V.Bota, Zs.Polgar, M.Varga Communications Department, Technical University Cluj-Napoca Performances of the H-ARQ Adaptive-QAM Transmissions over Multipath Channels

TUCN Data Transmissions Laboratory COST 289 "Power & Spectrum Efficient Broadband Communications" 4th Workshop Gothenburg April Overview Factors that affect the performances provided by the adaptive use of a set of (non-)coded QAM modulations over a mobile multipath channel within an OFDM transmission scheme governed or not by an H-ARQ protocol: 1. the ODFMA transmission scheme 2. the set of (non-)coded QAM configurations (code +modulation), Coded configurations Chunk-error probability Spectral efficiency provided by a configuration Selected set of coded configurations Considerations regarding the SNR thresholds that separate the SNR domains 3. the user-chunk allocation method (BFP, FH) 4. channel modeling - the channel state probabilities 5. the average efficiency of non-ARQ transmissions for various coding schemes 6. the average efficiency of SW H-ARQ transmissions for various coding schemes

TUCN Data Transmissions Laboratory COST 289 "Power & Spectrum Efficient Broadband Communications" 4th Workshop Gothenburg April I. TFL- ODFMA Transmission Scheme N sbc = 416 payload subcarriers with a frequency separation f s = kHz; an user-chunk consisting of A subcarriers x E OFDM symbol periods (A = 8, E = 12) that contains L-QAM payload symbols, L = 81; the maximum number of users N usM = N sbc /A = 52. chunk duration E OFDM-symbols Figure 1 OFDMA multiuser access principle and chunk structure. chunk bandwidth A OFDM subcarriers f s subcarrier separation OFDM symbol period time-frequency chunks the chunk rate C R = f s /[(1+Gi)E]= ch/s; a guard-interval Gi=0.125, the user-chunk bandwidth BW ch = A f s = kHz, [1], [2]. the chunk parameters allow for v ≤ 250 km/h and delay-variance of the multipath channel ≤ 6  s for a correlation factor of 0.5. the channel might be considered constant over the chunk bandwidth and during the chunk period.

TUCN Data Transmissions Laboratory COST 289 "Power & Spectrum Efficient Broadband Communications" 4th Workshop Gothenburg April II. A. Coded QAM Configurations an LDPC coded configuration is the assembly of a QAM constellation of n t bits/symb and a LDPC code of rate R ct and N t bits/codeword; the array-based regular L(2,q) LDPC codes, defined by parameters (k, j, p) with a triangular-shaped control matrix and girth equaling 6, [3]. the codeword is N t = kp bits long, with N it = (k-j)p information bits they “powerfull’ codes at rather high coding ratios and have a good ratio flexibility foe a given codeword length the configuration rate if only coded bits are mapped equals: (1) both coded and non-coded payload bits are mapped on the QAM symbols to increase the configuration rate, R cfg’ : (2)

TUCN Data Transmissions Laboratory COST 289 "Power & Spectrum Efficient Broadband Communications" 4th Workshop Gothenburg April II.A. Coded QAM Configurations the coded and non-coded bits are mapped on the QAM symbol using a 2-level Gray mapping, [4]. the coded bits are decoded using the Message-Passing algorithm (MPA), [4], with maximum B=15 iterations/codeword and the a posteriori probabilities of the bits demapped from a QAM symbol are extracted by means of the soft-demapping procedure [5], both for the coded and non- coded bits. the non-coded bits are decided using a soft decision algorithm that uses the corrected coded bits, delivered by the MPA, mapped on the same QAM symbol, [6], in a similar manner to the Trellis Coded Modulation, [7]. by appropriate bit-mapping and demapping and the soft-decision algorithm, the error probability of the non-coded bits is close to the one of the coded bits; so, the mapping of the non-coded bits increases the coding rate without affecting significantly the error performances, [6].

TUCN Data Transmissions Laboratory COST 289 "Power & Spectrum Efficient Broadband Communications" 4th Workshop Gothenburg April II.B. Chunk-Error Probability the symbol error probability of a QAM constellation with N t points and the bit- error rate, assuming a Gray mapping of the bits on the symbol, [9]: SNR t denotes the S/N ratio (in dB) considered for configuration t SNR t eq (3.c) is increased with the coding gain C Gt of the coded configuration t, referred to the non-coded constellation with the same number of bits/symbol. the coding gains were established by computer simulations, [9]. the probability of an L∙n t -bit chunk, transmitted with configuration t on a channel with SNR t, to be correctly received or decoded is: (4)

TUCN Data Transmissions Laboratory COST 289 "Power & Spectrum Efficient Broadband Communications" 4th Workshop Gothenburg April II.C. Spectral Efficiency Provided by a Configuration the nominal bit rate of a transmission using a configuration with n t bits/symb is: the throughput is obtained by multiplying the nominal bit-rate to the probability of correctly decoded chunks: Θ ct (SNR t ) = C R ·L·n t ·R cfgt  p ccht (SNR t ) the spectral efficiency results by dividing the throughput Θ ct by the chunk bandwidth BW c : For the particular OFDMA scheme of section I it is : D ct = C R ·L·n t ·R cfgt (bit/s) (5) (6) (7) (8)

TUCN Data Transmissions Laboratory COST 289 "Power & Spectrum Efficient Broadband Communications" 4th Workshop Gothenburg April II.D. Set of non-coded QAM configurations- NC the set of coded modulations to be employed adaptively should observe the following requirements: a.each configuration should provide the highest spectral efficiency, on a limited domain of SNR ; the extension of this domain depends of the SNR range that should be covered by the adaptive system and of the number of configurations included in it, which at its turn depends on the processing resources. b.the thresholds separating the SNR domains where each configuration ensures the highest spectral efficiency should be set differently, depending on the packet or chunk error-rates imposed c. the variation of the spectral efficiency between a configuration and its neighbors in the set should have a moderate value of about bps/Hz; such variations would ensure a smaller granularity of the spectral efficiency, which would affect less the average spectral efficiency of the adaptive system, when configurations are used outside their domains of optimality, due to erroneous channel estimation/prediction. This requirement also calls for a large number of configurations in the set.

TUCN Data Transmissions Laboratory COST 289 "Power & Spectrum Efficient Broadband Communications" 4th Workshop Gothenburg April II.D. Set of non-coded QAM configurations- NC the NC set consists of non-coded QAM modulations with n k = 1,..,11 bits/symb separated by thresholds T k – table 1.b figure 2.b presents the SNR domains where the QAM constellations are employed (channel states) for n k = 1,…,8 on an AWGN channel n k bit/sb T k [dB]T 1 -2 T 2 ; 8.3 T T T T n k bit/sb T k [dB]T T T 9 33 T T S7 S6 S8 S3 S4 S2 S1 S5

TUCN Data Transmissions Laboratory COST 289 "Power & Spectrum Efficient Broadband Communications" 4th Workshop Gothenburg April II.D. Set of LDPC-coded QAM configurations- C The C set consists of S =12 LDPC- coded QAM configs. based on 256,64,16, 4-QAM and 2-PSK – table 2.a and figure 2.a. The LDPC codes are defined by parameters k, j, p [10]. The configurations are defined by the numbers of coded and non- coded bits/symbol, by their coding rates and by the coding gains. The coding gains are referred to the non-coded QAM modulations with the same numbers of bit/symbol, n t. The thresholds T k of the SNR domains (channel states – S k ) where each configuration is optimum are also shown. IndCodentnt Configuration parameters tkjpn ct n nt R cfgt η ct [bps/Hz]T t [dB]G ct [dB]

TUCN Data Transmissions Laboratory COST 289 "Power & Spectrum Efficient Broadband Communications" 4th Workshop Gothenburg April the spectral efficiency varies slightly, with bps/Hz, between neighboring configurations; this feature has the disadvantage of requiring 12 configurations in the set (note that DoCoMo uses 14 [11], and Flarion uses 16, [12]) when a channel state prediction error occurs, the effects are not very significant, since the most probable prediction error would lead to the employment of a neighboring configuration instead of the correct one Figure 2.a. η vs. SNR of configurations of set ACM, table 2. II.D. Set of LDPC-coded QAM configurations- C

TUCN Data Transmissions Laboratory COST 289 "Power & Spectrum Efficient Broadband Communications" 4th Workshop Gothenburg April II.E. Considerations Regarding the SINR Thresholds that Separate the SNR Domains Two criteria were considered in threshold setting: 1.Imposing a CER = ; the BER required to ensure CER=10 -2 range between 2  10 -5, for 256-QAM, and 1.2  10 -4, for 2-PSK – see figure 2.c. this constraint ensures practically constant spectral efficiencies for each coded configuration, within its SNR domain, at a value > 0.99 of its nominal one. 2. Thresholds determined by the intersections of spectral efficiency curves (CI) These thresholds take the x-axis values of the intersection points of the  (SNR) curves of set C – see figure 2.a, previous slide. Their values are with dB smaller than the thresholds obtained imposing CER < The spectral efficiencies provided are no longer constant within one interval lg(CER) Figure 2.c. CER vs. SNR of the coded configurations of set C.

TUCN Data Transmissions Laboratory COST 289 "Power & Spectrum Efficient Broadband Communications" 4th Workshop Gothenburg April II.E. Considerations Regarding the SNR Thresholds that Separate the SINR Domains the spectral efficiencies provided, for 1 user with v = 70 km/h, by the adaptive use of set ACM using the thresholds provided by the two criteria within the OFDMA scheme, over the WP5 Macro channel [13]: the CI thresholds lead to higher spectral efficiency for low and medium SNR values (with 0.2 bps/Hz for SNR<15 dB) the CER values grow up to 5∙ the CI thresholds might be employed in non-ARQ environments, but in H-ARQ schemes they would lead to significantly poorer performances and to an increase of the latency inserted, due to the higher rate of retransmissions.  [bps/Hz SNR 0 [dB] CI CER Figure 2.d.  vs. SNR0 of set C employed adaptively on the WP5 Macro channel using the CI or the CER= thresholds

TUCN Data Transmissions Laboratory COST 289 "Power & Spectrum Efficient Broadband Communications" 4th Workshop Gothenburg April III. Joint Channel-Allocation Modeling the user-chunk allocation method ensures the frequency diversity, to compensate the variable attenuation of the Rayleigh fade of the mobile multipath channel; the method employed is Best Frequency Position (BFP), i.e. each user- chunk is allocated the group of C u sub-carriers that ensure the best average SINR for the bin-period envisaged, [2]; involves the state-prediction of all available bins, over a prediction time- horizon, performed by the user mobile station. the channel prediction is assumed to be perfect a multipath propagation channel defined by the WP 5 Macro model [13]. this channel together with the set of thresholds and BFP-allocation, define an equivalent channel that exhibits S states. the states are defined by the thresholds T t that separate the average SNR domains and by the probabilities w t to be in state S t, i.e. the average channel SNR to range between T t and T t+1. a detailed presentation of this joint modeling of the channel and user- chunk allocation method can be found in the complementary paper [14].

TUCN Data Transmissions Laboratory COST 289 "Power & Spectrum Efficient Broadband Communications" 4th Workshop Gothenburg April III. Joint Channel-Allocation Modeling the probabilities w t of the employed channel are presented in table 2, for a SNR 0 =16 dB of the firstly-arrived path for N us = 1; the T t are CER = Tk [dB]→ N us = 1 T T T T T T wt wt 02∙  ∙ ∙ due to the multipath propagation and to the BFP method, the SNR during more than 99% of the chunk periods is greater with 5-10 dB than the SNR ensured by the first arrived path, i.e. SNR 0 = 16 dB allowing the employment of large constellations with CER < Figure 2.a. η vs. SNR of configurations of set ACM, table 2.

TUCN Data Transmissions Laboratory COST 289 "Power & Spectrum Efficient Broadband Communications" 4th Workshop Gothenburg April IV. Average Spectral Efficiency of a non-ARQ Scheme the average probability of a chunk to be correctly decoded, considering all possible channel states, is expressed by (9); the average probability of an M-chunk long packet to be correctible received and the average probability of retransmission for such a packet are expressed by (10.a, 10.b) (9) (10) in an application not governed by an ARQ protocol, the nominal average bit rate D nav, the average throughput Θ n and the average spectral efficiency η av are shown in (11), where R ec denotes the rate of an external code applied to the whole M-chunk packet. the average time required for the transmission of an U-bit long packet (U not an integer multiple of the average chunk length) is given by (12). (11) (12)

TUCN Data Transmissions Laboratory COST 289 "Power & Spectrum Efficient Broadband Communications" 4th Workshop Gothenburg April IV. Average Spectral Efficiency of a non-ARQ Scheme the average spectral efficiency of the described transmission scheme in a non-ARQ environment is computed on a WP5 Macro channel for v=30 km/h. M = 8-chunk packets were considered [1]. the configurations adaptively employed at the chunk level are either non- coded, n k bits/symbol, NC slide 9, or LDPC-coded, n c +n n bits/symbol, C slide 10, with coding gain C gk and configuration rate R ck. the spectral efficiency and packet error rates vs. SNR 0 curves are shown in figures 6 and 7 on the next slide, for the following coding schemes: 1. non-coded, using adaptively configurations of table of slide 7; CER< T t 2. coded at chunk-level, using adaptively the configurations of slide 10; CI - T t 3. coded at frame-level with an external LDPC code, R ce =0.86, C Ge =6.5 – 7 dB, using adaptively configurations of slide 9; 4. same as above, but the external LDPC code has, R c = 0.91,C Ge = dB. the average numbers of bits mapped/QAM symbol for the coding schemes employed are shown in table 4, for several values of the SNR 0. It also includes the lengths of the external R ce =0.86 code employed (1 cwd/ packet).

TUCN Data Transmissions Laboratory COST 289 "Power & Spectrum Efficient Broadband Communications" 4th Workshop Gothenburg April IV. Average Spectral Efficiency of a non-ARQ Scheme Figure 3 Packet error probabilities vs. SNR 0 for Figure 4 Average spectral efficiency vs. SNR 0 for different coding schemes – 8 chunks/packet, different coding schemes – 8 chunks/packet SNR 0 (dB) n t av bits /symb non-coded & ext.-coded n t av bits /symb chunk coded Cwd length 8-chunk/packet Table 4. Average no. of bits/symbol and external codeword lengths, R ce =0.86, for M = 8 chunk/packet

TUCN Data Transmissions Laboratory COST 289 "Power & Spectrum Efficient Broadband Communications" 4th Workshop Gothenburg April IV. Average Spectral Efficiency of a non-ARQ Scheme. Comments the spectral efficiency of the non-ARQ transmissions is affected by two contradicting factors: a.the average number of bits mapped adaptively/symbol; columns 2 and 3 of table 6 show that this number is significantly higher for the chunk-coded scheme because the set of configurations is larger, i.e. smaller granularity, and because of the non-coded bits mapped, which increase the configuration rate and the first factor of (11.c). b.the packet-error probability, which is dependant of the packet length and of the correction capability of the code, and decreases the second factor of (11.c). the 1- P cp av for the chunk level coding is higher than the one of the packet level coding, see figure 6. This can be explained two facts: 1.the SNR thresholds of the coded set of slide 9 were imposed so that CER ≤ ; 2.the packet-error probability, depending on the packet length, the correction capability of the code and the set of thresholds, which decreases the second factor of (11.c).

TUCN Data Transmissions Laboratory COST 289 "Power & Spectrum Efficient Broadband Communications" 4th Workshop Gothenburg April IV. Average Spectral Efficiency of a non-ARQ Scheme. Comments the average spectral efficiency is a trade-off, see (11.c), between the average n k (including its granularity and the coding rates) and P cp av (depending of the C Gk ). the global computation of (11) presented in figure 4, shows that the chunk- coded scheme has a higher spectral efficiency, than the packet-coded scheme, though it exhibits higher packet error rates. this is because the first factor of (11.c) is larger for this coding scheme and compensates the smaller value of the second factor. the thresholds settings may be adapted to the application to ensure the desired trade-off between packet-error rate and spectral efficiency. (11)

TUCN Data Transmissions Laboratory COST 289 "Power & Spectrum Efficient Broadband Communications" 4th Workshop Gothenburg April IV. Average Spectral Efficiency of a non-ARQ Scheme. Comments Effects of channel-state misprediction, i.e. S t’ for S t : a. if t’ R cfgt, but poorer correction capability → chunk p ccht’ and packet, P pcav decreases, fig.2 → decrease of the η av, because the decrease of P pcav would prevail the increase of the first factor of (11.c) induced by the greater Rcfg’. b. if t’ > t, i.e. R cfgt’ < R cfgt, but greater correction capability, → chunk p ccht’ and packet, P pcav increase with less than 1%, due to the T t - CER < 10-2 →lower η av, because the increase of P pcav would be smaller than the decrease of the first factor of (11.c) induced by the smaller R cfg’

TUCN Data Transmissions Laboratory COST 289 "Power & Spectrum Efficient Broadband Communications" 4th Workshop Gothenburg April V. SW H-ARQ average spectral efficiency the throughput and spectral-efficiency performances of the proposed transmission scheme are now analyzed within an Stop & Wait Hybrid ARQ (SW H-ARQ) protocol [15] which employs adaptively a set of (non)coded modulations. the SW–ARQ employs an M-chunk long packet, performing one transmission and q retransmissions of the whole packet before count time-out. The count timeout lasts for T T seconds and the protocol resumes the transmission, after the count timeout, with the packet that generated the count time-out (Z-type protocol). A perfect (N)ACK transmission across the uplink connection is also assumed. for application governed by the H-ARQ protocol defined above, the average probability of an M-chunk long packet to be correctible received and acknowledged after its transmission (first attempt) P 0 av and the average probability of retransmission are: (13)

TUCN Data Transmissions Laboratory COST 289 "Power & Spectrum Efficient Broadband Communications" 4th Workshop Gothenburg April V. SW H-ARQ average spectral efficiency the average probability of such a packet to be positively acknowledged after the i-th retransmission P i av, and the average probability to reach the count time-out state after a transmission and q retransmissions, P T av are: (14) the impact of the T T is equivalated by a multiple d av of the average number of bits that could be transmitted during a packet: (15) the average total number of payload bits that are successfully acknowledged, after the (q+1) attempts, is: (16) the average total number of transmitted bits N t av required to successfully acknowledge the N u av bits after the q+1 attempts (including the count time-out):

TUCN Data Transmissions Laboratory COST 289 "Power & Spectrum Efficient Broadband Communications" 4th Workshop Gothenburg April V. SW H-ARQ average spectral efficiency the protocol efficiency, i.e. the ratio between the N u av and the N t av is: (18) the average throughput and spectral efficiency of the transmission governed by an H-ARQ protocol are: (19) Comments: if the protocol requirements are removed, i.e. no count timeout (d av = 0) and no retransmissions (q = 0), the ς H = P cp av, see (13) and (18), and the spectral efficiency is the one of the non-protocol schemes, see (11). for q > 0, the ς H is smaller than P cp av and increases with the increase of q; for an infinite number of retransmissions (q →  ) the ς H → P cp av and the spectral efficiency of the protocol scheme tends to the one of the non-protocol scheme.

TUCN Data Transmissions Laboratory COST 289 "Power & Spectrum Efficient Broadband Communications" 4th Workshop Gothenburg April V. SW H-ARQ average spectral efficiency the performances of configurations from sets NC and C, slides 9 and 10 were evaluated for an H-ARQ protocol in the conditions described before. the H-ARQ parameters are: q=3 retrs. d av = 5, M = 8 chunk/packet. the average spectral efficiencies ensured by the coding schemes of slide 17 are presented in figure 5. the chunk-level coded scheme provides higher spectral efficiencies than the packet-level coding schemes, due to the same reasons as before. the two contradictory factors that affect the  av, slide 19, (11.c), affect  H av in a similar manner, but P cp av is replaced by the second factor of ς H, (18). the values of  p av are smaller than in the non-protocol case due the count time- out interval C T, d av in (18), but the received packets are corrected with a probability equaling (1- P T av ).

TUCN Data Transmissions Laboratory COST 289 "Power & Spectrum Efficient Broadband Communications" 4th Workshop Gothenburg April V. SW H-ARQ average spectral efficiency Comments the channel-state prediction errors affect the performances in a similar manner as in the non-ARQ scheme. the average time required to transmit an M-chunk packet under the H-ARQ protocol is: (20) an U-bit long frame is spread into J packets (21) and is transmitted, in a time interval equaling J  t H av. the average delay inserted by the protocol is (22) and decreases with the increase of  H. (21) (22)

TUCN Data Transmissions Laboratory COST 289 "Power & Spectrum Efficient Broadband Communications" 4th Workshop Gothenburg April VI. CONCLUSIONS the average spectral efficiency of such transmissions is significantly affected by the number of configurations adaptively used for both non-ARQ and H-ARQ schemes. the coding rates of the employed configurations affect in two contradictory ways the  av : o by decreasing the number of payload bits transmitted o by increasing their probability of correct decoding. o the trade-off between these trends is accomplished within a limited range of SNR, where the respective coded configuration should be employed. due to the numerous factors that have contradicting influences, the efficiency provided by such a scheme should be analyzed for each particular case. for the particular case studied, the chunk-level coding scheme ensures higher spectral efficiencies for small packets, because it allows the adaptive employment of more coded QAM configurations, while for longer frames (more packets) the two coding schemes provide close spectral efficiencies. this conclusion holds for coding schemes that employ only one correcting code, either at the chunk-level or at the M-chunk packet level.

TUCN Data Transmissions Laboratory COST 289 "Power & Spectrum Efficient Broadband Communications" 4th Workshop Gothenburg April VII. Questions for Further Study the trade-off between the average spectral efficiency and packet-error rate might be balanced, for chunk-level coding which uses adaptively a set of coded modulations, to meet the service requirements, by modifying the thresholds that separate the SNR domains where the modulations are employed. a significant increase of the average spectral efficiency might be brought by the employment of concatenated codes, the outer code at the packet-level and the inner code at the chunk-level. The employment of concatenated LDPC codes, or LDPC-error detecting codes, together with a combined decoding might bring significant performance improvements, for both ARQ and non-ARQ schemes. the derivation of the average spectral efficiency presented in this paper may be applied for the coding scheme employing concatenated codes, both for non-ARQ and for H-ARQ transmissions. the employment of erasure codes at the packet-level coding could also improve the reliability of non-ARQ schemes

TUCN Data Transmissions Laboratory COST 289 "Power & Spectrum Efficient Broadband Communications" 4th Workshop Gothenburg April References (selected) [ 1] IST WINNER, “Final report on identified RI key technologies, system concept, and their assessment”, Report D2.10 v1.0, December [2] M. Sternad, T. Ottosson, A. Ahlen, A. Svensson, “Attaining both Coverage and High Spectral Efficiency with Adaptive OFDM Downlinks”, Proc. of VTC 2003, Orlando, Florida. [3] E. Eleftheriou, S. Olcer, “G.gen:G.dmt.bis:G.lite.bis: Efficient En­coding of LDPC Codes for ADSL”, ITU- T, Temporary Document SC-064, [4] D.J.C. McKay, “Good error-correcting codes based on very sparse matrices,” IEEE Trans. on Information Theory, vol. 45, March, [5] ITU-T, “LDPC codes for G.dmt.bis and G.lite.bis,” Temporary Document CF-060. [6] V. Bota, Zs. Polgar, M. Varga,,”Performances of LDPC-Coded OFDM Transmissions and Applications on Fixed and Mobile Radio Channels”, Proceedings of COST 289 Seminar on Spectrum and Power Efficient Broadband Communications, Barcelona, October [7] G.Ungerboeck, “ Trellis-Coded Modulation with Redundant Signal Sets, Part I and Part II”, IEEE Communications Magazine, vol.25, No.2, February [8] Th. S. Rappaport, Wireless Communications, New Jersey: Prentice Hall PTR, [9] V. Bota, M. Varga, Zs. Polgar, “Performances of the LDPC-Coded Adaptive Modulation Schemes in Multi-Carrier Transmissions”, Proceedings of COST 289 Seminar on Spectrum and Power Efficient Broadband Communications, July, 2004, Budapest, Hungary. [10] V. Bota, M. Varga, Zs. Polgar, “Convolutional vs. LDPC Coding for Coded Adaptive-QAM Modulations on Mobile Radio Channels”, Report at the 8th MCM of COST 289 Seminar on Spectrum and Power Efficient Broadband Communications, Madrid, October [11] H.Atarashi, N.Maeda, S.Abeta, M.Sawahashi - “Broadband Packet Wireless Access Based on VSF- OFCDM and MC/DS-CDMA”, NTT DoCoMo, PIMRC [12] R. Dineen, - “Flarion Technologies”, Ovum [13] IST WINNER, “Assessment of Radio-link technologies”, Report D2.3 ver 1.0, Feb [14] Zs. Polgar, V. Bota, M. Varga, “Modeling the Rayleigh-Faded Mobile Radio Channel”, submitted to WETTIT 2006, October 2006, Cluj-Napoca, Romania. [15] H. Tanembaum, “Computer Networks”, Prentice Hall, 1989.

TUCN Data Transmissions Laboratory COST 289 "Power & Spectrum Efficient Broadband Communications" 4th Workshop Gothenburg April Annex T k [dB]→ N us  T T T T T T ∙  ∙ ∙ ∙  ∙ ∙ ∙ ∙ ∙ ∙ ∙