Rohling H. (Ed.) OFDM: Concepts for Future Communication Systems

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76 3 Link-Level Aspects

[6] R.F.H. Fischer, “Widely-Linear Selected Mapping for Peak-to-Average Power

Ratio Reduction in OFDM,” IEE Electronics Letters, Vol. 43, No. 14, pp. 766–

767, July 2007.

[7] C. Siegl, R.F.H. Fischer, “Directed Selected Mapping for Peak-to-Average Po-

wer Ratio Reduction in Single-Antenna OFDM,” in Proceedings of 12th Int.

OFDM Workshop, Hamburg, Germany, August 2007.

[8] C. Siegl, R.F.H. Fischer, “Partial Transmit Sequences for Peak-to-Average

Power Ratio Reduction in Multi-Antenna OFDM,” EURASIP Journal on Wire-

less Communications and Networking, Special Issue on “Multicarrier Systems”,

Article ID 325829, 2008.

[9] C. Siegl, R.F.H. Fischer, “Joint Spatial and Temporal PAR Reduction in MIMO

OFDM,” in International ITG Conference on Source and Channel Coding 2008,

Ulm, Germany, January 2008.

[10] C. Siegl, R.F.H. Fischer, “Comparison of Partial Transmit Sequences and Se-

lected Mapping for Peak-to-Average Power Ratio Reduction in MIMO OFDM,”

in International ITG/IEEE Workshop on Smart Antennas,Darmstadt,Ger-

many, February 2008.

[11] R.F.H. Fischer, C. Siegl, “Peak-to-Average Power Ratio Reduction in OFDM

using Reed-Solomon Codes,” in International Zurich Seminar 2008, pp. 40–43,

Zurich, March 2008.

[12] R.F.H. Fischer, C. Siegl, “OFDM Peak-to-Average Power Ratio Reduction

based on the Simplex Code,” in Proceedings of the International Symposium

on Information Theory (ISIT 2008), Toronto, Canada, July 2008.

[13] C. Siegl, R.F.H. Fischer, “Tone Reservation for Peak-to-Average Power Ratio

Reduction in OFDM under Diﬀerent Optimization Constraints,” in Proceedings

of 13th International OFDM Workshop, Hamburg, Germany, August 2008.

[14] C. Siegl, R.F.H. Fischer, “Selected Sorting for PAR Reduction in OFDM Multi-

User Broadcast Scenarios,” in Proceedings of International ITG Workshop on

Smart Antennas (WSA 2009), Berlin, Germany, February 2009.

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Theory, Vol. 55, No. 4, pp. 1519–1528, April 2009.

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Proceedings of the IEEE International Conference on Communications (ICC

2009), Dresden, Germany, June 2009.

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tional OFDM Workshop, Hamburg, Germany, September 2009.

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80 3 Link-Level Aspects

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3.6 Single- vs. Multicarrier Transmission 81

3.6 Single- vs. Multicarrier Transmission in

MIMO and Multiuser Scenarios

R. Fischer, C. Stierstorfer, University of Erlangen-Nürnberg, Germany

3.6.1 Introduction

Since the invention of orthogonal frequency-division multiplexing (OFDM), the ques-

tion has arisen whether multicarrier (MC) or singlecarrier modulation is superior or

preferable over the competitor. In [25, 36] it has been shown, that in principle

OFDM and singlecarrier pulse amplitude modulation (PAM) with decision-feedback

equalization (DFE) can achieve the same transmission rate and both can utilize the

capacity of the underlying channel (cf. also [22,29]).

Since the fundamental insight (e.g., [28,30]) that by using antenna arrays in trans-

mitter and receiver, hence creating a multiple-input/multiple-output (MIMO) chan-

nel, spectral eﬃciency and thus data rate can dramatically be increased, this question

has been posed again: is MIMO OFDM or singlecarrier MIMO the better choice?

Moreover, this comparison is not only of interest in point-to-point MIMO (multi-

antenna) transmission, but as well for multipoint-to-point scenarios (multiple access

problem, uplink) and for point-to-multipoint scenarios (broadcast channel, down-

link), when the transmission paths exhibit intersymbol interference (ISI) and thus

call for some kind of equalization.

In this chapter, we brieﬂy compare single- and multicarrier MIMO transmission

with respect to the achievable performance. Besides the study of information- and

communication-theoretical bounds, the consequences on the code design when em-

ploying practical channel coding schemes are discussed, too.

3.6.2 Point-to-Point MIMO Transmission

In this section, we concentrate on point-to-point MIMO transmission, e.g., using

antenna arrays in both transmitter and receiver, each with N

antennas. When

considering transmission over MIMO ISI channels, two sources of (self) interference

occur: interference of the parallel data streams (spatial or multi-user interference

(MUI)) and intersymbol (temporal) interference. The possible equalization schemes

can be characterized by how they deal with these two types of interferences.

The ﬁrst approach for transmission over MIMO ISI channels is to treat MUI and

ISI jointly, i.e., to perform combined spatial/temporal equalization. An attractive

scheme is DFE over space and time (MIMO DFE), see [27]. Here, by applying a

feedforward ﬁlter, the end-to-end impulse response is shaped such that it exhibits

spatial and temporal causality, i.e., symbols transmitted at some time instant should

only interfere with receive symbols at subsequent time instances and symbols trans-

mitted at the same time instance over the antennas should also only interfere with

receive symbols for antennas with larger labels (spatial/temporal causality). Then,

the symbols are processed in a zig-zag fashion over space and time, taking already

detected symbols (via feedback) into account. Neglecting error propagation in the

82 3 Link-Level Aspects

feedback loop, MIMO DFE decouples the MIMO ISI channel into a set of N

par-

allel (near AWGN) channels with individual signal-to-noise ratios. Details on this

MIMO DFE can be found in [1,27].

The competing approach is to treat MUI and ISI separately. In MIMO systems

temporal equalization can be performed by applying an OFDM transmitter and

OFDM receiver (using a (inverse) discrete Fourier transform ((I)DFT) of length D)

to each transmit and receive antenna, respectively. Thereby, the MIMO ISI channel

is decomposed into a set of D independent ﬂat fading MIMO channels. Then, for

each of this parallel ﬂat fading MIMO channels (the tones), spatial equalization is

performed individually, e.g., by (sorted) DFE (aka V-BLAST) [28] per carrier. In

this situation, in total N

D parallel, independent (almost AWGN) channels, each

with its own signal-to-noise ratio, result.

Both strategies hence result in a set of parallel channels with varying reliability. In

such cases, performance can be (signiﬁcantly) improved by applying an optimized,

nonuniform distribution of total rate and total power to the parallel channels. In

particular, the loading algorithm given in [24] results in averaged channels; the SNR

of each channel is then given by the geometric mean of the initial channels.

Main result of [5] is that only when using this type of loading, single- (joint spa-

tial/temporal DFE) and multicarrier modulation (OFDM with DFE per carrier)

perform the same. This result holds for both, uncoded error rate, as well as achiev-

able sum capacity. If loading is not active, the SC scheme signiﬁcantly outperforms

the MC approach as, due to the combination in the feedforward ﬁlter, the SC schemes

is able to utilize the full diversity oﬀered by the channel. Without loading, OFDM

exhibits only the diversity order one, that of ﬂat fading channels. Employing rate

and power loading is hence the key that both systems provide the same performance.

3.6.3 Up- and Downlink Scenarios in Multiuser

Transmission

We now turn to the situation of multiuser communications, i.e., K individual users

want to communicate with a central base station (using N

≥ K antennas). Having

the uplink-downlink duality [19,33–35] in mind, both cases can be treated similarly to

a large extent. Compared to the problem discussed above, in the multiuser setting,

not (only) the sum capacity of the error rate is of interest but the rate regions, i.e.,

the region of admissible rates of the users have to be considered.

First, transmission in the multipoint-to-point scenario (uplink), where a multiple

access channel (MAC) is present, is studied. Here, the same receiver-side joint equal-

ization schemes as in the point-to-point situation above can be used, as none of them

requires joint transmitter-side operations. Consequently, the SC spatial/temporal

DFE and the MC OFDM/DFE per carrier systems achieve the same sum rate.

However, when assuming perfect feedback in the DFE, the user detected last in

each carrier of the MC scheme “sees” an interference-free (clean) channel. Hence,

with respect to the rate of a particular user it is best to detect this user last in

each carrier.

This user then has a rate as if there were no interference at all.

In most situations a global sorting in the DFE part of the OFDM scheme is suﬃcient. Sorting

per carrier oﬀers a higher degree of freedom for rate distribution between the users but does

3.6 Single- vs. Multicarrier Transmission 83

0 0.5 1 1.5 2

0.5

1.5

[bit/use] −→

0 0.5 1 1.5 2

0.5

1.5

[bit/use] −→

Figure 3.23: Uplink rate regions for exemplary 2 × 2 channel realization with four

taps and equal gain power delay proﬁle. Left: MIMO–DFE (light gray),

MIMO–OFDM (dark gray); Right: MIMO–DFE (light gray), MIMO-

–OFDM (dark gray), MIMO–OFDM with water-ﬁlling (black); ZF ap-

proach (solid), MMSE approach (dashed).

Maximum-ratio combining can be used, leading to the maximum SNR among all

receiving strategies [31] and hence to the maximum rate; no further increase is

possible. In particular the feedforward processing in the SC scheme results in lower

SNRs and rates. Hence, the bounds on the maximum individual rates of the users

are lower in the SC scheme compared to the MC scheme (ignoring the loss due

to the guard interval). Consequently, the rate regions of MC schemes are larger

than those of SC schemes. The decoupling of temporal and spatial equalization is

proved to be advantageous over a joint equalization by spatial/temporal DFE, both

in performance and ﬂexibility.

In Fig. 3.23, the achievable rate regions for an exemplary channel realization are

depicted for both single- and multi-carrier transmission. Zero-forcing approaches are

compared to the respective minimum mean-squared error (MMSE) variants. The

advantages of a power allocation according to the water-ﬁlling principles can be also

recognized.

Second, we turn to the point-to-multipoint scenarios (downlink), i.e., a broad-

cast channel (BC) is present. Basically, the transmission system for the downlink

(joint transmitter side processing) can be obtained from the uplink system (joint

receiver side processing) by ﬂipping the entire structure. The DFE (either joint

spatial/temporal or per carrier) is now replaced by Tomlinson-Harashima precoding,

the simplest implementation of the optimum philosophy of Costa precoding [23].

When applying the uplink-downlink duality the encoding ordering in THP is the

reversed decoding ordering of DFE, cf. [33] and the channel impulse responses as

well as the temporal processing have to be time-reversed, cf. [8].

Moreover, in contrast to the uplink scenario with a per user power constraint, in

downlink transmission only a total power constraint is active. Hence, the distribution

not oﬀer additional gains in enlarging the rate region.

84 3 Link-Level Aspects

0 0.5 1 1.5 2 2.5 3

0.5

1.5

2.5

[bit/use] −→

0 0.5 1 1.5 2 2.5 3

0.5

1.5

2.5

[bit/use] −→

Figure 3.24: Downlink rate regions for exemplary 2 × 2 channel realization with

four taps and equal gain power delay proﬁle. Left: MIMO–DFE (light

gray), MIMO–OFDM (dark gray); Right: MIMO–DFE (light gray),

MIMO–OFDM (dark gray), MIMO–OFDM with water-ﬁlling (black);

MMSE approach (dashed).

of the sum power on the users is an additional degree of freedom, and the rate region

of the downlink scenario is given by the convex hull over the union of the uplink rate

regions for all admissible power distributions [34]. The dominate face (rate tuples

of maximum sum rate) of the uplink rate region immediately gives the dominate

face of the downlink rate region; hence in the downlink case SC and MC approaches

support the same sum rate. However, as the uplink rate region is larger for the MC

setting, the downlink rate region is also larger for the MC system (OFDM with DFE

per carrier) compared to the SC scheme (joint spatial/temporal DFE). Noteworthy,

both approaches are clearly superior to frequency-division multiplexing in disjoint

frequency bands (orthogonal transmission of the users).

In Fig. 3.24 the respective rate regions are shown for downlink transmission.

3.6.4 Aspects of Channel Coding

The application of channel coding schemes is the most prominent way to increase

power eﬃciency of a digital transmission systems. When designing coding schemes

for (point-to-point) MIMO OFDM, the particular characteristics of this approach

have to be taken into account.

A stated above, the combination of OFDM and some spatial equalization scheme

per carrier (e.g., DFE) leads to a set of N

D parallel, independent, approximately

AWGN channels, each with its own signal-to-noise ratio. When coding over these

channels, a situation similar to that when transmitting over a ﬂat-fading channel

is present. From information theory it is known, that in principle a single code,

averaging over the fading states is suﬃcient to approach channel capacity, e.g., [17,

20]. However, using practical codes, the situation changes.

Additionally, it is well known that in OFDM transmission performance of uncoded

transmission can be signiﬁcantly increased by employing rate and power loading

3.6 Single- vs. Multicarrier Transmission 85

utilizing so-called loading algorithms, e.g., [12,24]. However, loading is based on (at

least partial) channel state information (CSI) at the transmitter and hence is not

always applicable. Moreover, loading and channel coding interact and depend on

each other.

It has been shown [3] that bit-interleaved coded modulation (BICM) [21] is a well-

suited solution to improve reliability for highly bandwidth eﬃcient transmission as

long as no rate and power loading is used. Furthermore, large signal constellations

should be avoided, i.e., the rate of the employed channel code has to be selected

carefully and taking the required signal constellation for achieving a certain spectral

eﬃciency into account (this holds for BICM in general and is not restricted to MIMO

OFDM).

As soon as rate and power loading can be applied, BICM cannot be recommended.

Here, the relevant performance measure is the parallel decoding capacity. Unfortu-

nately, this quantity cannot be (signiﬁcantly) improved by loading; some power

loading strategies, well-suited for uncoded transmission, even lead to a decrease in

capacity and hence are useless in coded transmission. In contrast to BICM, trellis-

coded modulation (TCM) [32]—due to the uncoded bits—does only provide gains in

combination with rate and power loading. However, neither conventional BICM nor

TCM can achieve convincing performance in MIMO OFDM. Uncoded but loaded

transmission oﬀers already good performance a the price of requiring partial TX

CSI.

When transmitter-side CSI is available, BICM can be improved by adapting the

employed bit interleaver [9,10]. Taking the actual SNRs of the parallel channels and

the used mapping into consideration, a set of equivalent bit levels can be established;

the entire modulation scheme is broken down into its fundamental building blocks.

Based on the capacities of these equivalent binary channels, the interleaver is then

designed such that within the relevant decoding window an optimized (equalized)

metric arrangement is present. Such an interleaver design shows gains over both,

conventional interleaving and BICM with rate and power loading. Concerning CSI,

only the interleaver sequence has to be exchanged between transmitter and receiver

and the additional complexity is almost negligible. Moreover, the capacities of these

equivalent binary channels can also be utilized to perform bit-loading in uncoded

transmission very eﬃciently, see [12, 13]. Finally, a bit-interleaver design for coded

multicarrier transmission using rate and power loading is also possible using the tool

of equivalent binary channels [14].

3.6.5 Summary

In summary it can be stated that MIMO OFDM is an attractive transmission scheme

for future communication systems. In point-to-point applications, singlecarrier mod-

ulation with joint spatial/temporal DFE performs as good as MIMO OFDM with

suited rate and power loading (uncoded transmission; the losses due to the guard

interval and error propagation in the DFE are ignored). Both approaches oﬀer

the same sum rate. The situation changes when multipoint-to-point or point-to-

multipoint scenarios are considered. Here, the rate region (which is the relevant as-

sessment factor) is always larger for the multicarrier scheme. Moreover, the OFDM