Wireless Future - Telenor

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50 models are described simply by a probability density function (PDF) for the fading amplitude, and the fading correlation properties. We shall make use of the well-known complex baseband model. Denoting the transmitted complex baseband signal at time index k by x(k), the received signal after transmission on a flat-fading channel can be written as y(k) = α(k) ⋅ x(k) + w(k). Here, α(k) is the fading envelope and w(k) is complex-valued additive white Gaussian noise (AWGN) with statistically independent real and imaginary components. The fading envelope (α(k)) is a complex stochastic variable representing the resultant gain after summing all received signal components (line-of-sight, reflected and scattered) at the receiver. In this paper we shall assume that the receiver is able to perform perfect coherent detection, effectively performing perfect phase compensation and thus turning α(k) into a real-valued variable. In general, the received channel signal-to-noise ratio (CSNR) at a given time k is defined as (1) where Pr is the received signal power and Pn is the received additive noise power. The CSNR is often the most useful way of describing the channel’s state. We shall assume that a constant average transmit power P [W] is used, and that the two-sided power spectral density of the AWGN is N0 / 2 [W/Hz]. For a given channel bandwidth B [Hz], we then have (2) with E[γ (k)] = γ – = GP / (N0B) where G = E[α 2 γ(k) = (k)] is the average received power attenuation. Pr(k) Pn(k) , γ(k) = α2 (k) · P N0B 2.2 Nakagami Multipath Fading: A General Flat-fading Channel Model Of special interest is the so-called Nakagami multipath fading (NMF) model [3]. This is a very general statistical model covering or approximating a lot of interesting special cases, including the more well-known Rayleigh and Rice fading channels. The NMF model has been empirically shown to be able to provide a good fit to the fading experienced in a wide range of real-world wireless channels. In the case of an NMF channel, the fading envelope1) a has a so-called Nakagami-m distribution, which causes the received CSNR to become gamma distributed with PDF � �m m−1 m γ pγ(γ) = (3) ¯γ Γ(m) Here, m 1/2 is the Nakagami fading parameter, restricted in this paper to be an integer, and Γ(m) is the Gamma function, equal to Γ(m) = (m – 1)!. The Nakagami fading parameter can be loosely interpreted as the ratio between received line-ofsight signal power and received signal power from scattering and reflections. In other words, the higher m is, the more line-of-sight power dominates, making for a better channel less prone to deep fades. exp � −m γ � , γ ≥ 0. ¯γ ≥ 3 What to Learn from Information Theory Information theory tells us that any communication channel is characterized by a maximal information rate, the channel capacity, which provides the ultimate upper limit for when reliable transmission is possible [4]. For any given channel with a certain average CSNR, this channel capacity is a constant number, regardless of how strict the demands on bit-error-rate (BER) may be. This number has come to represent the “holy grail” for designers of bandwidth-efficient transmission schemes. It may be stated as the maximal average number of information bits which may be carried per transmitted channel symbol, or – if multiplied by the maximum (Nyquist) channel symbol rate – as the maximal average number of information bits per second. For any information rate we may choose to specify below the channel capacity, theory tells us that there always exist a transmitter and a receiver which are able to communicate at this rate with arbitrarily low BER. For rates above the capacity, we can be sure that no such transmitterreceiver pairs exist. Of course, finding the optimal transmitter-receiver pair may be a very complex task even if the specified information rate lies below capacity. Also, even if found, the capacity-achieving transmitter-receiver pair may be extremely complex to implement. Most current-day communication systems thus operate at rates significantly less than the theoretical capacity, although the advent of modern error-control coding schemes has decreased the gap between theory and practice considerably for some channels, and almost closed it in some special cases. 1) We suppress the time dependence from now on for the sake of notational simplicity. Telektronikk 1.2001
3.1 Information Theory for <strong>Wireless</strong> Channels Claude Shannon developed the general theory behind channel capacity and derived famous formulas for some important channel models, most notably the AWGN channel [4]. However, for wireless channel models, closed-form capacity formulas, and the design of efficient transmission schemes approaching the capacity, have remained elusive – until the last 5 years or so. In [5] Goldsmith and Varaiya derived the channel capacity of a single-user flat-fading channel with arbitrary fading distribution, when perfect channel state information (CSI) is available both at the transmitter and the receiver. The CSI needed by the transmitter is the CSNR γ. For a general flat-fading channel where the CSNR has PDF pγ (γ), the capacity is given by � C = B log2(1 + γ)pγ(γ)dγ [bits/s] (4) when fixed average transmit power is assumed. Alouini and Goldsmith [6] used this result to determine a closed-form expression for the capacity per unit bandwidth, or maximum average spectral efficiency (MASE), of an NMF channel C em/¯γ = B ln(2) Encoder 1 Encoder 2 • • • • Encoder N allγ m−1 � k=0 Telektronikk 1.2001 � �k � m Γ −k, ¯γ m � ¯γ [bits/s/Hz], (5) where Γ(⋅,⋅) is the complementary incomplete Gamma function [7]. This function is commonly available in numerical software. To any channel capacity corresponds some specific transmission scheme, the so-called capacity-achieving transmission scheme for the channel under discussion. This is the scheme that must be used if we are to actually fully exploit the capacity. Goldsmith and Varaiya [5] showed that the channel capacity of an arbitrary flat- • + x(k) y(k) α(k) w(k) CSNR γ(k) fading channel with constant average transmit power can be approached using a certain adaptive transmission scheme. This very fact constitutes the main motivation behind the study of rate-adaptive coding and modulation. To achieve capacity, the signal constellation size, and hence the information rate, must be continuously updated according to the channel quality, as measured by the CSNR γ. The transmission rate should be high when the CSNR is high, decreasing smoothly as the CSNR decreases. A block diagram depicting the main principles of a rateadaptive scheme is given in Figure 1. Observe that the active encoder-decoder pair is determined by the CSNR at the receiver. 3.2 Practical Modifications The theoretically optimal scheme described in the previous section must in practice be approximated by schemes using discrete updating of the information rate. One must then choose a particular set of discrete channel signal constellations, e.g. quadrature amplitude modulation (QAM) constellations of varying size [8]. For coded transmission, one must also choose a particular set of channel (error control) codes. The transmitter will then switch between signal constellations (and, in the case of coded transmission, channel codes) of varying size/rate at discrete time instances. At any given time, the transmitter chooses symbols from the largest constellation meeting the BER requirements with the available CSI, thus ensuring maximum spectral efficiency for the given acceptable BER. There are different kinds of adaptive coding schemes [9] – [17]. Hereafter, we shall use the term adaptive coded modulation (ACM) as a collective term for all variants. As mentioned earlier, the CSNR determines the channel state at a given time. For any discrete ACM scheme, the CSNR must be periodically estimated at the receiver end. We assume that this estimation can be done without error. The set [0, ∞) of possible CSNR values is divided into N + 1 non-overlap- Decoder 1 Decoder 2 • • • • Decoder N Figure 1 Rate-adaptive transmission 51
Page 2 and 3: Telektronikk Volume 97 No. 1 - 2001
Page 4 and 5: Per Hjalmar Lehne (42) obtained his
Page 6 and 7: Stein Svaet (41) is Senior Research
Page 8 and 9: Pbit/day 6 150 125 100 75 50 25 0 F
Page 10 and 11: 8 Video communication as a utility
Page 12 and 13: 10 The idea of reconfigurable mobil
Page 14 and 15: 12 Switched lobe Dynamically phased
Page 16 and 17: Figure 10 The All IP vision Figure
Page 18 and 19: 16 The IP world has some problems t
Page 20 and 21: 18 Abbreviations and acronyms less
Page 22 and 23: Jorge Pereira (40) obtained his Eng
Page 24 and 25: (Millions) Figure 1 Exponential gro
Page 26 and 27: 24 Defining Generation based upon D
Page 28 and 29: Multi-mode Terminal by Software Rad
Page 30 and 31: distribution layer possible return
Page 32 and 33: 30 A Co-Ordinated Approach to 4G As
Page 34 and 35: Figure 2 Applications will grow fas
Page 36 and 37: Figure 5 Evolution from multi-mode
Page 38 and 39: Operator/Provider download librarie
Page 40 and 41: Radio network subsystem - service c
Page 42 and 43: Dr. Techn. Jørgen Bach Andersen (6
Page 44 and 45: Figure 3 Two arrays with M and N el
Page 46 and 47: Figure 5 Cumulative probability dis
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Page 50 and 51: 48 Conclusion The challenge of prov
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Figure 2 The first use case diagram
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Figure 10 Initiating call from PSTN
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Figure 13 Splitting the incoming st
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134 Telektronikk 1.2001
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Anne Lise Lillebø (52) is Adviser
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