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Theory Drilling Machines

Ofdm-Based Cooperative Communications in a Single Path Relay Network and a Multiple Path Relay Network Essays

Ofdm-Based Cooperative Communications in a Single Path Relay Network and a Multiple Path Relay Network Essays Ofdm-Based Cooperative Communications in a Single Path Relay Network and a Multiple Path Relay Network Essay Ofdm-Based Cooperative Communications in a Single Path Relay Network and a Multiple Path Relay Network Essay In this thesis, we investigate cooperation by applying OFDM signals to cooperative relay networks. We consider the single path relay network and the multiple path relay network. Using the amplify-and-forward relay algorithm, we derive the input-output relations and mutual informations of both networks. Using a power constraint at each relay, we consider two relay power allocation schemes.The ? rst is constant gain allocation, where the amplifying gain used in the amplify-and-forward algorithm is constant for all subcarriers. The second is equal power allocation, where each subcarrier transmits the same power. The former scheme does not require CSI (channel state information), while the latter one does. We simulate the mutual informations using the two relay power allocation schemes. Results indicate that equal power allocation gives a slightly higher mutual information for the single path relay network. For the multiple path network, the mutual information is practically the same for both schemes.Using the decode-and-forward relay algorithm, we derive the inputoutput relations for both networks. The transmitter and each relay are assumed to have uniform power distributions in this case. We simulate the BER (bit error rate) and WER (word error rate) performance for the two networks using both the amplify-and-forward and decode-and-forward relay algorithms. For the single path relay network, amplify-andforward gives very poor performance, because as we increase the distance between the transmitter and receiver (and thus, add more relays), more noise and channel distortion enter the system. Decode-and-forward gives signi? antly better performance because noise and channel distortion are eliminated at each relay. For the multiple path relay network, decode-and-forward again gives better performance than amplify-and-forward. However, the performance gains are small compared to the single path relay network case.Therefore, amplify-and-forward may be a more attractive choice due to its lower complexity. ix CHAPTER I INTRODUCTION Wireless communication systems inherently su? er from multipath propagation and channel fading. Time diversity, space diversity, frequency diversity [8], and combinations of the three are traditionally used to combat these e? cts. More recently, relays situated between the transmitter and receiver are also being exploited to improve information transfer. The relays are a network of transceiver nodes between the transmitter and receiver that facilitate the transfer of information. Thus, the relay network as a whole is an equivalent channel between the transmitter and receiver. This type of scheme is known as cooperation or cooperative communications in the literature because the relay network is cooperating with the transmitter and receiver to improve performance.In this thesis, we consider cooperation in the context of orthogonal frequency division multiplexing (OFDM) systems. 1. 1 Motivation The motivation for cooperati ve communications is obvious. Cellular phones, laptops and personal digital assistants (PDAs) are just three examples of wireless devices that are very prevalent today. These transceiver devices usually communicate independently from each other. As the authors in [6] note, this is wasting the broadcast nature of the wireless medium.For example, if a base station is communicating with a user’s cellular phone, his/her nearby laptop has the capability to receive the base station’s signals and relay them to the phone, improving the end-to-end performance of the base station-phone link. Unfortunately, laptops and cellular phones today are not designed this way. This illustration is an example of an ad-hoc network, where nodes spontaneously recognize each other and cooperate. In this thesis, we investigate structured networks, where each node knows the existence of all the other nodes a priori.Whether the nodes discover each other through an ad-hoc algorithm or they are pre- programmed to have this knowledge is beyond the scope 1 of this thesis. 1. 2 Related Literature The authors in [10], [11] have considered cooperation between intra-cell users in a code division multiple access (CDMA) cellular network. In this case, cooperation results in higher data rates and leads to lower power requirements for users. As well, the system is less sensitive to channel variations. Relaying of signals, as viewed from the physical layer, is not a trivial issue. The authors in [5], [6], [7] have provided several physical layer relay algorithms.These include amplifyand-forward, decode-and-forward and selection relaying. In amplify-and-forward, a node ampli? es its receive symbol, subject to a power constraint, before re-transmitting to the next node. This algorithm is obviously with low complexity. In decode-and-forward, a node fully decodes a symbol, re-encodes it and then re-transmits it. In other words, this scheme attempts to eliminate channel distortion and noise at each node. In selection relaying, a node only re-transmits a symbol if the measured receiving channel gain is above a certain threshold.If the threshold is not reached, the relay requests a re-transmission from the sender. In networking terminology, this is a type of automatic repeat request (ARQ) scheme. The authors in [6], [7] have investigated cooperation for the classical relay channel introduced in [1], [7]. Outage probability is used to characterize performance. Outage probability is the probability that the mutual information between the transmitter and receiver does not reach a certain throughput threshold. Without cooperation, the outage probability decays proportionally with 1/SNR, where SNR is the signal-to-noise ratio of the channel.Using cooperation and the amplify-and-forward scheme, the outage probability decays proportionally with 1/SNR2 , achieving full diversity. This results in large power savings for the transmitter. The authors in [3], [4] have investigated coo peration for a single path of relays connected in series. The motivation for this network structure is that broader wireless coverage can be achieved, while still maintaining a low power constraint at the transmitter. The authors consider analog relaying and digital relaying as two possible relay algorithms. These are 2 equivalent to the amplify-and-forward and decode-and-forward algorithms, respectively.A power budget is considered where each packet travelling through the network is only allowed to consume a total ? xed amount of power. As well, each node has a certain transmit power limit. The outage probability is then minimized by allocating power among the relay network under these power constraints. This power allocation accounts for the channel conditions in the network in order to achieve the optimal outage probability. Simulations indicate that 2 dB of total power can be saved for 5 relays by using optimal power allocation instead of uniform power allocation. This is for th e decode-and-forward case.However, at high SNR values, the decode-and-forward case approximates the amplify-and-forward case. The authors in [13] have investigated cooperation for multiple paths of relays connected in parallel. In the conventional scheme, all relays participate using amplify-and-forward. This is called all-participate amplify-and-forward (AP-AF). The authors also consider an algorithm where only one relay is selected in the transmission to maximize the mutual information. This is called selection amplify-and-forward (S-AF). S-AF selects the relay which results in the maximum mutual information between transmitter and receiver.Simulations of outage probability indicate that 5 dB of SNR can be saved for 3 relays by using S-AF instead of AP-AF. The authors in [9] derive symbol error probabilities for multiple paths of relays. 1. 3 OFDM in Cooperative Communications In this thesis, we continue to investigate cooperation by applying OFDM signals to cooperative relay netw orks. We consider a single path relay network and a multiple path relay network. Using the amplify-and-forward relay algorithm, we derive the input-output relations and the mutual informations of both networks. Using a power constraint at each relay, we consider two relay power allocation schemes.The ? rst is constant gain allocation, where the amplifying gain used in the amplify-and-forward algorithm is constant for all subcarriers. The second is equal power allocation, where each subcarrier transmits the same power. We simulate the mutual informations using these two relay power allocations. Using the decode-and-forward relay algorithm, we derive input-output relations for both 3 networks. We simulate bit error rates (BERs) and word error rates (WERs) for the two networks using both the amplify-and-forward and decode-and-forward relay algorithms. 1. 4Organization of Thesis The thesis is organized as follows. In Chapter 2, we consider the single path relay network in [3], [4]. In C hapter 3, we consider a modi? ed version of the multiple path relay network in [13] where the transmitter-receiver direct link is removed. Notice that these latter two relay con? gurations are series and parallel analogs of each other. As well, they do not involve a direct link between the transmitter and receiver. Finally, Chapter 4 concludes the thesis and provides future research directions. 4 CHAPTER II SINGLE PATH RELAY NETWORK 2. 1 2. . 1 Amplify-and-Forward System Model Figure 1 shows the single path relay network. In the ? gure, r0 is the transmitter, rm+1 is the receiver, and r1 , . . . , rm are m relay nodes connected in series forming a single path link between the transmitter and receiver. The relays perform amplify-and-forward (AF) relaying. We assume that OFDM with N subcarriers is used in the system. hk , . . . , hk (0) (m) (0) are the complex subchannel gains at the kth subcarrier in the link, for (m) k = 1 to N . nk , . . . , nk are the corresponding noises, which a re assumed to be mutually ndependent, zero-mean, circular symmetric complex Gaussians all with variance N0 B/N , where N0 is the power spectral density of the underlying continuous time noise process and B is the OFDM bandwidth of the system. Let pk = Ptot /N be the transmitter power on (l) the kth subcarrier, where Ptot is the net transmitter power. Let pk be the amplifying gain used in the amplify-and-forward algorithm at the lth relay, for l = 1 to m. The kth (0) receive symbol at rl is ampli? ed by pk before it is forwarded to the next node. (l) Let xk be the kth transmit symbol with zero mean and unit variance.Let yk be the kth receive symbol at the receiver. Using Figure 1, the input-output relation is (0) nk r1 nk hk (1) (m? 1) nk (m) rm+1 r0 hk (0) hk (m? 1) rm hk (m) Receiver Transmitter Figure 1: Single Path Relay Network 5 m yk = i=0 (i) hk (i) pk m xk + j=0 ? ? m (i) hk i=j+1 where we assume r i=q a(i) = 1 for q gt; r and any a(i) . We use this assumption throughout (i) (j) pk ? n k , ? (1) the rest of this paper. If we de? ne m hk = i=0 hk (i) pk , ? k = i=j+1 (i) (j) m hk (i) pk , (i) (2) ?k = and ?k (0)  ·  ·  · ? k (m) , nk = nk (0)  ·  ·  · nk (m) T , (3) wk = ? k nk , then (1) can be written as yk = hk xk + wk .Now, consider the variance of wk . Using (2), (3), and (4), we have Rw k w k ? = E [wk wk ] (4) (5) (6) (7) (8) (i) (i) bk p k ? , = E ? k nk nH ? H k k = ? k E nk nH ? H k k = N0 B N m j=0 ? m where E [ ·] is the expectation operator, ( ·)? is the complex conjugate operator for a scalar, ( ·)H is the Hermitian (complex transpose) operator for a vector or matrix, and bk = hk (i) (i) 2 ? i=j+1 ? (9) , for i = 0 to m. Rwk wk is positive for a nonzero N0 . We de? ne a transformed version of the system in (5) ? yk = hk xk + wk , ? ? (10) 6 ? where yk = yk / Rwk wk , hk = hk / Rwk wk , and wk = wk / Rwk wk .The variances of wk ? ? ? and yk are ? E [wk wk ] = E ? = wk Rwk wk ? wk Rw k w k (11) (12) (13) Rw k w k Rw k w k = 1 and E [? k yk ] = E y ? hk xk + wk ? ? hk xk + wk ? ? (14) (15) ? ? = hk h? + 1 k = 1 Rw k w k m i=0 bk p k (i) (i) + 1, (16) ? ? respectively. The cross terms do not appear in (16) because hk , wk , and xk are mutually independent. Note that the transformed system has unit variance noise. 2. 1. 2 Mutual Information To derive the mutual information, note that the di? erential entropy of a circular symmetric complex Gaussian vector, v, with covariance matrix, K, is h (v) = log2 det (? eK) [2].When the circular symmetric complex Gaussian is a scalar, v, the di? erential entropy is 2 2 h (v) = log2 ? e? v , where ? v is the variance of v. Let Ik be the mutual information between the transmitter and receiver on the kth subcarrier Ik = h (? k ) ? h (wk ) y ? = log2 ? e = log2 1 Rwk wk 1 Rw k w k m i=0 m i=0 (17) bk p k bk p k (i) (i) (i) (i) +1 ? log2 (? e) (18) (19) +1 , where the ? rst equality comes from basic mutual information calculations [1]. The total mutual information betwe en the transmitter and receiver, I, is the sum of all Ik divided by N . That is, after substituting (9) into (19), we have I = 1 N NIk k=1 (20) 7 = 1 N N k=1 log2 ? 1 + SNR ? T ? ? bk (0) (i) (i) m i=1 bk pk (i) (i) m i=j+1 bk pk m j=0 , (21) where SNR = Ptot /N0 B. If we denote b(i) = for i = 0 to m and T b1 (i)  ·  ·  · bN (i) and p(i) = p1 (i)  ·  ·  · pN (i) T , (22) eN = 1  ·Ã‚ ·Ã‚ · 1 N ones , (23) then (21) can be written in matrix form. First, let m zsingle = b(0) ? ? i=1 b(i) ? p(i) where the ? and ? operators both represent element-wise matrix multiplication and the ? /? ? m j=0 ? m i=j+1 b(i) ? p(i) , (24) ?/ operator represents element-wise matrix division. Then, (21) in matrix form is I= 1 T e log2 eN + SNR zsingle , N N (25) here log2 ( ·) of a vector is the vector of the logarithms of the vector’s entries. 2. 1. 3 Relay Power Allocation We assume that the net transmit power at the transmitter and at each each relay is Ptot . At the transmit ter, we assume a uniform power distribution, that is, pk (0) = Ptot /N . To (l) derive the power constraint at each relay and thus, possible power allocations, consider vk , the kth transmit symbol of rl vk = (l) (l) pk ? ? l? 1 i=0 N hk (i) pk (l) 2 (i) l? 1 xk + j=0 ? ? l? 1 i=j+1 hk (i) (i) (j) pk ? n k ? . ? ? (26) The constraint is Ptot = k=1 N E ? vk . Thus, l? 1 j=0 (l) (0) P Ptot = pk ? k tot N k=1 l? 1 i=1 bk p k (i) (i) N0 B + N ? ? l? 1 i=j+1 (i) (i) bk pk (27) 8 or pk ? (0) bk N k=1 N (l) ? l? 1 i=1 (i) (i) bk p k Note that (28) is de? ned recursively. The power constraint for pk depends on pk , . . . , pk pk is the base case in the recursion, which follows from (28), when l = 1. (1) 1 l? 1 ? l? 1 (i) (i) b p = 1. + SNR j=0 i=j+1 k k (l) ? (28) (1) (l? 1) . (l) One power allocation at the lth relay is to set pk constant for all subcarriers. This results in moving pk in (28) out of the summation because it is no longer a function of k pk,ct = pct = (l) (l) (l) N SNRN k=1 ? We call this constant gain allocation (CT). Note that this power allocation does not require each relay to have any CSI (channel state information). The lth relay only has to multiply its entire OFDM receive symbol by a constant, pct , such that the total transmit power is (l) ?SNRb(0) k l? 1 i=1 (i) (i) bk pct l? 1 + j=0 ? ? l? 1 i=j+1 (i) (i) bk pct . (29) Ptot . We call constant gain capacity, Cct , as the mutual information in (25) resulting from this power allocation. A second power allocation is to choose pk such that every subcarrier transmits the same power at the lth relay.The transmit power on the kth subcarrier is the kth summand on the right hand side of (27). Since they are all equal to Ptot /N , we have Ptot (l) (0) P = pk,eq ? bk tot N N pk,eq = SNRbk (0) (l) (l) ? l? 1 i=1 (i) (i) bk pk,eq N0 B + N l? 1 j=0 ? ? l? 1 i=j+1 or (i) (i) bk pk,eq (30) SNR l? 1 i=1 bk pk,eq (i) (i) l? 1 + j=0 ? ? l? 1 i=j+1 We call this equal power allocation (EQ). Note that this power allocation does require each relay to have the CSI of its upstream channels. We call equal power capacity, Ceq , as the mutual information in (25) resulting from this power allocation. 2. 1. 4 Capacity Simulations k pk,eq ? (i) (i) ?. (31) We simulate Cct and Ceq assuming that all distances between any two adjacent transceiver nodes are the same. Therefore, all path loss e? ects are normalized to 0 dB. Shadowing 9 between nodes is assumed to be log-normally distributed. That is, the received power gain due to shadowing in dB is a zero-mean Gaussian with variance of 8 dB, which is typical for cellular land mobile applications [12]. We model frequency selective fading e? ects as Typical Urban (TU) channels and Hilly Terrain (HT) channels [12]. We use an OFDM bandwidth of 800 kHz divided into N = 128 equal blocks.Maintaining OFDM orthogonality, this translates into an OFDM symbol period of Ts = 160  µs. Results are shown in Figures 2 and 3. The plots exhibit the familiar monot onically increasing shape for mutual information in the case of direct transmission between a transmitter and receiver. This is expected if we look at the mutual information in (25). We can think of this con? guration as still being direct transmission where the channel is the single path relay network, characterized by zsingle . Note that zsingle also determines the power allocations in the relays.In other words, (25) is a system level representation of the mutual information. As we increase the distance between the transmitter and receiver (and thus, add more relays), more noise and channel distortion enter the system. Consequently, the mutual information decreases. Equal power allocation results in a slightly higher mutual information than that of constant gain allocation. TU channels and HT channels give very similar results. 2. 2 2. 2. 1 Decode-and-Forward System Model In decode-and-forward (DF), each relay fully recovers the information bits (with possible errors) after receiv ing an OFDM symbol.It then converts the information bits back into an OFDM symbol and then transmits it. The transmitter and all the relays transmit with the same uniform power distribution. That is, pk = pk = for k = 1 to N and for l = 1 to m. (l) (0) Let xk be the kth transmit symbol from the transmitter and xk be the kth transmit (m+1) be the symbol from the lth relay, all with with zero mean and unit variance. Let yk (0) (l) Ptot , N (32) 10 8 7 8 Cct Ceq 7 Cct Ceq Capacity (bits/s/Hz) 6 5 4 3 2 1 0 Capacity (bits/s/Hz) 0 3 6 9 12 15 18 21 24 6 5 4 3 2 1 0 0 3 6 9 12 15 18 21 24 SNR (dB) (a) m=1 8 7 8 SNR (dB) (b) m=2 Cct CeqCct Ceq 7 Capacity (bits/s/Hz) 6 5 4 3 2 1 0 Capacity (bits/s/Hz) 0 3 6 9 12 15 18 21 24 6 5 4 3 2 1 0 0 3 6 9 12 15 18 21 24 SNR (dB) (c) m=3 SNR (dB) (d) m=4 Figure 2: Capacity in a single path relay network with TU channels using AF. N = 128, m = 1, 2, 3, and 4. 11 8 7 8 Cct Ceq 7 Cct Ceq Capacity (bits/s/Hz) 6 5 4 3 2 1 0 Capacity (bits/s/Hz) 0 3 6 9 12 15 18 21 24 6 5 4 3 2 1 0 0 3 6 9 12 15 18 21 24 SNR (dB) (a) m=1 8 7 8 SNR (dB) (b) m=2 Cct Ceq Cct Ceq 7 Capacity (bits/s/Hz) 6 5 4 3 2 1 0 Capacity (bits/s/Hz) 0 3 6 9 12 15 18 21 24 6 5 4 3 2 1 0 0 3 6 9 12 15 18 21 24 SNR (dB) (c) m=3 SNR (dB) (d) m=4Figure 3: Capacity in a single path relay network with HT channels using AF. N = 128, m = 1, 2, 3, and 4. 12 output 1 input output 2 output 3 Figure 4: Convolutional encoder. kth receive symbol at the receiver and yk be the kth receive symbol at the lth relay. Using (l) Figure 1, the input-ouput relation at the lth relay is yk = hk (l) (l? 1) Ptot (l? 1) (l? 1) + nk . x N k (33) The input-output relation at the receiver is yk (m+1) = hk (m) Ptot (m) (m) + nk . x N k (34) 2. 3 BER and WER Simulations We simulate bit error rates (BERs) and word error rates (WERs) for both the amplify-andforward and decode-and-forward cases.At the transmitter (and at the transmitter structure of a relay using decode-and-forward), each information word contains 83 bits. Using the convolutional encoder shown in Figure 4, the information word is encoded into a 255 bit codeword. A zero bit is padded at the end to make 256 bits. The bits are then interleaved and modulated onto N = 128 QPSK (quadrature phase shift keying) subcarriers to form one OFDM symbol. At the receiver (and at the receiver structure of a relay using decodeand-forward), the codeword is recovered (with possible errors) using a matched ? lter and 13 deinterleaving.A Viterbi decoder is used to decode the codeword. Both hard decisions and soft decisions are used. We assume that all distances between any two adjacent transceiver nodes are the same. Therefore, all path loss e? ects are normalized to 0 dB. Shadowing is assumed to be lognormally distributed. That is, the received power gain due to shadowing in dB is a zero-mean Gaussian with variance of 8 dB, which is typical for cellular land mobile applications [12]. We model frequency selective fading as Typical Urban (TU) channels and Hilly Terrain (HT) channels [12]. We use an OFDM bandwidth of 800 kHz divided into N = 128 equal blocks.Maintaining OFDM orthogonality, this translates into an OFDM symbol period of Ts = 160  µs. 2. 3. 1 Amplify-and-Forward The BER versus SNR and WER versus SNR plots for a single path relay network with TU channels using amplify-and-forward are shown in Figures 5 and 6, respectively. The corresponding plots for HT channels are shown in Figures 7 and 8, respectively. As expected, soft decisions in Viterbi decoding give better performance than hard decisions. In particular, there is up to 4 dB of SNR gain for the constant gain allocation and m = 1 case, as shown in Figures 5(a), 6(a), 7(a), and 8(a).In general, using hard decisions with constant gain allocation results in the worst performance. Soft decisions with equal power allocation gives the best performance, except for the m = 1 case, where soft decisions with constant gain allocation is slightly better. As w e increase the distance between the transmitter and receiver (and thus, add more relays), more noise and channel distortion enter the system. Consequently, the error rate (BER and WER) performance becomes worse and as a result, all four curves are very close together at low to medium SNR values. TU channels and HT channels give very similar results. . 3. 2 Decode-and-Forward The BER versus SNR and WER versus SNR plots for a single path relay network with TU channels using decode-and-forward are shown in Figures 9 and 10, respectively. The 14 10 0 10 0 10 ?1 10 ?1 BER 10 ?2 BER hard, constant gain allocation hard, equal power allocation soft, constant gain allocation soft, equal power allocation 0 3 6 9 12 15 18 21 24 10 ?2 10 ?3 10 ?3 10 ?4 10 ?4 hard, constant gain allocation hard, equal power allocation soft, constant gain allocation soft, equal power allocation 0 3 6 9 12 15 18 21 24 SNR (dB) (a) m=1 10 0 SNR (dB) (b) m=2 10 0 10 ?1 10 ?1 BER 10 ?2 BER ard, constant gain allocati on hard, equal power allocation soft, constant gain allocation soft, equal power allocation 0 3 6 9 12 15 18 21 24 10 ?2 10 ?3 10 ?3 10 ?4 10 ?4 hard, constant gain allocation hard, equal power allocation soft, constant gain allocation soft, equal power allocation 0 3 6 9 12 15 18 21 24 SNR (dB) (c) m=3 SNR (dB) (d) m=4 Figure 5: BER in a single path relay network with TU channels using AF. N = 128, m = 1, 2, 3, and 4. 15 10 0 10 0 WER 10 ?1 WER hard, constant gain allocation hard, equal power allocation soft, constant gain allocation soft, equal power allocation 0 3 6 9 12 15 18 21 24 10 1 10 ?2 10 ?2 hard, constant gain allocation hard, equal power allocation soft, constant gain allocation soft, equal power allocation 0 3 6 9 12 15 18 21 24 SNR (dB) (a) m=1 10 0 SNR (dB) (b) m=2 10 0 WER 10 ?1 WER hard, constant gain allocation hard, equal power allocation soft, constant gain allocation soft, equal power allocation 0 3 6 9 12 15 18 21 24 10 ?1 10 ?2 10 ?2 hard, constant gain alloc ation hard, equal power allocation soft, constant gain allocation soft, equal power allocation 0 3 6 9 12 15 18 21 24 SNR (dB) (c) m=3 SNR (dB) (d) m=4 Figure 6: WER in a single path relay network with TU channels using AF.N = 128, m = 1, 2, 3, and 4. 16 10 0 10 0 10 ?1 10 ?1 BER 10 ?2 BER hard, constant gain allocation hard, equal power allocation soft, constant gain allocation soft, equal power allocation 0 3 6 9 12 15 18 21 24 10 ?2 10 ?3 10 ?3 10 ?4 10 ?4 hard, constant gain allocation hard, equal power allocation soft, constant gain allocation soft, equal power allocation 0 3 6 9 12 15 18 21 24 SNR (dB) (a) m=1 10 0 SNR (dB) (b) m=2 10 0 10 ?1 10 ?1 BER 10 ?2 BER hard, constant gain allocation hard, equal power allocation soft, constant gain allocation soft, equal power allocation 0 3 6 9 12 15 18 21 24 10 ?2 10 ?3 10 ?3 10 4 10 ?4 hard, constant gain allocation hard, equal power allocation soft, constant gain allocation soft, equal power allocation 0 3 6 9 12 15 18 21 24 SNR ( dB) (c) m=3 SNR (dB) (d) m=4 Figure 7: BER in a single path relay network with HT channels using AF. N = 128, m = 1, 2, 3, and 4. 17 10 0 10 0 WER 10 ?1 WER hard, constant gain allocation hard, equal power allocation soft, constant gain allocation soft, equal power allocation 0 3 6 9 12 15 18 21 24 10 ?1 10 ?2 10 ?2 hard, constant gain allocation hard, equal power allocation soft, constant gain allocation soft, equal power allocation 0 3 6 9 12 15 18 21 24SNR (dB) (a) m=1 10 0 SNR (dB) (b) m=2 10 0 WER 10 ?1 WER hard, constant gain allocation hard, equal power allocation soft, constant gain allocation soft, equal power allocation 0 3 6 9 12 15 18 21 24 10 ?1 10 ?2 10 ?2 hard, constant gain allocation hard, equal power allocation soft, constant gain allocation soft, equal power allocation 0 3 6 9 12 15 18 21 24 SNR (dB) (c) m=3 SNR (dB) (d) m=4 Figure 8: WER in a single path relay network with HT channels using AF. N = 128, m = 1, 2, 3, and 4. 18 10 0 10 0 hard soft ?1 ? 1 hard soft 10 10 BER 10 ?2 BER 0 3 6 9 12 15 18 21 24 10 ?2 10 ?3 0 ?3 10 ?4 10 ?4 0 3 6 9 12 15 18 21 24 SNR (dB) (a) m=1 10 0 SNR (dB) (b) m=2 10 0 hard soft ?1 ? 1 hard soft 10 10 BER 10 ?2 BER 0 3 6 9 12 15 18 21 24 10 ?2 10 ?3 10 ?3 10 ?4 10 ?4 0 3 6 9 12 15 18 21 24 SNR (dB) (c) m=3 SNR (dB) (d) m=4 Figure 9: BER in a single path relay network with TU channels using DF. N = 128, m = 1, 2, 3, and 4. corresponding plots for HT channels are shown in Figures 11 and 12, respectively. As expected, soft decisions in Viterbi decoding give better performance than hard decisions. In particular, there is up to 5 dB of SNR gain, as shown in the plots.As we increase the distance between the transmitter and receiver (and thus, add more relays), more noise and channel distortion enter the system. However, the error rate (BER and WER) performance su? ers only slightly as m increases. TU channels and HT channels give very similar results. 2. 3. 3 Comparison The BER versus SNR and WER versus SNR plots for a single path relay network with TU channels using amplify-and-forward and decode-and-forward are shown in Figures 13 and 19 10 0 10 0 hard soft hard soft WER 10 ?1 WER 0 3 6 9 12 15 18 21 24 10 ?1 10 ?2 10 ?2

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What do you think hitler's view would be on western expansion - Assignment Example Hitler had this in mind since he masterminded the Second World War (Muller & Gerd 49). After annexing Austria, Hitler’s view was that Germany needed to be powerful at the expense of eastern nations like Russia and Poland. To Hitler, these nations were populated by ‘Sub-humans’, hence, their territories needed to be taken away. Germany was rising in terms of power, and led by Hitler, they believed that whatever suited them needed to be taken by them. Hitler first went to German speaking regions that had initially been taken away from German by the Versailles Treaty. German first took the Saar Basin and later attacked the Rhineland. After taking Austria, they moved up to the Southern region of Czechoslovakia which was called Sudentenland. Hitler’s view was that there were many German nationals in these regions. Hitler then went ahead and took the whole of Czechoslovakia. None of the Western Alliance powers were able to stop Hitler. This marked the beginning of the Second World War. This had been a ploy by Hitler to form a large alliance that w ould fight for him in the Second World War (Muller & Gerd 78). Yes. At that time, there was a battle for supremacy. Hitler fathomed that German’s allies in the First World War would not support them in case another major war came up. Hitler wanted to conquer the whole of Europe, hence he triggered the war. By annexing most German speaking regions, he formed a formidable

Financial accounting Essay Example | Topics and Well Written Essays - 1750 words - 2

Financial accounting - Essay Example There has been continued political as well as public pressure to have better regulation standards to ensure that there is economic growth. Scholars affirm that regulation of financial reports should start with solid corporate governance, making sure that the spirit of novelty is not negatively affected (Gibson 2012). Therefore, this paper seeks to offer a rational critical evaluation on financial reporting regulation and whether or not it should be reduced. Research shows that regulation of financial reports can be either right or wrong, depending on the nature of the firm and the extent to which such disclosures are regulated. However, it is evident that there are numerous drawbacks that come with having excessive guidelines; hence, they should be reduced to promote innovation, healthy competition, guarantee fiscal growth, and stability. Regulation is defined as a principle that governs a particular practice or behaviour. Various firms such as Enron have gone bankrupt and have reported failures in accounting because of unethical practices. As a result, most nations have focused on heavily regulating the financial reports and accounts to avoid failures such as those that happened in renowned firms like Lehman Brothers and Parmalat among others. Although regulation of financial reports is important and might appear sound, it should not be excessive as it damages the nation’s spirit of competitive innovation (Unerman &O’Dwyer 2004). Excessive regulation constrains innovation and business practices; hence, regulation of financial reporting should be minimised. It is important to understand that for a nation to be positively impacted by such standards, then, rules ought to start with solid corporate governance. It is the duty of the shareholders as well as the members of the board to examine carefully and e nsure that their firms are led in the right path to realise their goals (Whittington 2006). Encouraging accountability,

Societal Standards Essay Example for Free

Societal Standards Essay Imagine a 62 man with broad shoulders, deep voice, hairy body, masculine personality, and pink glittery nail polish. His friends give him a hard time about it, they say that he is not a real man. He decides to hang out with more woman and when more and more people start to consider him gay, he becomes it. Men do not have the wiggle room to explore the feminine stereotypes. Masculine stereotypes are more confining than feminine stereotypes in the social and professional world. Social masculine stereotypes are more confining than feminine stereotypes. Men are more strictly contained while women are more open to explore a variety of stereotypes. In a recent, USA Today article Gender Stereotypes author Seine Wenig writes on a strict line drawn between masculine and female stereotypes. Yet how this line is slowly fading the woman. Wenig reiterates how for girls There is ample room to maneuver and how Ever-growing range of tomboys sports options which in the past were mostly the domain of boys. Girls can now be free and engage in activities and sports which boys dominate. While male stereotypes and stereotypical fathers cause men to have a more confined space in which they could explore and move due to the fact that stereotypical fathers expect athletic success rather than academic success. Girls are Given more room to explore their counterparts culture while males are stuck in a much tighter box to move about in meaning they are not able to explore the feminine stereotypes. Therefore ,masculine stereotypes are more confined than feminine stereotypes in the social aspect. Masculine stereotypes are more professionally confining than feminine stereotypes. There are fewer choices for careers for men that then for women due to stereotypes. In a 2011 article from USA Today, Gender Stereotypes Easing More for Girls than Boys. Author Seth Wenig describes the ultimate confinement for men in the professional mainstream society. He restates how, women now make up close to half to enrollment in US law and medical schools up from 25% a few decades ago. Now due to the ever-changing world girls now have more choices for careers then their male counterparts. More females are going and graduating from schools which prepare them for a lifelong career not just being nurse as it was thought to be in the past. Men choose not to be nurses because main stream society would not find being a nurse very masculine because it is a mostly female occupied feel due to the fact it has to do with the Female stereotype of caring for another human being. Women are given more opportunities than men to succeed in the professional world, which leave men with fewer choices for careers. Therefore masculine stereotypes are more professionally confining than feminine stereotypes. Addressing the problems of social standards of man and woman requires the ultimate settlement of what it means to be a man and what it what it means to be a woman. Men do not have them of wiggle room to explore the female stereotypes while free to roam all round all stereotypes. When a female try to succeed in a mostly male dominant profession, she is led to shine while when a man tries to do the same he is shun. If men continue to be confined by so societal standards, this will cause a civilization in which it is easier to be a woman than to be a man. Leading men to either join the female standard and gender or collapse under the confinement of their own standards.

Essay --

Vivian Nguyen Amicangelo 8Celtics 22 February 2014 JOSEPH STALIN Joseph Stalin was a man who many people had mixed feelings for. Some say he was a dictator and a tyrant, but others say that as a ruler, he shaped Russia and pushed it in the right direction. Both sides are correct, and there are many examples to back them up. Stalin did accomplish benefiting Russia‘s image, but he was a man who killed many. Stalin was born as Iosif Vissarionovich Dzhugashvili (later became Joseph Stalin) on December 18, 1879 and his parents were Besarion Jughashvili (father) and Ketevan Geladze (mother). When he was young, his father, Beso, had beaten his mother and him several times. They had a troublesome marriage and often argued about Stalin’s future. His mother wanted him to be a priest because she thought he was smart, so she did everything to get him a good education. His father wanted him to be a cobbler, and said that since he [Stalin’s father] was a cobbler, Stalin would follow the family job and become a cobbler. Fortunately, Stalin‘s mother defeated her husband and she even humiliated him. Stalin ended up doing what his mother wanted-- for a while (Radzinsky 17-31). Stalin is a very interesting man who always changed how he thought of everybody (he also called himself Stalin because â€Å"stalin† means steel) (Montefiore 30 â€Å"Young Stalinâ€Å").He had a huge effect on Russia; in a bad way. When Stalin used to work with Lenin and Trotsky, it wasn’t a competition of who was the best and who should control the country of Russia, but then it all changed. After that, he got people to turn against them and got rid of t... ...lowing him. Another reason was identity. Napoleon only represented Stalin, and that really brought out his characteristics. Since Napoleon was meant to represent Stalin, all of Stalin’s traits, most of his bad deeds, and events occurred in the book. For example, in Animal Farm, Orwell made Snowball seem smarter than Napoleon, but made Napoleon more powerful. This is true in real life because Lenin was a lot more educated than Stalin, but Stalin ended up with the power (Radinsky 97) Although Stalin had been tyrannical and crazy, he made Russia seem stronger, and is still seen as a good person today. Many people look at him like he was a murderous person, but other look at him as the man who made Russia better. He was a great leader, in a way, but that only depends on what the Russians believed in, and whether or not they (or someone they know) worked for Stalin. Essay -- Vivian Nguyen Amicangelo 8Celtics 22 February 2014 JOSEPH STALIN Joseph Stalin was a man who many people had mixed feelings for. Some say he was a dictator and a tyrant, but others say that as a ruler, he shaped Russia and pushed it in the right direction. Both sides are correct, and there are many examples to back them up. Stalin did accomplish benefiting Russia‘s image, but he was a man who killed many. Stalin was born as Iosif Vissarionovich Dzhugashvili (later became Joseph Stalin) on December 18, 1879 and his parents were Besarion Jughashvili (father) and Ketevan Geladze (mother). When he was young, his father, Beso, had beaten his mother and him several times. They had a troublesome marriage and often argued about Stalin’s future. His mother wanted him to be a priest because she thought he was smart, so she did everything to get him a good education. His father wanted him to be a cobbler, and said that since he [Stalin’s father] was a cobbler, Stalin would follow the family job and become a cobbler. Fortunately, Stalin‘s mother defeated her husband and she even humiliated him. Stalin ended up doing what his mother wanted-- for a while (Radzinsky 17-31). Stalin is a very interesting man who always changed how he thought of everybody (he also called himself Stalin because â€Å"stalin† means steel) (Montefiore 30 â€Å"Young Stalinâ€Å").He had a huge effect on Russia; in a bad way. When Stalin used to work with Lenin and Trotsky, it wasn’t a competition of who was the best and who should control the country of Russia, but then it all changed. After that, he got people to turn against them and got rid of t... ...lowing him. Another reason was identity. Napoleon only represented Stalin, and that really brought out his characteristics. Since Napoleon was meant to represent Stalin, all of Stalin’s traits, most of his bad deeds, and events occurred in the book. For example, in Animal Farm, Orwell made Snowball seem smarter than Napoleon, but made Napoleon more powerful. This is true in real life because Lenin was a lot more educated than Stalin, but Stalin ended up with the power (Radinsky 97) Although Stalin had been tyrannical and crazy, he made Russia seem stronger, and is still seen as a good person today. Many people look at him like he was a murderous person, but other look at him as the man who made Russia better. He was a great leader, in a way, but that only depends on what the Russians believed in, and whether or not they (or someone they know) worked for Stalin.

Has the law proven effective regulating the banking industry or are the limits of a bankers business too complex to be laid down by the law.

Introduction It will be determined in this study whether the limits of a bankers business can ever be laid down by the law or whether a bankers business should in fact be left undefined. This will be done in light of the recent financial crisis so that a determination can be made as to whether banking law has proven effective in regulating bankers or whether unnecessary risk are still being taken. In doing so, the powers and responsibilities of the Financial Services Authority (FSA) will be examined in order to decide whether the activities currently being undertaken by the FSA are sufficient enough to regulate the financial market. Literature Review The main objectives of a bank is to provide financial services to individuals and organisations by allowing money to be either borrowed or deposited whilst at the same time acting as a means for credit to be created. Nevertheless, given the complexity of the modern banking business, it seems as though a lack of regulation exists which is especially evident in light of the recent financial crisis. This is because; banks appear to have taken extortionate risks without any intervention which is highly detrimental to both the economy and consumers. It is quite difficult to determine what a bankers business should consist of, however, which is why great difficulty remains when trying to assess how they ought to be regulated. And, although some attempt to define a bankers business has been made by the courts; Commissioners of the State Savings Bank of Victoria v Permwan & Anor (1914) 19 CLR 45 and United Dominions Trust Ltd v Kirkwood [1966] 1 QB 783 a bankers business still remains ill-de fined. It is unclear whether a bankers business should be laid down by the law, however, since the activities undertaken by banks are often to wide-ranging to classify. This would impose too much restriction on banks and certain activities would be prevented from being undertaken; Woods v Martins Bank (1959) 1 QB 55. Despite this, it is important that some form of restriction is in place so that unnecessary risks are avoided. This was highlighted by Benston and Kaufman (1996, p. 1) when they pointed out that; â€Å"to protect our money, banks should not be allowed to take great risks that might cause them to fail.† Therefore, some restrictions are needed so that banks are not free to do as they wish as this would be extremely damaging to the economy. The Financial Services Authority (FSA) was in fact introduced in order to regulate the activities of bankers, yet it remains arguable whether this has been successfully achieved. This is because, although the FSA has been provided with s tatutory powers under the Financial Services and Markets Act (FMSA) 2000 to regulate the financial services industry more effectively, given the recent financial crisis, it is questionable just how efficient the FSA is. However, as noted by the FSA themselves; â€Å"as a risk-based regulator, our approach is based on a clear statement of the realistic aims and limits of regulation.† Not all agree with this, however, and instead it has been argued that the FSA are no longer relevant in today’s society (House of Commons Treasury Committee, 2009, p. 4). In view of this, it has thus been noted by Awrey that; â€Å"perhaps most glaringly, conventional financial theory failed to adequately account for the complexity of modern financial markets and the nature and pace of financial innovation.† This signifies how the FSA have been unable to keep up-to-date with the advances that are continuously being made within society and that further regulatory procedures are thereby required if the banking industry is to be restored to an acceptable state. Modern financial markets thereby appear to complex for the FSA and so it is important that more stringent regulatory practices are instilled upo n the banking industry so that banks do not abuse their powers and responsibilities. Proposed Methodology In acquiring the relevant information for this study, various academic opinion, case law and legal theory will be analysed. These will be acquired by accessing text books, journal articles, governmental reports and online legal databases. Secondary research will be the main forma of research used for this assignment so that existing data can be collected and analysed in order to reach a conclusion. This will be a more cost effective and time saving way of undertaking the research, which is applicable for this assignment given the difficulty in obtaining primary research from large organisations such as the FSA. Quantitative and qualitative research methods will be used so that information can be gathered that is in numerical form, whilst also gathering information that is not in numerical form but which contains descriptive data. Outline of the WorkOverview of the Banking Industry A brief overview of the banking industry will be provided here in order to determine the main objectives of bankers and the effects in which their activities can have on the economy.Powers and Responsibilities of Bankers It will be considered here whether a bankers business can be defined by the law or whether the activities are too complex to be defined.Regulation of the Banking Industry An evaluation as to whether the banking industry ought to be regulated more efficiently will be made by looking at the existing regulatory procedures and considering whether they have so far been effective or whether more needs to be done in order to prevent further financial crisis’ from arising.Financial Services Authority’s Powers and Responsibilities The powers and responsibilities of the FSA will be considered in order to determine whether additional powers ought to be conferred upon the FSA or whether modern banking is too compl ex to enable the FSA to regulate financial activities. Thus, it will be shown that whilst banking activities do remain complex, the FSA should still be provided with the ability to regulate the banking industry so that a robust system is in place. If the activities of bankers were not was in needed so that any problems that are likely (FSA, 2009, p. 5). Hence, it is vital that the risks taken by bankers are severely limited since much ambiguity would ensue if restraints were not being imposed upon the financial sector and as noted by Johnston (1960, p. 347; â€Å"the difficulty is increased by the fact that banking, like other forms of business, continues to develop and expand its activities to meet its competitors and provide wider services for the public with the result that any attempt to squeeze the concept into the confines of a definition may prove successful today but inadequate tomorrow.†Are the Powers and Responsibilities of the FSA acceptable in today’s soci etyHere, it will be discussed whether the powers and responsibilities of the FSA are acceptable in today’s society where modern banking is more complex than ever. Hence, it will be shown that the FSA has come under much scrutiny since the financial crisis was first instigated, yet rather than taking a step back, the FSA need to take a more interventionist approach so that future financial crisis’ can be prevented. It has thereby been said that the FSA should investigate â€Å"how financial services firms manage their Information Security Risks; how these risks are evolving; the risks they pose to our objectives; and the role industry and government bodies play in assisting regulated firms to address these Information Security Risks† (FSA, 2004, P. 3). If a more interventionist approach is undertaken by the FSA, financial crimes similar to those that caused the economic crisis will be more easily identified and therefore dealt with appropriately. Strong financial crime deterrent messages[1] will also be sent out by the FSA and financial crime will inevitably be reduced. References Awrey, D. (2011) Complexity, Innovation and the Regulation of Modern Financial Markets, Harvard Business Law, Oxford Legal Studies Research Paper No 49/2011, [Online] Available: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1916649 [14 February, 2013]. Benston, G. and Kaufman, G., (1996) Why Regulate Banks, Res, [Online] Available: http://www.res.org.uk/society/mediabriefings/pdfs/1996/July/benston.pdf [13 February 2013]. FSA. (2004). Countering Financial Crime Risks in Information Security, Financial Crime Sector Report, [Online] Available: www.fsa.gov.uk/pubs/other/fcrime_sector.pdf [14 February, 2013]. FSA., ‘Delivering a Reduction of Financial Crime’ (2011) FSA Annual Report 2011/12, [Online] Available: www.fsa.gov.uk/pubs/annual/ar11-12/section5.pdf [14 February, 2013]. FSA. (2009) The Turner Review; A Regulatory Response to the Global Banking Crisis, Financial Services Authority, [Online] Available: http://www.fsa.gov.uk/pubs/other/turner_review.pdf [14 February, 2013]. FSA., (2012) What we Do: Regulatory Approach, Financial Services Authority, [Online] Available: http://www.fsa.gov.uk/pages/about/what/approach/index.shtml [13 FEBRUARY, 2013]. House of Commons Treasury Committee. (2009) Banking Crisis: Dealing with the Failure of UK Banks, Seventh Report of Session 2009-09, Report Together with Formal Minutes, HC 416, [Online] Available: http://www.publications.parliament.uk/pa/cm200809/cmselect/cmtreasy/416/416.pdf [14 February, 2013]. Johnston, C. C. (1960) Judicial Comment on the Concept of Banking Business. 2 Osgoode Hall 347. [1] FSA., ‘Delivering a Reduction of Financial Crime’ (2011) FSA Annual Report 2011/12, fsa.gov.uk/pubs/annual/ar11-12/section5.pdf> [Accessed 20 August, 2012].