements and priorities throughout the network. The intent is that the UE requests a QCI and sees similar user experience on every eNodeB. QCI include:

Priority level:
prioritizes data streams within a UE and between UE’s, lower priority streams are at risk when resources are constraint
Packet Delay Budget (PDB):
target upper limit for data block delivery (that target may not be met during network congestion)
Packet Error Loss Rate (PELR):
percent loss allowed during transfer.
Resource Type:
set to either GBR for guarantied bearer rate, minimum maintained rate, or non-GBR.

LTE network operators define a different service class for each CQI, that define target bitrates, packet error rates, and delay budgets, according to the type of service they intend as well as a target user of experience. Key performance indicators (KPI’s) are defined for each of these types of service flows, and are monitored and optimized by network providers. The RAN scheduler will handle different QCI with different priorities and requirements. And the core routed network may create different queues and priorities for each QCI.

LTE QoS can be used for instance to differentiate types of services (voice, video, or best effort data). QoS can also vary depending on time of day, emergency services, or service levels defined in the HSS customer profiles and priorities. 6

Bearer services can be defined statically in MME and HSS with the following parameters:

QoS Class Identifier (QCI):
controls bearer level packet forwarding treatment.
GBR or non-GBR
For GBR bearer additional parameters:
GBR Guaranteed Bearer Rate:
The GBR parameter determines the minimum bit rate provided by a GBR bearer.
MBR Maximum bit rate:
The MBR parameter limits the bit rate provided by a GBR bearer
Evolved ARP:
(allocation and retention priority) The evolved ARP parameter decides whether a bearer establishment or modification request can be accepted or needs to be rejected in case of resource limitations.
The Aggregate Maximum Bit Rate (AMBR):
is described using the following parameters:
Access point name – aggregate max bit rate is the total bit rate that can be expected across all non-GBR bearers and across all PDN connections of the same APN. (Note: APN-AMBR can be modified by the PGW through negotiation with the Policy and Charging Rules Function).
The UE-AMBR limits the aggregate bit rate that can be expected across all non-GBR bearers of a UE. The MME sets the UE-AMBR to the sum of the APN-AMBR of all active APNs up to the value of the subscribed UE-AMBR.

8.3.4 Voice over LTE

QoS is important for services such as voice; and wireless carriers are looking at adding voice over the LTE physical layer (VoLTE), and potentially migrate to an LTE only network in the long run. Several initiatives (IMS, VoLGA) are in the works, as well as fallback solutions to circuit switched standards (CSFB).

Codecs Several voice coders-decoders codecs are available from very efficient bitrate to high rate high quality voice transmission.

Voice Capacity Capacity aims at exceeding 3G voice (see 2.2 and equation (2.5)). These estimates are now well verified from commercial systems; although they still vary with terrain, cell sized, mobility, soft handoff, and various key voice quality metrics, capacity estimates tend to revolve around 100 simultaneous calls in a 5MHz spectrum block (FDD 5+5MHz). Various LTE estimates have been devised, tested, and published for data, but voice capacity estimates are still in their modeling phase, and few reports exist with good field data. [145]

Typical mobile wireless VoLTE can assume the G722.2 12.65kbps (plus some overhead); Further assuming 5MHz FDD LTE, 2x2 MIMO, leads to estimates ranging in the 70 to 375 simultaneous VoLTE calls depending on modulation. Empirical verification is still needed; loaded systems will be more readily available soon for a more accurate estimation.

Important parameters for VoLTE capacity include frequency (700MHz to 2.5GHz), propagation environment, link budget, shadowing statistics, channel bandwidth (e.g. 5MHz FDD), modulation (QPSK–64QAM), FEC (rate 1/2 to 1), interference mitigation features (eICIC, CoMP), MIMO rank, protocol (RTP), header compression (ROHC for RTP/UDP/IP), and of course vocoder rate (e.g. 12.2kbps G.722.2–AMR).

VoIP Calls over LTE were tested in different environments and showed the following key parameter indicators (KPI), and how they compare to typically accepted values for acceptable quality (in parentheses)

In summary: LTE capacity for carrying voice has been demonstrated, and is likely to work well in future LTE-only systems. Major wireless carriers will continue to rely on well established 3G voice until their data plans need to reclaim that spectrum, and subsequently rollout voice over LTE systems.

8.4 LTE-Advanced

The LTE physical layer is described above, and remains similar for all releases so far. LTE-Advances provides further features that aim at significantly improving throughput in different ways.

8.4.1 Enhanced Local Access

The term enhanced local area access refers to techniques dealing with the increasing base station density and presence of small base stations in larger umbrella coverage. Rel-12 will continue Rel-11’s effort, allowing for instance the network to send stationary traffic to small cells, but high speed traffic to larger cells. It will also focus on different frequency modes such as: dual connectivity to macro cell and small cell (even at different frequencies such as 3.5GHz in small cells); uplink and downlink separation on different frequencies; refinement of mobility and handover commands (between wide and local cells).

8.4.2 Carrier aggregation

LTE started with a flexible channel assignment between 1.4MHz and 20MHz. As few carriers own 20MHz contiguous, yet all want to increase throughput, carrier aggregation within a band, and then across different bands was added in LTE-Advanced.

Carrier aggregation can combine channels up to 5 carriers, therefore up to 100MHz (though that limit might be removed in later releases). When channels are non continuous (and optionally in different bands), multiple transmitters (and receivers) are powered simultaneously.

The primary carrier operates as usual, and the other component carriers are secondary. The scheduler allocates data for transmission in each available carrier (according to their DCI).

8.4.3 eICIC

Inter-cell interference cancellation (ICIC) is important for efficiency at the edge. Rel-8-9 implemented ICIC, which allows for exchange of load balancing information between sites over the X2 interface. It then lowers power of some subchannels to limit interference (in the frequency domain) in these channels at the edge.

Rel-10 enhances the scheme to eICIC, which adds the ability to produce almost blank subframes (ABS), which is a time domain interference cancellation scheme at the UE (with resulting backhaul timing implications). Rel-11 further enhances ICIC (feICIC) by providing Cell specific Reference Symbols (CRS) information to the UE to mitigate its interference. And Rel-12 further enhances interference cancellation schemes with network assisted interference cancellation and suppression NAICS.

8.4.4 CoMP

CoMP is an important feature of LTE for efficiency at the edge, where it coordinates resource between sectors to minimize interference. Both uplink and downlink CoMP are being standardized.

In the downlink: multiple sector transmission is coordinated to the mobile unit (data is present at multiple CoMP cooperating sets at different locations). Signal is either transmitted coherently from multiple points (coherent joint transmission), or only transmitted from the one point at a given time (dynamic point selection).

In the uplink, the idea is similar: mobile unit data transmitted is either received jointly by multiple sites, or coordinated scheduling / beamforming can be used for a specific site. (Uplink CoMP is especially efficient, much like soft handoff was).

A 3GPP CoMP study reports that data rates could be improved between 25 to 50% for mobiles at cell edges with neighboring interference. So CoMP enhancements continue, especially on downlink multipoint CSI feedback (which were introduced in Rel-11). CoMP will also focus on relaxing backhaul requirements (currently requiring dark fiber for CPRI often limits its practical applicability too much).

8.4.5 MIMO enhancements

LTE MIMO was extended in release 11 to 8 dowlink spatial streams, and 4 uplink. Release 12 will continue these multiantenna enhancements:

Active arrays for 3D beamforming:
Most multiantenna systems rely on a passive, one-dimensional antenna array, and a fixed antenna downtilt, and most of the beam or null forming is azimuthal. Active antenna arrays have been used since the nineties, but were prohibitively expensive, they are now considered again for 3D MIMO. Active two-dimensional antenna arrays provide added degrees of freedom and finer spatial resolution, which are handy (especially for MU-MIMO, when users move throughout a multifloor building).
Massive MIMO:
Massive MIMO research is considering the use of many more antenna elements and spatial streams (tens or even hundreds). They are especially interesting for use with millimeter waves where antenna sizes become manageable.

8.4.6 Device to Device

Device to device (D2D) communication provides direct communication between devices without tying base station resources. It has several advantages in some close proximity of device scenarios, and saves resources, power, and improves throughput and latency. Applications related to proximity detection and social media, as well as Internet of things make the feature very interesting. There are of course drawbacks in the complexity of spectrum/RB management (as well as authentication and security and privacy concerns). Also battery drain of discovery techniques is a major issue.

Initial techniques investigated the use of Bluetooth and wi-fi, but hey are limited in range. Within an operator, all devices can listen to a common announcement. To achieve operator interoperability, devices would have to be allowed to listen to another operator band (though still only transmit in its own band). Alternatively, operators in a country could agree on one unique announcement spectrum (or a couple for fairness of who shares that capacity).

8.4.7 Machine-Type Communications

LTE can handle many MTC scenarios, but more work is underway to enhance support for low-cost, simple, low power devices, extended coverage, large number of devices per cell, and infrequent transmission needs and high sleeping time, e.g. allow high cycles of discontinuous reception (DRX) and minimize signaling.

8.4.8 Unlicensed Operations

LTE currently focuses on license bands (both FDD and TDD), but an important new area for LTE expansion is in unlicensed bands, especially 5GHz and 3.5GHz. Of course operations in 5GHz will have to follow part 15 rules in the US, which restricts power levels. It will also have to coexist with existing Wi-Fi systems, which is the cause of some concerns in the industry. Also, some portions of the 5GHz band have pre-existing protected systems, such as radar – to that effect, the FCC mandates dynamic frequency selection (DFS) in the 5.470-5.725GHz range.

Some countries (especially in the EU) require that any unlicensed operations scan for existing signal prior to transmitting (a mode of operations called listen-before-talk or LBT). In the US however, unlicensed (part 15) bands require no such scheme. A spectrum etiquette exists that encourages operations to limit interference with existing service, but no strict rules are in place, nor does the FCC get involved in any potential dispute.

Licensed Assist Access (LAA)
3GPP first extended LTE-Advanced to unlicensed spectrum in release 13; in LAA a licensed link remains the primary radio link, and a secondary unlicensed link may assist. Rel-13 first standardizes downlink supplemental link, Rel-14 includes the unlicensed uplink. LAA insists on listen before talk standard to abide by EU mandates. For this reason and because the 3GPP consensus approach, may be time consuming, some industry members would prefer a faster timeline.
LTE-Unlicensed (LTE-U)
LTE-U can be ambiguous, generally not referring to unlicensed LTE in general, but to the specific LTE-U forum standard – see The LTE-U forum works with no restrictions like FAA LBT, to achieve faster timelines. LTE-U is also restricted to using unlicensed bands to assist a primary licensed band (and is currently focused on supplemental downlink in FDD CA, 5,10,15, or 20MHz primary band 2(PCS), 4(AWS), or 13(700MHz) + 1 or 2 20MHz unlicensed carriers)
LTE - Wi-Fi link aggregation (LWA)
LWA aggregates an LTE channel with an unlicensed channel using the W-Hi physical layer (rather than the LTE physical payer in the unlicensed band).
Another approach is to allow unlicensed-only operations of LTE. The MuLTEfire alliance (a Qualcomm initiative) proposes LTE in unlicensed bands (such as 3.5GHz or 5GHz) without the need for a licensed band. The alliance is producing a technical specification (MuLTEfire Release 1) for 2016, with equipment expected by mid 2017.

The initiative caused some concerns in the industry worried about coexistence with existing Wi-Fi services. The LTE physical layer normally uses pilots that never back off (like Wi-Fi) and would significantly impact colocated Wi-Fi services. MuLTEfire therefore relies on a duty-cycle approach, and only transmits a portion of the time to allow for coexistence with Wi-Fi.

8.5 LTE Releases

Subsequent releases of 3GPP LTE have been published:

published December 2008, is the first release for LTE.
published December 2009, added location services, MBMS support, multi-standard support, and regional requirements for North America.
published March 2011, the first release for LTE-Advanced, adds:
2013, continues improving LTE-Advanced:
expected mid-2018:

8.6 Other Wireless Standards

Many other wireless standards exist and are continually in development for a wide range of applications. Figure 8.10 shows a summary of the most popular ones with their typical throughput, range, and domain of applications.

Such table is difficult to keep up-to-date as standards work focuses on new needs and new opportunities; and incorporate the latest technology innovations into them as needed. Some of them become extremely successful and successful, while others miss their window of opportunity and disappear. They range over a wide industry interest such as wireless cellular, LAN’s, smart grids, RFID tagging, entertainment, consumer electronics, and much more.


Figure 8.10: A comparison table between many wireless standards shows their approximate throughput, range, and applications.

8.7 Homework

  1. Derive equation (8.2) using the definition of Fourier transform in 8.1.2.
  2. An 802.11a system uses Nc = 48 subcarriers for data and 4 more for pilot.
    1. What is the nearest power of two N = 2p ?
    2. 802.11a uses 20MHz channels, what is Δf between subcarriers in such a channel?
    3. What is each user information bitrate? (Assume a BPSK modulation, i.e. only one bit transmitted per symbol)
    4. Compare to the spectral efficiency of WCDMA where 3.84 Mc/s are transmitted in 5MHz. (Again assume 1 chip is 1 symbol for that comparison)

      Other non standard solutions are becoming popular, such as one by Flarion (later owned by Qualcomm). The proposal was the basis of work to another IEEE group to be created: 802.20. The proposal initially used 113 subcarriers, 17 of which are used for pilots. (The next four questions refer to this solution)

    5. What is the nearest power of two N = 2p ?
    6. This uses 1.25MHz channels (convenient for current CDMA providers). What is Δf between subcarriers in such a channel?
    7. What is each user information bit rate? (Assume a BPSK modulation, i.e. only one bit transmitted per symbol)
    8. Compare to the spectral efficiency of 802.11a above.
  3. Beside spectral efficiency, what advantages and disadvantages can you think of between the solutions presented in the previous problem? (Hint: think of fading characteristcs and 8.1.5).
  4. The following 14-bit sequence 00001111001101 is to be encoded on an OFDM system. Represent each bit by a BPSK symbol, 1. Ignore any pilot signal, i.e. every subcarrier is for data transmission.
    1. Implement a system within 1 MHz of spectrum bandwidth with the nearest power of two subcarriers . Specify how many subcarriers are used and their frequency separation.
    2. Compute complex coefficients for each subcarrier by IFFT. (Zero out the Nz trailing ports). Use matlab for instance, and compute the IFFT.
    3. Show the approximate spectral shape, i.e. the modulus of the sum of all subcarrier with their associated coefficient. (Use matlab, or any other graphic software, or approximate by hand drawing; in any case, show details of your method).
    4. Truncate the result to the first 14 bits, again fill in the remaining bits by zero, compute the FFT and explain how to retrieve data from the original bit stream.
  5. We consider a Wi-Fi 802.11g system where approximately 64 subcarriers are used in a 20MHz channel.
    1. Assuming that symbol periods must be greater than 10 times delay spread (Ts > 10στ), what is the maximum delay spread in which this system performs well.

      (For simplicity, ignore guard bands, cyclic prefix, etc, and assume that the entire symbol duration is for user data).

    2. What happens if the delay spread is much greater?
    3. Searching for typical delay spreads in various sources, is Wi-Fi subcarrier spacing adequate for most indoor environments?
    4. We now consider a WiMAX 802.16d system with 256 subcarriers over a 3.5 MHz channel. Searching again for typical delay spreads in various sources, in what environment would this system be appropriate? (indoors? in rural areas? in major cities?)
    5. 802.16e now standardizes 512 subcarriers for 3.5 MHz channels. In what environment might this be an improvement?
    6. Explain why WiMAX is better suited for providing wireless access throughout a city than Wi-Fi access points.
  6. Examine subcarrier spacing of the 802.11ac physical layer to derive the throughput values of table 8.2, recreate that table in a spreadsheet.

    Then create a second table if you now assume a long guard interval of 0.8μs instead of short GI (hint: the useful symbol length remains 3.2μs, the total symbol length is increased to 4μs instead of 3.6μs used in table 8.2.)

  7. A city is interested in a system providing city-wide coverage:
    1. Suggest a few state-of-the-art wireless systems for the city’s consideration and justify your choices (Wi-Fi? WiMAX? LTE? others?).
    2. Make a table showing advantages of these technologies for a carrier to provide extensive wireless coverage for a city. Include at least considerations around: spectrum, cell sizes (consider power allowed, propagation, and delay spread), indoor service availability, mobility (Doppler, handoff), and cost of customer premise equipment (CPE).
    3. The city is also interested in having its police, fire department and other first response emergency services communicate on that system. Are there any additional important arguments to consider for this type of use? Would they preclude any of your above systems — why?
  8. Using information in this chapter: Estimate the LTE capacity (in terms of aggregate maximum simultaneous bit rate) of an LTE sector using FDD 5+5MHz of spectrum, and 2x2 MIMO.
    1. Estimate capacity near the base. Clearly list any choice and assumption that you need to make for your capacity estimation.
    2. Estimate capacity near the edge where the modulation is only QPSK, FEC rate 1/2.
    3. If we were to use the above sector for voice (VoLTE) instead of data (with a vocoder of your choice), how many simultaneous voice calls would that sector be able to carry? (consider two simplistic scenarios where all callers are either near center or near the edge).

Copyright 2018 Thomas Schwengler.