A PAPR Reduction Method Based on Artificial Bee Colony Algorithm for OFDM Signals

I. INTRODUCTION

• OFDM’s high PAPR occurs when subcarrier subsymbols add coherently and can impose a severe transmitter power penalty, particularly in portable wireless systems.The introduction also describes trade-offs in other approaches: clipping degrades BER and causes noise, coding has complexity and data-rate costs, and SLM requires multiple IFFTs.Source: §I · p. 1
• Other constellation-modification and extension methods reduce PAPR at the cost of increased transmit power and transmitter computation.These include tone injection, active-set extension, symmetric constellation extension, and constellation extension methods.Source: §I · p. 1
• PTS is distortionless, combining signal subblocks with constant phase shifts, but exhaustive search over phase combinations grows exponentially with the number of subblocks.The paper notes that suboptimal PTS methods have therefore been developed, including iterative flipping, neighborhood search, simulated annealing, and swarm and genetic algorithms.Source: §I · p. 1
• ABC-PTS searches for better PTS phase combinations and is reported to reduce PAPR with far less computational complexity than previous PTS techniques.Like original PTS, the proposed scheme also requires sending side information.Source: §I · p. 2

II. OFDM SYSTEM AND PAPR

• An OFDM system splits a high-rate data stream into N low-rate streams transmitted simultaneously on subcarriers, and the IDFT generates the ready-to-transmit signal.The subcarriers are orthogonal, with f_n = nΔf and Δf = 1/NT, where T is the symbol period.Source: §II · p. 2
• PAPR is defined as the ratio of the maximum instantaneous power of x(t) to its average power.The supplied passage introduces this definition but does not include the displayed formula.Source: §II · p. 2
• The CCDF measures the probability that an OFDM symbol’s PAPR exceeds a given threshold.An oversampling factor L = 4 is stated to provide a sufficiently accurate PAPR estimate.Source: §II · p. 2

III. PTS TECHNIQUES

• PTS partitions the input data block into M disjoint subblocks, applies phase weighting factors to their oversampled time-domain signals, and combines them to minimize PAPR.The subblock signals are obtained by an IDFT of length NL on each subblock concatenated with (L − 1)N zeros.Source: §III · p. 2
• The allowed phase factors are drawn from a finite set of W elements, and one phase factor can be fixed without performance loss, leaving M − 1 free variables.The phase combinations are searched to find the global optimum.Source: §III · p. 2
• Exhaustive search over the phase combinations grows exponentially with M, the number of subblocks..Source: §III · p. 2

IV. MINIMIZE PAPR USING MODIFIED ABC ALGORITHM

• The modified ABC algorithm is proposed as a lower-complexity suboptimal method for finding a phase combination with better PAPR performance.The method is named ABC-PTS.Source: §IV · p. 2
• The PTS phase-optimization problem is framed as finding the minimum PAPR.Source: §IV · p. 2
• The phase choices are restricted to φ_m ∈ {2πk/W | k = 0, 1, …, W − 1}.Source: §IV · p. 3

A. Artificial Bee Colony Algorithm

• The colony has employed bees, onlookers, and scouts, with food-source positions representing possible solutions and nectar amounts representing their fitness.Source: A. Artificial Bee Colony Algorithm · p. 3
• Each cycle has employed bees evaluate nearby sources, onlookers select sources using shared nectar information, and scouts search randomly for new sources.Source: A. Artificial Bee Colony Algorithm · p. 3
• Employed bees retain an improved neighboring source; onlookers choose sources with probability based on nectar, while a source unimproved for the limit trials is replaced by a scout's random source.Source: A. Artificial Bee Colony Algorithm · p. 3

B. Modified Artificial Bee Colony Algorithm to Reduce PAPR

• The original ABC is suited to continuous numerical optimization, so ABC-PTS adapts it to search PTS phase factors selected from {-1, 1} or {-1, 1, j, -j}.Source: B. Modified Artificial Bee Colony… · p. 3
• Each food source represents a phase vector from the initial population, and its nectar or fitness value evaluates that solution.Source: B. Modified Artificial Bee Colony… · p. 3
• Employed bees generate candidate sources from neighboring positions; the discrete-coordinate update maps the candidate to one of the allowed phase values.The update uses a random number between -1 and 1; the mapping differs for two- and four-value phase sets.Source: B. Modified Artificial Bee Colony… · p. 3
• Onlookers choose food sources according to each source's associated probability value.Source: B. Modified Artificial Bee Colony… · p. 3
• A source that cannot be improved for more than the predetermined limit is abandoned, and its employed bee becomes a scout that searches randomly.Source: B. Modified Artificial Bee Colony… · p. 3
• The algorithm initializes sources and limits, cycles through employed-bee and onlooker updates, replaces abandoned sources, records the best source, and stops at the maximum iteration count.Source: B. Modified Artificial Bee Colony… · pp. 3–4

C. Complexity Analysis for ABC-PTS and the Existing PAPR Reduction Methods

• IPTS complexity is proportional to (M-1)W, while gradient-descent neighborhood search complexity is proportional to C_r^n.For IPTS, complexity is linearly proportional to the number of subblocks; n is identified as the binomial coefficient.Source: C. Complexity Analysis for ABC-PTS and… · p. 4
• ABC-PTS search complexity is proportional to SK, compared with W^(M-1) for exhaustive PTS; fixing a phase factor reduces the exhaustive search without performance loss.S is the initial population size and K the maximum iteration number.Source: C. Complexity Analysis for ABC-PTS and… · p. 4
• The compared methods have complexities LN for TS, SG for PSO-PTS, and PG + (M-1)W for MDGA.N is the number of subcarriers, L the oversampling factor, S the swarm size, G the maximum generations, and P the MDGA population size.Source: C. Complexity Analysis for ABC-PTS and… · p. 4

V. SIMULATION RESULTS

• The simulations used 16-QAM, N = 256 subcarriers, W = 2, 100,000 OFDM symbols, and oversampling factor L = 4; ABC-PTS parameters included S, K, and Limit.The study varied iteration count, population size, and Limit to evaluate PAPR reduction.Source: §V · p. 4
• At Pr(PAPR > PAPR0) = 10^-3, ABC-PTS with K = 40 had a 0.25 dB gap to OPTS while using 3.66% of its search complexity.Its PAPR was also better than RS and GD at the compared search complexities.Source: §V · pp. 4–5, Figure 2 · p. 4
• At M = 16, ABC-PTS reduced PAPR by 0.3 dB versus PSO-PTS at the same search complexity and by 0.2 dB versus MDGA at almost the same complexity.The comparison uses W = 2, S = P = 30, and G = K = 30.Source: §V · p. 5, Table I · p. 5
• At Pr(PAPR > PAPR0) = 10^-3, ABC-PTS with S = 30 and S = 40 had PAPR gaps of approximately 0.35 dB and 0.25 dB from OPTS, respectively.Their search complexities were 2.75% and 3.66% of OPTS, respectively.Source: §V · p. 5, Figure 3 · p. 5
• At Pr(PAPR > PAPR0) = 10^-3, ABC-PTS with Limit = 3 and Limit = 8 each achieved 6.8 dB, versus 6.5 dB for OPTS.The paper reports negligible PAPR difference between the two Limit settings and little improvement from increasing Limit.Source: §V · p. 5, Figure 4 · p. 5
• Across 100 experiments comparing ABC-PTS, PSO-PTS, and MDGA for an OFDM symbol with M=16, S=P=30, and G=K=60, ABC-PTS mean best-cost performance became better than both baselines as iterations increased.The mean PAPR for K=30 was less than 0.1 dB below that for K=60, so the authors identify K=30 as a suitable choice.Source: §V · pp. 5–6, Figure 5 · p. 6

• ABC-PTS provides better PAPR performance while significantly reducing computational complexity for larger PTS subblocks.Source: §VI · p. 6
• The proposed modified artificial bee colony algorithm searches for better phase-factor combinations in PTS for OFDM signals.Source: §VI · p. 6
• With only three control parameters, ABC-PTS is described as easy to adjust.Source: §VI · p. 6